RU2589345C1 - Method of authenticating electronic image (versions) - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: invention relates to protection of authenticity of electronic images (EI), compressed by EI compression algorithms, transmitted over public transmission channels. At sender, EI is subjected to wavelet conversion, obtained wavelet factors are quantized, and divided into code blocks, of which ordered binary sequences are formed that are encoded in encoded sequences. Before encoding secret initial coding interval boundaries are set in accordance with secret key. Encoded EI is transmitted to recipient. Authenticity of EI is verified: coded sequences are decoded in ordered binary sequences, wherein prior to decoding secret initial decoding interval boundaries are set in accordance with secret key; action is repeated of authentication received code units up to completion of their reception. Received EI is considered authentic, if authentic are all received code units.

EFFECT: reduced difference in length of encoded message and providing EI authentication, compared with length of encoded message without providing authentication of EI.

8 cl, 38 dwg

Description

The claimed technical solutions are united by a single inventive concept and relate to the field of telecommunications and information technologies, namely to the technique of protecting the authenticity of electronic images (EI), compressed by EI compression algorithms, such as JPEG2000, H.264, etc., transmitted by the sender to the recipient by public transmission channels in which the violator can take actions to impose on the recipient non-authentic EI.

The claimed objects of the invention can be used to ensure the authenticity of EI transmitted in modern information and telecommunication systems.

Known methods of authentication EI based on the calculation by the sender and the recipient to verify the imitation of the binary sequence (DP) of this image. These methods relate to cryptographic methods of authenticating EI and are described, for example, in state standard 28147-89. Information processing systems. Cryptographic protection. Cryptographic conversion algorithm. - M.: Gosstandart of the USSR. 1989, pp. 9-14. In these methods, EIs are compressed in accordance with the JPEG2000 algorithm prescribed by the international standard ISO / IES 15444. The binary sequence of the compressed electronic image JPEG is divided at the sender into consecutive blocks of length n bits, where usually n = 64. According to the cryptographic function of forming an insert using a secret key (SC) pre-generated for the sender and receiver of the binary sequence (DP), the encrypted current block is formed sequentially from each block taking into account the previous encrypted block until the PD EI arrives. From the last encrypted block, the DP EI insertion inserts of length l <n bits are extracted. Then, the EI DP and DP insertions are transmitted via a communication channel or recorded on electronic media, for example, CD or DVD discs. The EI received by the recipient is checked, for which purpose its DP is again divided into consecutive received blocks of length n bits, according to the cryptographic function of forming an insert using DPSC, the next encrypted received block is formed sequentially from each received block taking into account the previous encrypted received block until the DP arrives accepted EI. From the last encrypted received block, a bit l <n of the DP of the received EI received is emitted and, with full coincidence of the newly formed and received received inserts, the received EI is considered authentic.

The disadvantages of these analogues are:

- the impossibility of verifying the authenticity of the part authenticated using the EI simulation insert;

- reducing the bandwidth of the transmission channels or the need to use mass storage devices due to the inclusion and subsequent transmission of the electronic image insertion via the communication channel.

There are also known methods of authentication EI based on the calculation and embedding of digital watermarks (CEH) in an electronic image. These methods relate to steganographic methods for verifying the authenticity of EI and are described, for example, in the method of authenticating EI according to US patent 7313696 IPC H04L 9/00 (2006.01) dated 12.25.07. This authentication method of EI consists in the preliminary formation for the sender and recipient of the DP SK, the cryptographic hash function and the cryptographic encryption function. At the sender, EI is divided into M≥2 blocks each of size n ₁ × n ₂ pixels, where n ₁ ≥2 and n ₂ ≥2, over each mth, where m = 1, 2, ..., M, the EI block performs a wavelet the transformation obtained as a result of transforming the wavelet coefficients is quantized and converted into the DP wavelet of the coefficients of the mth EI block, which transform into N≥2 UDP the wavelet coefficients of the mth EI block. From K, where K = N-1, the UDP VC of the mth EI block calculates its hash sequence using a preformed cryptographic hash function. Then, from the hashing sequence of the m-th block of EI, its DP of the digital watermark is calculated using the previously generated cryptographic encryption function and the DP SK. The m-th EI block is authenticated, for which they integrate the DP CVC of the m-th EI block into the N-th UDP VK of this EI block by replacing the N-th UDP VK of this EI block with its DP TsVZ.

Received UDP VCs with a built-in DP CVC of the m-th EI block are encoded using arithmetic coding into the encoded sequences of this block, including markers, and the authentication actions from the sender of the EI blocks are repeated until their arrival is completed.

An authenticated EI is transmitted to the recipient, where the authenticity of the EI received by the recipient is verified, for which purpose the DP received by the EI received by the recipient is divided into binary sequences of its received blocks, which are divided into encoded sequences of the mth received block of EI, decode them and select N UDP VC of the mth received block EI. Allocate from the Nth UDP VC of the m-th received block of EI DP TsVZ of the m-th received block of EI and remember it.

From the K UDP UDP of the mth received EI block, its hash sequence is calculated using a preformed cryptographic hash function. Then, from the hashing sequence of the m-th received block of EI, calculate its DP CVC using pre-formed cryptographic encryption function and DP SC and compare it with the previously allocated and stored DP CEH of the mth received block EI. If they match, the m-th received block of EI is considered authentic. The authenticity of the received EI blocks is repeated until the reception is completed. Accepted EI is considered authentic if the M received EI blocks are authentic.

The disadvantage of these analogues is the relatively low stability of the authenticated EI to the effects of transmission channel errors. This is due to the fact that when the transmission channel errors in any DP bit of the mth received authenticated BEI in this binary sequence, error propagation occurs due to the use of the hashing function to calculate it, and as a result, this BEI is considered non-authentic.

The closest in technical essence to the claimed authentication methods of EI is the method of authentication of EI described in the international standard for protecting EI: Document ISO / IEC FCD15444-8: Information technology - JPEG2000 image coding system. Part 8. Secure JPEG2000. Geneva, 2004, pp. 66-89. The prototype method of authentication EI consists in preliminary formation for the sender and recipient DP SC and cryptographic hash function. The sender performs the wavelet transform over the EI, the resulting wavelet transform coefficients are quantized and divided into N≥2 code blocks of quantized wavelet coefficients each of size n ₁ × n ₂ coefficients, where n ₁ ≥2 and n ₂ ≥2, quantized wavelet coefficients n th, where n = 1, 2, ..., N, the code block of the quantized wavelet coefficients is converted into binary sequences of the quantized wavelet coefficients of the nth code block, which convert the ordered binary sequences (UDP) of the quantized wave the input of the coefficients of the nth code block, from the first K, where 1≤K≤L, UDP of the quantized wavelet coefficients of the nth code block using the pre-generated cryptographic hash function and the DP SK, the digital watermark (CEH) of the n-th code is calculated block, which is embedded in the last T, where K≤T≤L, UDP of the quantized wavelet coefficients of the same block, the numbers of which determine the preformed DP SK, UDP of the quantized wavelet coefficients of the nth code block, including UDP of the wavelet coefficients with of the given DP of the CEH of the nth code block, is encoded using arithmetic coding into the coded sequences of this block, after the arithmetic coding of the UDP of the quantized wavelet coefficients of the nth code block, the code block separation marker is written in the DP of the encoded EI, and the authentication actions are sent by the sender of the code blocks blocks are repeated until completion of their receipt.

The encoded EI is transmitted to the recipient, where the authenticity of the EI received by the recipient is verified, for which the DP received by the recipient EI is divided into binary sequences of its received blocks, which are divided into encoded sequences of the received code blocks, decoded encoded sequences of the nth received code block using arithmetic decoding and extracted L UDP of the quantized wavelet coefficients of the n-th received code block, from the last T UDP of the quantized wavelet coefficients of the n-th received of the code block, the numbers of which determine the preformed DP SK, allocate the DP DEC of the n-th received code block, which is stored from the first K UDP quantized wavelet coefficients of the n-th received code block using the pre-formed cryptographic hash function and the DP SC calculate the DP DEC of the nth received code block, which is bitwise compared with the memorized allocated DP of the CEH of this block, if they coincide, the nth received code block is considered authentic, the actions of verifying the authenticity are repeated If the received code blocks are valid until their reception is completed, the received EI is considered authentic if N received code blocks are genuine.

The prototype method of authentication of EI provides authentication of the EI, compressed using compression algorithms such as JPEG2000, etc.

The disadvantage of the closest analogue (prototype) is a significant increase in the length of the coded with the authentication of EI compared with the length of the coded without providing authentication of EI. This increase in length is due to the fact that during authentication, a significant number of sufficiently long binary sequences of the CEH are embedded in each n-th code block into the encoded EI. In order to provide high security for attempts by an intruder to replace a genuine authenticated EI with a non-authentic EI, the length of the binary sequences of the CEH of each code block must be at least 32 bits, and the number of code blocks in the electronic image is large enough, which causes a significant increase in the length of the coded EI with authentication compared to the length of the encoded without providing authentication EI.

The technical result of the proposed solutions is to reduce the difference in the length of the coded with the authentication of EI compared to the length of the coded without providing authentication of EI.

The specified technical result in the first embodiment of the proposed method for authenticating an EI using setting the secret initial boundaries of the encoding and decoding intervals is achieved by the fact that in the known method of authenticating EI, which consists in preliminarily generating a secret key for the sender and recipient of the binary sequence of the key, the sender performs the wavelet over the EI the transformation obtained as a result of the conversion of the wavelet coefficients is quantized and divided into N≥2 code blocks of quantized ve each entry of the coefficients of the size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, the code block of quantized wavelet coefficients are converted to binary quantized sequence the wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, the ordered binary sequences of quantized wavelet coefficients of the nth code block are encoded using arithmetic about encoding into the encoded sequences of this block, at the end of the arithmetic encoding of the UDP of the quantized wavelet coefficients of the nth code block, the code block separation marker is written into the binary sequence of the encoded EI, and the authentication steps from the sender of the code blocks are repeated until their arrival is completed, the encoded EI is transmitted to the recipient where they verify the authenticity of the received EI by the recipient, for which they divide the DP of the received EI by the recipient into binary sequences of it at taken blocks using the separation marker of each code block, which are divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding into L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat the validation actions of the received code blocks until the completion of their reception, the accepted EI is considered genuine, if authentic about be ordered N received code blocks for further pre sender and receiver compute the length of the ordered sequence of binary code block of quantized wavelet coefficients.

Prior to encoding the UDP of the quantized wavelet coefficients of the nth code block using the arithmetic coding, the sender sets the secret initial boundaries of the coding interval of the arithmetic coding in accordance with the pre-formed DP SK or in accordance with the pre-formed DP SK and the number of the n-th code block.

Before decoding the encoded sequences of the nth received code block using arithmetic decoding, the receiver sets the secret initial boundaries of the decoding interval of the arithmetic decoding in accordance with the pre-formed DP SK or in accordance with the pre-formed DP SK and the number of the n-th received code block. After decoding the ordered binary sequences of quantized wavelet coefficients of the nth received code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length are compared with the pre-calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match each of the L calculated lengths, the n-th received code block is considered authentic.

Thus, in the first embodiment of the authentication method EI use the setting of the secret initial boundaries of the coding interval of the arithmetic coding and the decoding interval of the arithmetic decoding in accordance with the pre-formed DP SC.

The specified technical result in the second embodiment of the proposed method for authenticating an EI using setting secret initial probabilities of encoded and decoded zero characters and single characters is achieved by the fact that in the known method of authenticating EI, which consists in preliminarily generating a binary key sequence for the sender and receiver, the sender over the EI perform the wavelet transform; the resulting wavelet transform coefficients are quantized and yayut N≥2 to code blocks of quantized wavelet coefficients of each size n ₁ × n ₂ coefficients where n ₁ ≥2 and n _2> 2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, codeblock quantized wavelet coefficients are converted into binary sequences of quantized wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, ordered binary sequences of quantized wavelet coefficients of the nth code block they are audited using arithmetic coding into the coded sequences of this block; upon completion of the arithmetic coding of UDPs of the quantized wavelet coefficients of the nth code block, a code block separation marker is written into the binary sequence of the encoded EI, and the authentication steps from the sender of the code blocks are repeated until completion of their receipt, transmit encoded EI to the recipient, where the authenticity of the EI received by the recipient is verified, for which the DP of the received E is divided And into the binary sequences of its received blocks using the separation marker of each code block, which are divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding into L ordered binary sequences of quantized wavelet coefficients n- of the received code block, repeat the steps to verify the authenticity of the received code blocks until the reception is completed, accepted EI considered authentic if the received original are N code blocks, further pre sender and receiver compute the length of the ordered sequence of binary code block of quantized wavelet coefficients.

Prior to encoding the UDP of the quantized wavelet coefficients of the nth code block using the arithmetic coding, the sender establishes the secret initial probability values of the encoded zero characters and single characters in accordance with a pre-formed DP SK or in accordance with a pre-formed DP SK and the number of the n-th code block .

Before decoding encoded sequences of the nth received code block using arithmetic decoding, the receiver sets the secret initial probabilities of the decoded zero characters and single characters in accordance with the pre-formed DP SK or in accordance with the pre-formed DP SK and the number of the n-th received code block . After decoding the ordered binary sequences of quantized wavelet coefficients of the nth received code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length are compared with the pre-calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match each of the L calculated lengths, the n-th received code block is considered authentic.

Thus, in the second embodiment of the authentication method, the EI uses the setting of the secret initial probabilities of the encoded zero characters and single characters and the secret initial probabilities of the decoded zero characters and single characters in accordance with a pre-formed DP SC.

The specified technical result in the third embodiment of the proposed method for authenticating an EI using a key change of the boundaries of the encoding interval of the arithmetic coding and the decoding interval of the arithmetic decoding for each encoded and decoded bit, which consists in preliminary generation of the binary sequence of the secret key for the sender and receiver, over the electronic image perform the wavelet transform obtained as a result of transforming the wavelet coe cients quantized and divided into code blocks N≥2 quantized wavelet coefficients of each size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N , the code block of the quantized wavelet coefficients is converted into binary sequences of quantized wavelet coefficients of the nth code block, which transform into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, the UDP of the quantized wavelet coefficients of the nth code block is encoded using using arithmetic coding in the encoded sequences of this block, at the end of the arithmetic coding of UDP of the quantized wavelet coefficients of the nth code block, the separation block of the code block is written into the DP of the encoded EI, and the authentication steps from the sender of the code blocks are repeated until their arrival is completed, the encoded EI is transmitted to the recipient , where the authenticity of the received by the recipient EI is verified, for which the binary sequence of the received by the recipient EI is divided into binary the sequences of its received blocks using the separation marker of each code block, which are divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding into L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat the authentication steps of the received code blocks until the reception is completed, the accepted EI is considered n long, are authentic if N received code blocks for further pre sender and receiver compute the length of the ordered sequence of binary code block of quantized wavelet coefficients.

Before the coding of the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using the arithmetic coding, the sender of the arithmetic coding interval changes the boundaries of the coding interval of the arithmetic coding in accordance with the preformed DP SK or in accordance with the preformed DP SK and the number of the n-th code block, at the sender the receiver before decoding the next bit of the next encoded sequence of the n-th received code block using an arithmetic decoder Bani alter boundaries decoding arithmetic decoding interval in accordance with the pre-formed IC DP or in accordance with pre-formed IC DP and number of the received n-th code block. After decoding the ordered binary sequences of quantized wavelet coefficients of the nth received code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length are compared with the previously calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match for each of the L calculated lengths, the nth received code block considered genuine.

Thus, in the third embodiment of the EI authentication method, a key change of the boundaries of the arithmetic coding encoding interval is used before encoding the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding and a corresponding change by the key of the boundaries of the arithmetic decoding decoding interval before decoding the next bit the next coded sequence of the nth received code block using arithmetic one decoding in accordance with pre-formed IC DP.

The specified technical result in the fourth embodiment of the proposed method of authentication EI, using a secret key to change the probability values of the encoded and decoded zero and single characters for each encoded and decoded bits, which consists in preliminary formation for the sender and recipient of the binary sequence of the secret key from the sender over the electronic image perform the wavelet transform; the resulting wavelet transform coefficients are quantized and pour N ≥ 2 code blocks of quantized wavelet coefficients each of size n ₁ × n ₂ coefficients, where n ₁ ≥2 and n ₂ ≥2, quantized wavelet coefficients of the nth, where n = 1, 2, ..., N, of the code block the quantized wavelet coefficients are converted into binary sequences of the quantized wavelet coefficients of the nth code block, which convert to L≥2 ordered binary sequences of the quantized wavelet coefficients of the nth code block, the UDP of the quantized wavelet coefficients of the nth code block is encoded using arithmetic code in the encoded sequence of this block, at the end of the arithmetic encoding of the UDP of the quantized wavelet coefficients of the nth code block, the dividing marker of the code block is written in the DP of the encoded EI, and the authentication steps from the sender of the code blocks are repeated until their arrival, the encoded EI is transmitted to the recipient, where they verify the authenticity of the received EI by the recipient, for which they divide the binary sequence of the received EI by the recipient into binary sequences of its decimal blocks using the separation marker of each code block, which are divided into encoded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding in L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat the validation actions of the received code blocks until the completion of their reception, the accepted EI is considered genuine, if genuine are proved N received code blocks for further pre sender and receiver compute the length of the ordered sequence of binary code block of quantized wavelet coefficients.

After the coding of the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using the arithmetic coding, at the zero value of the next bit of the preformed DP SK or the next bit of the preformed DP SK and the number of the n-th code block, the sender increases the probability of the encoded zero characters after encoding of the next zero bit, otherwise the probability of encoded single characters is increased, and with a single value of the next bit, previously with of the generated DP SK or the next bit of the pre-formed DP SK and the numbers of the nth code block reduce the probability of encoded zero characters after encoding the next zero bit, otherwise the probability of encoded single characters is reduced. After decoding the next bit of the next encoded sequence of the nth received code block, the receiver using arithmetic decoding at the zero value of the next bit of the preformed DP SK or the next bit of the preformed DP SK and the numbers of the n-th received code block increase the probability of decoded zero characters after decoding the next zero bit, otherwise the probability of decoded single characters is increased, and at a single value, bits of preformed DP SC or next bit preformed DP SC and n-number of the received code block is reduced likelihood decoded zero symbols after the decoding of the next bit is zero, or reduce the likelihood of the decoded single character.

After decoding the ordered binary sequences of quantized wavelet coefficients of the nth received code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length are compared with the previously calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match for each of the L calculated lengths, the nth received code block considered genuine.

Thus, in the fourth embodiment of the authentication method EI use the change in the probability values of the encoded and decoded zero and single characters for each encoded and decoded bits in accordance with a pre-formed DP SK.

These new sets of actions according to the four options due to the adaptation of arithmetic coding to the secret key change of the boundaries of the coding interval or the probability values of the encoded zero and single characters of the arithmetic coding can reduce the length of the encoded with the authentication of EI. Therefore, these new sets of actions can reduce the difference in the length of the coded with the authentication of EI compared with the length of the coded without providing authentication of EI.

The claimed method (options) is illustrated by drawings, which show:

- in FIG. 1 - general authentication scheme EI;

- in FIG. 2 - figures explaining the preliminary formation of the DC SC and calculating the length of the ordered binary sequence of quantized wavelet coefficients of the code block;

- in FIG. 3 - algorithm for the formation of authenticated EI when setting the secret initial boundaries of the encoding interval;

- in FIG. 4 is a timing diagram of the formation of an authenticated n-th code block;

- in FIG. 5 is a timing diagram of the coding of UDP KVK n-th code block using arithmetic coding in the encoded sequence of this block without setting the secret initial boundaries of the encoding interval;

- in FIG. 6 is a state table of arithmetic coding of the UDP CPC of the n-th code block into the encoded sequences of this block without setting the secret initial boundaries of the encoding interval;

- in FIG. 7 is a timing diagram of the encoding of UDP CPC n-th code block using arithmetic coding in the encoded sequence of this block when setting the secret initial boundaries of the encoding interval;

- in FIG. 8 is a state table of arithmetic coding of the UDP CPC of the n-th code block into the encoded sequences of this block when setting the secret initial boundaries of the encoding interval;

- in FIG. 9 is a timing diagram of the authentication of the nth received code block;

- in FIG. 10 - authentication algorithm of the received EI when setting the secret initial boundaries of the decoding interval;

- in FIG. 11 is a timing diagram of decoding encoded sequences of the nth received code block using arithmetic decoding when setting the secret initial boundaries of the decoding interval;

- in FIG. 12 is a state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding when setting secret initial boundaries of a decoding interval;

- in FIG. 13 is a timing diagram of decoding encoded sequences of the nth received code block using arithmetic decoding without setting the secret initial boundaries of the decoding interval;

- in FIG. 14 - values of the length and compression coefficient encoded to ensure authentication of the EI for the prototype method and the first variant of the claimed method of authentication EI;

- in FIG. 15 is an algorithm for generating authenticated EI when setting secret initial probabilities of encoded zero and single characters;

- in FIG. 16 is a timing diagram of the coding of UDP KVK n-th code block using arithmetic coding in the encoded sequence of this block when setting the secret initial probability values of the encoded zero and single characters;

- in FIG. 17 is a state table of arithmetic coding of the UDP CPC of the n-th code block into the encoded sequences of this block when setting the secret initial probability values of the encoded zero and single characters;

- in FIG. 18 is a validation algorithm of a received EI when setting secret initial probabilities of decoded zero and single characters;

- in FIG. 19 is a timing diagram of the decoding of encoded sequences of the nth received code block using arithmetic decoding when setting secret initial probabilities of decoded zero and single characters;

- in FIG. 20 is a state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding when setting secret initial probabilities of decoded zero and single characters;

- in FIG. 21 is a timing diagram of the decoding of encoded sequences of the nth received code block using arithmetic decoding without setting secret initial probabilities of decoded zero and single characters;

- in FIG. 22 - values of the length and compression coefficient encoded to ensure authentication of the EI for the prototype method and the second variant of the claimed method of authentication EI;

- in FIG. 23 is an algorithm for generating authenticated EI when changing by secret key the boundaries of the coding interval of the arithmetic coding for each encoded bit;

- in FIG. 24 is a timing diagram of the coding UDP UDPKK of the n-th code block when the secret key changes the boundaries of the encoding interval of the arithmetic coding for each encoded bit;

- in FIG. 25 is a state table of the arithmetic encoding of the UDP CPC of the n-th code block into the coded sequences of this block when the secret key of the boundaries of the coding interval of the arithmetic coding is changed for each encoded bit;

- in FIG. 26 is a verification algorithm of the received EI when changing the key of the boundaries of the decoding interval of the arithmetic decoding for each decoded bit;

- in FIG. 27 is a timing diagram of the decoding of encoded sequences of the nth received code block using arithmetic decoding when changing the secret key of the boundaries of the decoding interval of the arithmetic decoding for each decoded bit;

- in FIG. 28 is a state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding when the secret key changes the boundaries of the decoding interval of the arithmetic decoding for each decoded bit;

- in FIG. 29 is a timing diagram of decoding encoded sequences of the nth received code block using arithmetic decoding without changing the secret key of the boundaries of the decoding interval of the arithmetic decoding for each decoded bit;

- in FIG. 30 - values of the length and compression ratio coded to ensure authentication of the EI for the prototype method and the third version of the claimed method of authentication EI;

- in FIG. 31 is an algorithm for generating an authenticated EI when changing with a secret key the probability values of encoded zero and single characters for each encoded bit;

- in FIG. 32 is a timing diagram of the coding of UDP KVK of the n-th code block when the secret key changes the probability values of the encoded zero and single characters for each encoded bit;

- in FIG. 33 is a state table of arithmetic coding of the UDP CPC of the n-th code block into the coded sequences of this block when the secret key changes the probability values of the encoded zero and single characters for each encoded bit;

- in FIG. 34 - authentication algorithm of the received EI when changing with a secret key the probability values of decoded zero and single characters for each decoded bit;

- in FIG. 35 is a timing diagram of the decoding of encoded sequences of the nth received code block using arithmetic decoding when the secret key changes the probability values of the decoded zero and one characters for each decoded bit;

- in FIG. 36 is a state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding when the secret key changes the probability values of the decoded zero and one characters for each decoded bit;

- in FIG. 37 is a timing diagram of decoding encoded sequences of the nth received code block using arithmetic decoding without changing the secret key probability values of the decoded zero and single characters for each decoded bit;

- in FIG. 38 - values of the length and compression coefficient encoded with the authentication of EI for the prototype method and the fourth variant of the claimed method of authentication EI.

The implementation of the claimed methods (options) is presented on the example of an authentication system of an electronic information device, including a unit for generating an authenticated electronic information device 1 and a verification unit for the received electronic information device 2, which interact through transmission channel 4 (Fig. 1). The sender at the first and second inputs of the unit of formation of a certified EI 1 transmit authenticated EI and DP SK, respectively. From the output of the authenticated EI generation unit 1, the EI encoded with authentication is transmitted over the transmission channel 4 to the receiver. Also, in the transmission channel 4, the intruder using the block of interception and the imposition of non-authentic EI 3 can intercept the encoder transmitted by the sender, which ensures authentication of EI. The intruder tries to modify the intercepted EI into a non-authentic EI that is beneficial to him, which the intruder transmits to the recipient through transmission channel 4. At the recipient, the received EI is authenticated in the block of verification of the received EI 2 using DP SC. The result of the authentication of the received EI is read from the outputs of the verification unit of the received EI 2 "genuine EI" and "non-authentic EI", respectively.

In the method according to the first embodiment of authentication EI, when setting the secret initial boundaries of the intervals of encoding and decoding, the following sequence of actions is implemented.

Preliminary formation for the sender and recipient of the DP SK is as follows. This sequence is formed using a random pulse generator that generates random equally probable zero and single pulses independent of each other. Methods of randomly forming symbols of the DC SK are known and described, for example, in the book:, for example, in GOST 28147-89. An exemplary view of DP SC is shown in figure 2 (a). Single bit values in the figures are shown in the form of shaded pulses, zero bit values in the form of unshaded pulses.

The methods for preliminary calculation of the length of an ordered binary sequence of quantized wavelet code block coefficients for the sender and receiver are known and described, for example, in the book “Video coding. H.264 and MPEG-4 - new generation standards” by J. Richardson. - M., Technosphere, 2005, pp. 38-80. To do this, choose the size of the code block of the quantized wavelet coefficients of the EI, consisting of n ₁ × n ₂ coefficients, where n ₁ ≥2 and n ₂ ≥2. Typical values of the code block size of quantized wavelet EI coefficients are, for example, 16 × 16, 32 × 32 coefficients, etc., as described, for example, in the book “Video coding. H.264 and MPEG-4 - standards by J. Richardson. new generation". - M., Technosphere, 2005, pp. 38-40. The length of the ordered binary sequence of quantized wavelet coefficients of the code block is calculated as the product of n ₁ and n ₂ . For example, for the selected code block sizes of the quantized wavelet coefficients n ₁ = 32 and n ₂ = 32, the pre-calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block is L0 = 1024. An exemplary form of an ordered binary sequence of quantized wavelet coefficients of a code block with a pre-calculated length L0 is shown in Figure 2 (b). For example, let a pre-calculated length of an ordered binary sequence of quantized wavelet code block coefficients be L0 = 6.

The algorithm for the formation of authenticated EI when setting the secret initial boundaries of the encoding interval is presented in figure 3.

Authenticated EI is represented by a matrix of pixels of an electronic image of size w ₁ × w ₂ pixels, where w _l ≥2 and w ₂ ≥2. An exemplary view of the pixel luminance (PS) values of the EI, alternately read from left to right line by line, is shown in Figure 4 (a).

Known methods for performing EI wavelet transforms are described, for example, in S. Lyu, N. Farid's book "Steganalysis Using Higher-Order Image Statistics", IEEE Transactions on Information Security and Forensics, vol. 1, pp. 111-119, 2006. A k-level is performed over the EI, where k = 1, 2, 3, ... K, and 1≤K≤10, a wavelet transform with the formation of a matrix of coefficients of the wavelet transform EI of the same size as the size of the original EI in pixels. The matrix of coefficients of the wavelet transform EI consists of matrices of horizontal, vertical, high-frequency and low-frequency coefficients of the wavelet transform EI. In FIG. 4 (b) shows an example of the values of the low-frequency, vertical, high-frequency and horizontal coefficients of the first level of the wavelet transform EI. It can be seen that the wavelet EI coefficients take both positive and negative values and can be non-integer.

The methods of quantization of the values of VC EI obtained as a result of the conversion are known and described, for example, in the book by J. Richardson "Video coding. H.264 and MPEG-4 - new generation standards." - M., Technosphere, 2005, pp. 78-80. The values of VK EI are quantized by rounding them to the nearest integer value. An exemplary view of quantized wavelet coefficients (CVC) EI is shown in figure 4 (c).

Methods for dividing quantized wavelet coefficients into N≥2 code blocks each of size n ₁ × n ₂ coefficients, where n ₁ ≥2 and n ₂ ≥2, are known and described, for example, in the book “Video coding. H.264 and MPEG by J. Richardson. -4 - new generation standards. " - M, Technosphere, 2005, pp. 38-40. From the matrix of quantized wavelet coefficients of the EI, starting, for example, from its upper left corner, a matrix of coefficients of size n ₁ rows and n ₂ columns is selected, which forms the nth, where n = 1, 2, ..., N, a code block, in in this case, the first code block. Then, to the right or bottom of the selected matrix of coefficients, the next matrix of coefficients of the same size is selected, which forms the next code block, and so on, all coefficients are not selected from the matrix of quantized wavelet coefficients of EI. The size of the code blocks is selected, for example, on the order of 16 × 16, 32 × 32 coefficients, etc., which is determined by the number of code block coefficients generated by the wavelet. An exemplary view of the quantized wavelet coefficients of the first (n = 1) code block is shown in Figure 4 (g).

Methods of converting the quantized wavelet coefficients of the nth code block to their DP are known and described, for example, in the book: ISO / IES 15444-1. Information technology - JPEG2000 image coding system. Geneva. 2001, pp. 219-222. KVK n-th code block according to a fixed coding rule is converted into DP KVK this block. It consists in converting the integer value of each TEC of the nth code block into a binary sequence in which each subsequent bit is 2 times different in informational significance, and the leading binary symbol of this binary sequence encodes the sign of the quantized wavelet coefficient. A positive value of a quantized wavelet coefficient is encoded, for example, with a single binary symbol, and a negative value is encoded with a zero binary symbol. For example, the value of the first KVK of the first (n = 1) code block, equal to -8 = - (8 + 0 + 0 + 0), is converted to the first DP of the KVK of this block of the form 01000, and the value of the second KVK of this block is + 273 = 256 + 16 + 1, is converted into the second DP of the KVK of this block of the form 1110010001, and the value of the last n ₁ × n of the _2nd KVK of this block, equal to + 241 = 128 + 64 + 32 + 16 + 1, is converted to n ₁ × n _2nd DP KVK of this block type 111110001. An exemplary view of the DP KVK of the first (n = 1) code block is shown in figure 4 (e).

Methods for converting binary KVK sequences of the nth code block to L≥2 ordered binary KVK sequences of this block are known and described, for example, in the book of V. Vorobyov, V. Gribunin, “Theory and Practice of Wavelet Transformation”. - SPb., VUS, 1999, p. 159-161. They consist in sequentially writing the first bits of all binary sequences of the KVK of the nth code block to the first ordered binary sequence of the KVK of this block, sequentially writing the second bits of all binary sequences of the KVK of the n-th code block to the second CCD of this block, etc. The ordering of the binary sequences of the KVK of the n-th code block consists in the selected order of sequential recording of bits of the binary sequences of the KVK of the n-th code block EI in the UDP of the KVK of this block. The number L is chosen as the smallest integer providing a relation of the form: the value 2 ^L-1 must be not less than the absolute value of the highest value of the quantized wavelet coefficients of the nth code block, taking into account the sign. An exemplary view of the UDP KVK n-th code block is shown in figure 4 (e). For example, the first UDP KVK of the first code block has the form 0111 ... 1.

The methods for setting the sender's secret initial boundaries of the coding interval of the arithmetic coding in accordance with the pre-formed DP SC are as follows.

Known methods for setting the initial boundaries of an encoding interval of an arithmetic encoding without using a secret key are to set the initial lower value of its encoding interval to a minimum value, the initial upper value of its encoding interval to a maximum value. For example, when representing encoding interval values with sixteen binary characters, the initial lower value of the arithmetic encoding encoding interval L [0] is set to a minimum value equal to zero in decimal or 0000000000000000 in binary representation, where the most significant binary characters are written to the left and the initial upper value the coding interval of the arithmetic coding H [0] is set to a maximum value of 65535 in decimal or 1111111111111111 in binary dstavlenii. An example of the initial state (Start state) of arithmetic coding without setting the secret initial boundaries of the coding interval is shown in FIG. 5.

, а начальное значение вероятности кодируемых единичных символов p₁[0] вычисляют по формуле вида $$p_1[0]=\frac{N_1[0]}{N[0]}$$

, где N₀[0] - начальное число закодированных нулевых символов, N₁[0] - начальное число закодированных единичных символов, а N[0] - начальное число закодированных нулевых и единичных символов, равное N[0]=N₀[0]+N₁[0]. В известных способах, описанных, например, в книге Д. Ватолин, А. Ратушняк, М. Смирнов, В. Юкин "Методы сжатия данных. Устройство архиваторов, сжатие изображений и видео". - М., ДИАЛОГ-МИФИ, 2002, стр. 124-130, устанавливают начальное число закодированных нулевых символов равным N₀[0]=1, а начальное число закодированных единичных символов - равным N₁[0]=1, то есть начальные значения вероятности кодируемых единичных и нулевых символов устанавливают равными: p₁[0]=p₀[0].Known methods for setting the initial state of arithmetic coding also include setting the initial probability value of the encoded zero characters p ₀ [0] and the initial probability value of the encoded single characters p ₁ [0]. When setting the initial probability value of the encoded null characters p ₀ [0] and the initial probability value of the encoded null characters p ₁ [0] to the selected values, a restriction of the form: p ₀ [0] + p ₁ [0] = 1 must be fulfilled. The initial probability value of the encoded null characters p ₀ [0] is calculated by the formula of the form $$p_0[0]=\frac{N_0[0]}{N[0]}$$

, and the initial probability value of encoded single characters p ₁ [0] is calculated by the formula of the form $$p_{\mathrm{one}}[0]=\frac{N_{\mathrm{one}}[0]}{N[0]}$$

, where N ₀ [0] is the initial number of encoded zero characters, N ₁ [0] is the initial number of encoded single characters, and N [0] is the initial number of encoded zero and single characters, equal to N [0] = N ₀ [0 ] + N ₁ [0]. In the known methods described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. The device archivers, image and video compression." - M., DIALOGU-MIFI, 2002, pp. 124-130, set the initial number of encoded null characters to N ₀ [0] = 1, and the initial number of encoded single characters to N ₁ [0] = 1, that is, the initial the probability values of the encoded single and zero characters are set equal to: p ₁ [0] = p ₀ [0].

The initial value of the coding interval of the arithmetic encoder I [0], equal to I [0] = H [0] -L [0], is divided into the initial values of the sub-interval of zero characters D ₀ [0] and the sub-interval of single characters D ₁ [0], length which are directly proportional to the initial probabilities of the encoded null characters p ₀ [0] and unit characters p ₁ [0], respectively. The initial length of the sub-interval of single characters D ₁ [0] is determined by the formula of the form D ₁ [0] = I [0] × p ₁ [0], and the initial length of the sub-interval of single characters of D ₀ [0] is determined by the formula of the form D ₀ [0] ] = I [0] -D ₁ [0]. For example, without setting the secret start boundaries of the encoding interval, the initial length of the subinterval of unit characters D ₁ [0] has a decimal value of 32768 or 1000000000000000 in binary representation, and the initial length of the subinterval of zero characters D ₀ [0] has a decimal value of 32767 or 0111111111111111 in binary representation. A sub-interval of single characters is located above the sub-interval of null characters, as shown, for example, in FIG. 5. The upper boundary of the null-character subinterval is designated as the Q value, and this subinterval starts from the bottom of the lower bound of the arithmetic coding coding interval to the Q value exclusively, and the single-character subinterval extends from the Q value inclusive to the upper limit of the arithmetic coding coding interval exclusively. The initial Q value has a decimal value 32767, as shown in FIG. 6 in the first row at t = 0.

When setting the secret initial boundaries of the encoding interval in accordance with a preformed DP SC, the following actions are performed. For this, for example, the first and second binary subsequences 16 bits in length each are read from the DP SK in turn, starting from the left bits. Binary subsequences are converted to decimal numbers, considering, for example, their left characters as the most significant and compare decimal numbers with each other. The initial lower limit of the arithmetic encoding encoding interval L [0] is set to a value equal to a lower decimal number, and the initial upper boundary of the arithmetic encoding encoding interval H [0] is set to a value equal to a larger decimal number. For example, in accordance with the PD SC shown in FIG. 4 (a), the initial lower bound of the arithmetic encoding encoding interval L [0] is set to 16384 in decimal or 010 ... 0 in binary representation, and the initial upper bound of the arithmetic encoding encoding interval H [0] is set to 32678 in decimal notation or 100 ... 0 in binary notation. Examples of established secret initial boundaries of the coding interval of the arithmetic coding in accordance with a pre-formed DP SC are presented in FIG. 7.

, а начальное значение вероятности кодируемых единичных символов p₁[0] вычисляют по формуле вида $$p_1[0]=\frac{N_1[0]}{N[0]}$$

. В кодируемых УДП КВК n-го кодового блока устанавливают, например, начальное число закодированных нулевых символов равным N₀[0]=1, а начальное число закодированных единичных символов - равным N₁[0]=1, как показано на фиг. 8. Начальную длину подинтервала единичных символов D₁[0] определяют по формуле вида D₁[0]=I[0]×p₁[0], а начальную длину подинтервала нулевых символов D₀[0] определяют по формуле вида D₀[0]=I[0]-D₁[0]. Для примера, показанного на фиг. 8, при установленных начальных значениях интервала кодирования значение Q, численно равное длине подинтервала нулевых символов D₀[0], составило десятичное значение 24575 или двоичное значение 0101…1.The initial value of the encoding interval of the arithmetic coding I [0] when setting the secret initial boundaries of the encoding interval in accordance with the pre-formed DP SC is set to I [0] = H [0] -L [0]. For example, the initial upper H [0] = 32768 and lower L [0] = 16384 values of the coding interval of the arithmetic coding at t = 0 are shown in FIG. 8. The initial value of the coding interval for arithmetic coding I [0] is divided into the initial values of the sub-interval of zero characters D ₀ [0] and the sub-interval of single characters D ₁ [0], the lengths of which are directly proportional to the initial values of the probabilities of the coded zero characters p ₀ [0] and unit characters p ₁ [0], respectively. The initial probability value of the encoded null characters p ₀ [0] is calculated by the formula of the form $$p_0[0]=\frac{N_0[0]}{N[0]}$$

, and the initial probability value of encoded single characters p ₁ [0] is calculated by the formula of the form $$p_{\mathrm{one}}[0]=\frac{N_{\mathrm{one}}[0]}{N[0]}$$

. In the encoded UDP CPCs of the n-th code block, for example, the initial number of encoded zero characters is set to N ₀ [0] = 1, and the initial number of encoded single characters is set to N ₁ [0] = 1, as shown in FIG. 8. The initial length of the sub-interval of single characters D ₁ [0] is determined by the formula of the form D ₁ [0] = I [0] × p ₁ [0], and the initial length of the sub-interval of single characters of D ₀ [0] is determined by the formula of the form D ₀ [0] = I [0] -D ₁ [0]. For the example shown in FIG. 8, at the set initial values of the coding interval, the Q value, numerically equal to the length of the zero-character subinterval D ₀ [0], was the decimal value 24575 or the binary value 0101 ... 1.

The features of the sender’s installation of the secret initial boundaries of the encoding interval in accordance with the previously formed DP SC and the number of the nth code block are as follows. The decimal number of the nth code block is converted to its binary sequence. The pre-formed binary sequence of SK and the binary sequence of the number of the nth code block are summed, starting with the least significant binary bits, modulo 2. Methods of summing two binary sequences are known and described, for example, in the book: A. Sikarev, O. Lebedev, Microelectronic devices for generating and processing complex signals. " - M., Radio and Communications, 1983, pp. 107-108 based on modulo 2 adders. Then, the previously described actions are performed by setting the secret initial boundaries of the coding interval of the arithmetic coding in accordance with the resulting total binary sequence of SK and binary sequence of n- th code block.

Methods of encoding the next, from the first to the Lth, UDP CPC of the nth code block using arithmetic coding into the encoded sequences of the nth code block are known and described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. Device archivers, image and video compression." - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequential coding of the next binary characters of the UDP KVK of the n-th code block in accordance with the current values of the coding interval of the arithmetic coding and the current values of the probabilities of the coded zero characters and single characters with the sequential generation of coded sequences of the n-th code block.

An exemplary coding shown in FIG. 4 (e) of the first UDP DCC of the nth code block in the form of a binary sequence "011111" with a length of 6 binary symbols using arithmetic coding into the encoded sequences of the nth code block with setting the sender's secret initial boundaries of the encoding interval shown in FIG. 7.

Upon receipt of the input of the arithmetic coding of the first encoded character, which is a binary binary character, the value of the encoding interval of the first character I [1] is set equal to the initial value of the sub-interval of zero characters D ₀ [0], therefore, the lower value of the encoding interval of the first character L [1] is set to the initial lower value of the encoding interval of the arithmetic encoder L [0], equal, for example, 16384, and the upper value of the encoding interval of the first character of the arithmetic encoding H [1] is set t equal to the current value of Q, equal, for example 24575, as shown in FIG. 7. The leftmost bit of the binary representation of the value L [1] is compared with the leftmost bit of the binary representation of the value H [1], for example, of the form 010 ... 0 and 0101 ... 1, respectively. When they coincide, the value of the leftmost bit of the binary representations of the values L [1] and H [1] is read as the encoded bit of the encoded sequence of the nth code block. For example, when encoding the UDP DCC of the nth code block in the form of a binary sequence “0111111”, the first encoded bit of the encoded sequence of this block is the zero binary symbol coincident in comparison, as shown in FIG. 8, the second row from above at t = 1. The read bit is removed from the binary representations of the values L [1] and H [1], which are reduced to a length of 15 bits of the form 100 ... 0 and 1011 ... 1, respectively. The binary symbols of the binary representations of the values L [1] and H [1] are shifted from right to left by one digit and are added to the right by a zero binary symbol. Methods for reading binary characters with the removal of read characters are known and described, for example, in the book: V. Shilo "Popular digital circuits." - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences. The operations of shifting from right to left by one bit and appending a binary binary symbol to the right increase the values of L [1] and H [1] by 2 times and are called normalization of arithmetic coding parameters. Methods of shifting one bit in the direction of the higher bits of binary sequences and writing to the freed low order of the zero binary symbol are known and described, for example, in the book: V. Shilo "Popular Digital Circuits". - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences, and in essence are multiplication by two decimal values of the lower and upper values of the encoding interval.

и текущее значение вероятности кодируемых единичных $$p_1[1]=\frac{N_1[1]}{N[1]}=\frac{1}{3}$$

. В соответствии с этим длина подинтервала нулевых символов D₀[1] становится в 2 раза больше длины подинтервала единичных символов D₁[1], а параметр Q принимает значение 43686, как показано на фиг. 7 и на фиг. 8, пятая строка сверху.After each normalization run, the leftmost bit of the binary representation of the lower value of the encoding interval is compared again with the leftmost bit of the binary representation of the upper value of the encoding interval. When they match, the value of the leftmost bit of these binary representations is read as the next encoded bit of the encoded sequence of the nth code block. For example, after the first normalization, the leftmost bits of binary representations of the form 100 ... 0 and 1011 ... 1 are compared with each other and the coincident single binary symbol is read as the second encoded bit of the encoded sequence of the nth code block, as shown in FIG. 8, the third line from the top. After the second normalization run, the leftmost bit of the binary representation of the lower value of the encoding interval is compared again with the leftmost bit of the binary representation of the upper value of the encoding interval, the match of the compared bits is again detected and the matched zero binary symbol is read as the third encoded bit of the encoded sequence of the nth code block as shown in FIG. 8, the fourth line from the top. After coding of each successive bit of the UDP DCC of the n-th code block, the number of encoded zero characters and single characters is specified. Since the first encoded bit is zero, the number of encoded zero characters is increased by a unit value and it is N ₀ [1] = 2, and the number of encoded zero and single characters becomes N [1] = N ₀ [1] + N ₁ [1] = 3. Recalculate the current probability value of encoded null characters $$p_0[\mathrm{one}]=\frac{N_0[\mathrm{one}]}{N[\mathrm{one}]}=\frac{2}{3}$$

and the current probability value of the encoded units $$p_{\mathrm{one}}[\mathrm{one}]=\frac{N_{\mathrm{one}}[\mathrm{one}]}{N[\mathrm{one}]}=\frac{\mathrm{one}}{3}$$

. Accordingly, the length of the zero-character subinterval D ₀ [1] becomes 2 times the length of the single-character subinterval D ₁ [1], and the parameter Q takes the value 43686, as shown in FIG. 7 and in FIG. 8, the fifth line from the top.

If the leftmost bit of the binary representation of the lower value of the encoding interval does not coincide with the leftmost bit of the binary representation of the upper value of the encoding interval, then proceed to encoding the next bit of the UDP KVK and the nth code block and so on until the end of the encoded bits of the UDP KVK of this block. For example, the second bit of the UDP DCC of the n-th code block is a single binary symbol, as shown in FIG. 8, the fifth row from the top, t = 2. When a single binary character is input to the arithmetic coding, the value of the coding interval of the arithmetic coding is set equal to the value of the previous sub-interval of single characters, therefore, the lower value of the coding interval L [2] is set equal to the value Q, and the upper value of the coding interval H [2] is set equal to the previous upper value of the encoding interval H [1]. For example, as shown in FIG. 7, the value of L [2] is set equal to 43686, and H [2] remains equal to the previous value 65528. Again, the leftmost bit of the binary representation of the value L [2] is compared with the leftmost bit of the binary representation of the value H [2] and, if they match, the value the leftmost bit of the binary representations of the values L [2] and H [2] is read as the next encoded bit of the encoded sequence of the nth code block, and so on, until the end of the UDP TAC of the nth code block. For example, the result of encoding the first UDP DCK of the nth code block in the form of a binary sequence "011111" is a binary sequence of the form "0101111".

After encoding the last binary symbol of the next ordered binary sequence of the KVK of the n-th code block, the end coding combination of the next UDP in the form of a binary representation of the lower value of the coding interval is read into the coded sequence of the n-th code block. For example, after encoding the UDP KVK of the nth code block in the form of a binary sequence "011111" with a length of 6 binary symbols, the end coding combination (end comb.) Of this UDP is of the form "0011 1100 01111100", as shown in FIG. 8, the last line.

If not all ordered binary KVK sequences of the nth code block are encoded, then continue the arithmetic coding of the next UDP KVK of this block.

An exemplary form of encoding UDP TEC of the nth code block in the form of a binary sequence “011111” with a length of 6 binary symbols using arithmetic coding into the encoded sequences of the nth code block without setting the sender's secret initial boundaries of the encoding interval is shown in FIG. 5, and successive arithmetic coding states are shown in FIG. 6. The encoding result is a binary sequence of the form “011111” with the end coding combination “0011 1100 1101 0110”, which differs significantly from the encoding result of the same binary sequence with the sender setting the secret initial boundaries of the encoding interval shown in FIG. 8. The encoding actions to be performed when the sender sets the secret initial boundaries of the encoding interval without the same installation are the same, but the encoding result is different.

The methods for writing the code block separator marker at the end of the arithmetic coding of the TDC KVK of the nth code block in the DP of the compressed EI are known and described, for example, in the book: V. Shilo "Popular Digital Chips". - M., Radio and Communications, 1987, 104-123, using shift registers with parallel and sequential write / read of binary sequences. The code block dividing marker is designed to ensure the separation of the DP received by the recipient EI into binary sequences of its received code blocks. The code block separation marker is a unique binary sequence a priori known to the sender and receiver of the view. An exemplary view of the code block dividing marker in the form of a unique binary sequence of the form 0101 ... 01 is shown in FIG. 4 (g).

An exemplary view of coded sequences from the first to the Lth UDP of the DCC of the n-th code block is shown in FIG. 4 (g).

An exemplary view of the binary sequence of the encoded EI, consisting of binary sequences from the first to the Nth code blocks, is shown in FIG. 4 (h).

Methods of transmitting encoded EI to a recipient are known and described, for example, in A.G. Zyuko, D.D. Klovsky, M.V. Nazarov, L.M. Fink "Theory of signal transmission." - M .: Radio and communications, 1986, p. 11. An exemplary view of the binary sequence received by the recipient of EI is shown in FIG. 9 (a).

The authentication algorithm of the nth received code block when setting the secret initial boundaries of the decoding interval is shown in FIG. 10.

Methods for separating the DP received by the recipient of EI into coded sequences of received code blocks are known and described, for example, in the book: A. Sikarev, O. Lebedev "Microelectronic devices for the formation and processing of complex signals." - M., Radio and Communications, 1983, pp. 72-80. They consist in dividing the DP received by the recipient of EI into coded sequences of its received code blocks using a separator marker of a code block of the form known to the recipient, indicating the boundaries of each received block. An exemplary view of the CP of the n-th received code block is presented in figure 9 (b).

The methods for setting the secret initial boundaries of the decoding interval in accordance with the previously generated DP IC, or in accordance with the pre-formed DP IC and the number of the mth received EI block, exactly correspond to the previously described methods for setting the secret initial boundaries of the encoding interval.

и начальное значение вероятности декодируемых нулевых символов равно $$p{p}_0[0]=\frac{N{N}_0[0]}{NN[0]}=\frac{1}{2}$$

. Верхнее значение подинтервала декодирования нулевых символов обозначают как значение QQ, и данный подинтервал начинается снизу от нижнего значения интервала декодирования до значения QQ исключительно, а подинтервал декодирования единичных символов простирается от значения QQ включительно до верхнего значения интервала декодирования исключительно. Начальное значение QQ имеет десятичное значение 24575, как показано на фиг. 12 в первой строке при t=0.The initial state of arithmetic decoding with setting the secret initial boundaries of the decoding interval in accordance with the pre-formed DP SC, or in accordance with the pre-formed DP SC and the number of the mth received EI block, is shown in FIG. 11. The initial value of the decoding interval of the arithmetic decoder II [0], equal to II [0] = HH [0] -LL [0], where LL [0] is the initial lower value of the decoding interval of the arithmetic decoder, and HH [0] is the initial the upper value of the decoding interval of the arithmetic decoder is divided into the initial values of the decoding subinterval DD ₀ [0] and the decoding subinterval of single characters DD ₁ [0], the lengths of which are directly proportional to the initial probability values of the decoded zero character pp ₀ [0] and unit character pp ₁ [0], respectively, governmental. The initial length of the decoding sub-interval of single characters DD ₁ [0] is determined by the formula of the form DD ₁ [0] = II [0] × pp ₁ [0], and the initial length of the decoding sub-interval of decoding of zero characters DD ₀ [0] is determined by the formula of the form DD ₀ [0] = II [0] -DD ₁ [0]. For example, as shown in FIG. 11, the initial values LL [0] = 16384 and HH [0] = 32768 are set. It can be seen that the secret initial boundaries of the encoding interval and the decoding interval coincide. In FIG. 12 shows a state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding when setting the secret initial boundaries of the decoding interval. For example, the initial number of decoded zero characters is NN ₀ [0] = 1, and the initial number of decoded single characters is NN ₁ [0] = 1, respectively, the initial number of decoded zero and single characters is NN [0] = NN ₀ [0 ] + NN ₁ [0] = 1 + 1 = 2. Accordingly, the initial probability value of decoded unit symbols is $$p{p}_{\mathrm{one}}[0]=\frac{N{N}_{\mathrm{one}}[0]}{NN[0]}=\frac{\mathrm{one}}{2}$$

and the initial probability value of the decoded zero characters is $$p{p}_0[0]=\frac{N{N}_0[0]}{NN[0]}=\frac{\mathrm{one}}{2}$$

. The upper value of the decoding interval of the decoding of zero symbols is designated as the QQ value, and this sub-interval starts from the bottom from the lower value of the decoding interval to the QQ value exclusively, and the decoding interval of single symbols extends from the QQ value inclusive to the upper value of the decoding interval exclusively. The initial QQ value has a decimal value of 24575, as shown in FIG. 12 in the first line at t = 0.

For comparison, the initial state of arithmetic decoding without setting the secret initial boundaries of the decoding interval is shown in FIG. 13.

Methods for decoding encoded sequences of the nth Ex the code block using arithmetic decoding are known and described, for example, in the book by D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin "Data compression methods. Device archivers, image and video compression." - M., DIALOGUE-MEPhI, 2002, pp. 35-43. They consist in sequential decoding using arithmetic decoding of the encoded sequences of the nth Pr. code block in accordance with the current values of the decoding interval of the arithmetic decoder and the current values of the probability of the decoded zero character and a single character.

The arithmetic decoding input with the secret initial boundaries of the decoding interval set is encoded with sequences of the nth Pr. a code block, for example, KP of the first UDP KVK of the form 0101 1110 0111 1000 1111 100 with a length of 23 binary symbols formed by arithmetic coding with established secret initial boundaries of the encoding interval. As previously described arithmetic coding, arithmetic decoding operations use the same bit depth of the operations performed, for example, 16 bits. Therefore, the input data from the first 16 bits of the encoded sequence of the form 0101 1110 0111 1000 is read to the input of the arithmetic decoding, which corresponds to the decimal number 24184. The current value of the read encoded sequence indicated in FIG. 11 by an arrow, compare with the boundaries of the initial value of the decoding interval of the decoding of null characters DD ₀ [0], which are, for example, in the range from 16384 to 24575 and with the boundaries of the initial values of the decoding sub-interval of the decoding interval of the single characters DD ₁ [0], for example, ranging from 24575 to 32768. Depending on the extent to which the character decoding subinterval turned out to be the current value of the read encoded sequence, a decision is made to decode the next character of the ordered binary sequence of KVK n- th received code block. For example, since the current value of the read encoded sequence turned out to be less than the QQ value, the first decoded symbol is zero and the following boundaries of the decoding interval are set to the corresponding boundaries of the initial value of the decoding sub-interval of zero characters DD ₀ [0].

To decode the next character, the lower value of the arithmetic coding decoding interval LL [1] is set equal to the previous LL [0] value, for example, LL [0] = 16384, and the upper value of the arithmetic coding decoding interval HH [1] is equal to the QQ value, for example, QQ = 24575. The leftmost bit of the binary representation of the LL [1] value is compared with the leftmost bit of the binary representation of the value HH [1], for example, of the form 010 ... 0 and 0101 ... 1, respectively. When they coincide, the arithmetic decoding is normalized: the value of the leftmost bit of the binary representations of the LL [1] and HH [1] values is deleted and the binary characters of the binary representations of the LL [1] and HH [1] values are shifted from right to left by one digit and from right to them append to a binary binary character. At the same time, the value of the leftmost bit of the input data is deleted and the binary characters of the input data are shifted from right to left by one bit, and the next binary character of the decoded sequence is added to them, for example, a single character, the seventeenth account in the CP of the first UPC KVK. As, for example, shown in FIG. 12 in the line "first normalization", the input data acquires the binary representation 1011 1100 1111 0001 and the decimal value 48369. The variable LL [1] takes the decimal value 32768 and the binary representation 100 ... 0, and HH [1] the decimal value 49150 and the binary representation 1011 ... 0. Since the leftmost bits of the binary representations LL [1] and HH [1] coincide, they perform the second normalization of arithmetic decoding in the same way, for example, as described in FIG. 12 in the line "second normalization". As a result of the second normalization, the leftmost bits of the binary representations LL [l] and HH [1] coincide again, which requires the third normalization of arithmetic decoding in a similar way, for example, described in FIG. 12 in the line "third normalization". As a result of the third normalization, the variable LL [1] takes the decimal value 0 and the binary representation 000 ... 0, and HH [1] takes the decimal value 65528 and the binary representation 111 ... 1000.

и по формуле вида $$p{p}_1[1]=\frac{N{N}_1[1]}{NN[1]}=\frac{1}{3}$$

, соответственно. Устанавливают текущие длины подинтервалов декодирования единичных символов и нулевых символов и устанавливают текущее значение QQ=43686 с двоичным представлением вида 1010 1010 10100110.After decoding each symbol, the current probability value of the decoded zero symbol and the current probability value of the decoded zero symbol are recalculated, for example, after decoding the first symbol that is zero, according to the formula $$p{p}_0[\mathrm{one}]=\frac{N{N}_0[\mathrm{one}]}{NN[\mathrm{one}]}=\frac{2}{3}$$

and according to the formula of the form $$p{p}_{\mathrm{one}}[\mathrm{one}]=\frac{N{N}_{\mathrm{one}}[\mathrm{one}]}{NN[\mathrm{one}]}=\frac{\mathrm{one}}{3}$$

, respectively. Set the current lengths of the decoding intervals of single characters and zero characters and set the current value QQ = 43686 with a binary representation of the form 1010 1010 10100110.

As a result of the third normalization, the input data acquires the binary representation 1111 0011 1100 0111 and the decimal value 62407. The current decimal value of the input data is compared with the boundaries of the current value of the decoding subinterval of zero characters and the decoding subinterval of single characters. The current decimal value 62407 of the input data was within the decoding sub-interval of single characters, so the next decoded character is single.

To decode the next symbol, the lower value of the decoding interval LL [2] is set to, for example, QQ = 43686, and the upper value of the decoding interval HH [2] is equal to the previous value LL [1]. The leftmost bit of the binary representation of the LL [2] value is compared with the leftmost bit of the binary representation of the HH value [2] and, if they coincide, the arithmetic decoding is normalized, etc.

If the current decimal value of the input data becomes equal to the lower value of the decoding interval, then decoding the encoded sequence of the next UDP KVK m-th EI block is finished. If the current value is greater than the lower value of the decoding interval, then decoding continues. For example, when decoding the sixth character, the current decimal value of the input data becomes equal to the lower value of the decoding interval (value 40510), as shown in FIG. 12 at t = 6. The calculated length value equal to 6 coincides with the previously calculated length of the ordered binary sequence of wavelet coefficients of the code block.

To decode all six characters from the KP of the first UDP KVK of the form 0101 11100111 1000 1111 100, the first 22 binary characters were required.

After the decoding of the encoded sequence of the next UDP KVK m-th Pr. block EI perform decoding the encoded sequence of the next UDP of this block until the decoding of the last L-th UDP. If each of the L calculated length values matches the previously calculated length of the ordered binary sequence of the wavelet coefficients of the code block, then the nth received code block is considered authentic.

The intruder intercepts the transmitted EI, divides it into coded sequences and attempts to decode the encoded sequences of the UDP CPC received code blocks. Arithmetic decoding is performed by the intruder in the same way as the receiver, with the exception of setting the secret initial boundaries of the decoding interval due to the lack of knowledge of the SC SK. The intruder arbitrarily selects his initial state of arithmetic decoding, for example, sets the initial boundaries of the decoding interval of the form LL [0] = 0 and HH [0] = 65535, the initial probability values of the decoded zero symbol pp ₀ [0] = 1/2 and a single symbol pp ₁ [0] = 1/2, as shown in FIG. 13. The input of such arithmetic decoding receives coded sequences of the nth received code block, for example, the KP of the first UDP KVK of the form 0101 1110 0111 1000 1111 100 with a length of 23 binary symbols formed by arithmetic coding with the encryption interval set for the secret key. The input data from the first 16 bits of this encoded sequence of the form 0101 1110 0111 1000, which corresponds to the decimal number 24184, is read to the arithmetic decoding input. As a result of the sequential arithmetic decoding operations shown in FIG. 13 decode a sequence of the form “0100111 ...” with a length of 7 binary symbols, while decoding the encoded sequence of the next UDP TAC of the n-th received code block is not completed, since the current decimal value of the input data is not equal to the lower value of the decoding interval. As a result, the length of the decoded sequence of the next UDP DCC of the n-th received code block does not correspond to the initial length of this coded sequence and as a result, the value of this length is not equal to the previously calculated length of the ordered binary sequence of the wavelet coefficients of the code block and this received code block will not be recognized as genuine.

Methods for calculating the length of each of the L ordered binary sequences of quantized wavelet coefficients of the nth received code block are known and described, for example, in the book A. Sikarev, O. Lebedev "Microelectronic devices for generating and processing complex signals." - M., Radio and Communications, 1983, pp. 125-131, based on the use of binary counters.

Methods for comparing the calculated length of each of the L ordered binary sequences of wavelet coefficients of the nth received code block with the previously calculated length of the ordered binary sequence of wavelet coefficients of the code block are known and described, for example, in A. Sikarev, O. Lebedev's book Microelectronic Devices for Formation and Processing complex signals. " - M., Radio and Communications, 1983, pp. 178-183. They consist in a bitwise comparison of the binary representations of the compared length values using digital comparators that generate a control signal when there is a mismatch of pairwise compared length values in any binary digit being compared. Then, using binary counters, described, for example, in the book by A. Sikarev, O. Lebedev "Microelectronic devices for the formation and processing of complex signals." - M., Radio and Communications, 1983, pp. 107-131, count the number of matching lengths and compare the counted number of matches with the number L. If the counted number of matches is equal to the number L, then the nth received code block is considered authentic. A received EI is considered authentic if N received code blocks are authentic.

Verification of the theoretical premises of the claimed method of authentication EI (the first option), using the setting of the secret initial boundaries of the intervals of encoding and decoding, was verified by its analytical studies.

In the first version of the claimed method of authenticating EI using setting the secret initial boundaries of the encoding and decoding intervals, electronic images were encoded, each of which contained N = 15480 code blocks each with a size of 32 × 32 quantized wavelet coefficients. The quantized wavelet coefficients of each code block were converted into L≤11 ordered binary sequences of quantized wavelet coefficients of the nth code block, which were encoded using arithmetic coding into the encoded sequences of this block. Before encoding the UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding, the secret initial boundaries of the coding interval of the arithmetic coding were established in accordance with the previously generated DP SK. The secret initial lower and upper boundaries of the arithmetic coding coding interval were set in the range of decimal values from 0 to 65535, when representing the values of the coding interval with sixteen binary characters. The size of the uncompressed EI and the size of the encoded EI in bytes were calculated. The compression coefficient of EI was also calculated in times by dividing the size of the uncompressed EI by the size of the encoded EI. The coding results of three different EIs in the first embodiment of the claimed EI authentication method using setting secret initial boundaries of the encoding and decoding intervals are shown in the table in FIG. 14. In the prototype method, in order to provide security against attempts by an intruder to substitute a genuine authenticated EI for a non-authentic EI, the length of the binary CEH sequences of each code block should be at least 32 bits, which causes an increase in the length of the coded with authentication compared with the length of the coded without providing authentication EI . For comparison, the table shows the results of encoding the same EI using arithmetic coding without authentication. It is seen that providing authentication when encoding EI using arithmetic coding leads to an increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication by 7374 ... 7426 bytes, and causes a slight decrease in the compression coefficient of EI by about 0.25 times. However, when using the prototype method, the increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication is 7920 bytes, and the decrease in the compression coefficient of the EI is from 2.05 to 2.1 times, as shown in FIG. fourteen.

Thus, in the first embodiment of the claimed method of authenticating EI using setting the secret initial boundaries of the intervals of encoding and decoding, a reduction in the difference in the length of the coded with providing authentication of EI is achieved compared with the length of the coded without ensuring authentication of EI.

The differences of the second variant of the authentication method of EI from the first variant of the method are to set the secret initial probabilities of encoded and decoded zero and single characters in accordance with a pre-formed DP SC.

An algorithm for generating authenticated EI when setting secret initial probabilities of encoded zero and single characters is shown in FIG. fifteen.

Ways to set the sender with secret initial probabilities of encoded zero and single characters are as follows. Set the initial number of encoded null characters N ₀ [0] and the initial number of encoded unit characters N ₁ [0] in accordance with a pre-formed binary sequence SK. For this, for example, the first and second binary subsequences of 9 bits in length, each from the right-handed bits, are sequentially read from the DP DC. The read first and second binary subsequences are converted to the first and second decimal numbers, respectively, considering, for example, their left characters as the most significant. The initial number of encoded null characters N ₀ [0] is set equal to the first decimal number, and the initial number of encoded single characters N ₁ [0] is set equal to the second decimal number.

, а секретное начальное значение вероятности кодируемых единичных символов p₁[0] вычисляют по формуле вида $$p_1[0]=\frac{N_1[0]}{N[0]}$$

, где N[0] - начальное число закодированных нулевых и единичных символов, равное N[0]=N₀[0]+N₁[0]=600+250=850. Например, как показано на фиг. 16, секретное начальное значение вероятности кодируемых нулевых символов равно $$p_0[0]=\frac{N_0[0]}{N[0]}=\frac{600}{850}$$

, а секретное начальное значение вероятности кодируемых единичных символов равно $$p_1[0]=\frac{N_1[0]}{N[0]}=\frac{200}{850}$$

.For example, the first nine binary characters of the preformed binary sequence of SK of the form “1001011000”, which is the decimal number 600, are used to set the initial number of encoded zero characters N ₀ [0] to the decimal number 600, and the second 9 binary characters of the preformed binary sequence SK of the form "011111010", which is a decimal number 250, is used to set the initial number of encoded single characters N ₁ [0] equal to the decimal number 250. In this case, the secret began The probability value of encoded null characters p ₀ [0] is calculated by a formula of the form $$p_0[0]=\frac{N_0[0]}{N[0]}$$

, and the secret initial probability value of encoded single characters p ₁ [0] is calculated by the formula of the form $$p_{\mathrm{one}}[0]=\frac{N_{\mathrm{one}}[0]}{N[0]}$$

where N [0] is the initial number of encoded zero and unit characters equal to N [0] = N ₀ [0] + N ₁ [0] = 600 + 250 = 850. For example, as shown in FIG. 16, the secret initial probability value of the encoded null characters is $$p_0[0]=\frac{N_0[0]}{N[0]}=\frac{600}{850}$$

, and the secret initial probability value of encoded single characters is $$p_{\mathrm{one}}[0]=\frac{N_{\mathrm{one}}[0]}{N[0]}=\frac{200}{850}$$

.

, а начальную длину подинтервала единичных символов D₁[0] определяют по формуле вида D₁[0]=I[0]-D₀[0]=65535-46259=19276. Например, на фиг. 17, для t=0, при установленных секретных начальных значениях вероятностей кодируемых нулевых и единичных символов начальное значение Q, численно равное длине начального подинтервала нулевых символов D₀[0], составило десятичное значение 46259 или двоичное значение 1011 0111 1011 0011.The initial value of the coding interval of the arithmetic encoder I [0], equal to I [0] = H [0] -L [0], is divided into the initial values of the sub-interval of zero characters D ₀ [0] and the sub-interval of single characters D ₁ [0], length which are directly proportional to the secret initial probabilities of the encoded zero characters p ₀ [0] and single characters p ₁ [0], respectively. The initial length of the sub-interval of zero characters D ₀ [0] is determined by the formula of the form $$D_0[0]=I[0]\times p_0[0]=65535\times \frac{600}{850}=46259$$

, and the initial length of the sub-interval of single characters D ₁ [0] is determined by the formula of the form D ₁ [0] = I [0] -D ₀ [0] = 65535-46259 = 19276. For example, in FIG. 17, for t = 0, with established secret initial probabilities of encoded zero and single characters, the initial value Q, numerically equal to the length of the initial sub-interval of zero characters D ₀ [0], was the decimal value 46259 or the binary value 1011 0111 1011 0011.

Also, the initial number of encoded null characters N ₀ [0] and the initial number of encoded single characters N ₁ [0] are set in accordance with a pre-formed binary sequence SK and the number of the nth code block. For this, the pre-formed binary sequence of SK and the binary sequence of the number of the nth code block are summed, starting with the least significant binary bits, modulo 2. Then, the previously described actions are performed, setting the initial number of encoded zero characters N ₀ [0] and the initial number of encoded single characters N ₁ [0] in accordance with the received total binary sequence of SK and the binary sequence of the number of the n-th code block.

Encoding the next, from the first to the Lth, UDP KVK of the n-th code block using arithmetic coding in the encoded sequence of the n-th code block when setting the secret initial probability values of the encoded zero and single characters is performed similarly to the previously described first embodiment of the claimed invention. In FIG. 16 shows an exemplary encoding type of UDP DCC of the n-th code block in the form of a binary sequence “011111” with a length of 6 binary symbols using arithmetic coding in the encoded sequences of this block when setting the secret initial probability values of the encoded zero and single characters, and in FIG. 17 is a state table of arithmetic coding of this UDP. The sender is set to the initial state of the boundaries of the coding interval, for example, L [0] = 0 and H [0] = 65535, as shown in FIG. 16. For the given example, the UDP DCC of the nth code block, the encoding result is a binary sequence of the form "10110100". After encoding the last binary symbol of the next ordered binary sequence of the KVK of the n-th code block, the end coding combination of the next UDP in the form of a binary representation of the lower value of the coding interval is read into the coded sequence of the n-th code block. For example, after encoding the first TDC KVK of the n-th code block, the end coding combination of this UDP is of the form “0100 1010 1111 0000”, as shown in FIG. 17, the last line.

The authentication algorithm of the nth received code block when setting secret initial probabilities of decoded zero and single characters is shown in FIG. eighteen.

, а секретное начальное значение вероятности декодируемых единичных символов равно $$p{p}_1[0]=\frac{N{N}_1[0]}{NN[0]}=\frac{200}{850}$$

.The methods for setting the recipient's secret initial probabilities of decoded zero and single characters are identical to the methods for setting the sender's secret initial probabilities of encoded zero and single characters. For example, as shown in FIG. 19, the secret initial probability value of decoded zero characters is $$p{p}_0[0]=\frac{N{N}_0[0]}{NN[0]}=\frac{600}{850}$$

, and the secret initial probability value of decoded unit symbols is $$p{p}_{\mathrm{one}}[0]=\frac{N{N}_{\mathrm{one}}[0]}{NN[0]}=\frac{200}{850}$$

.

Features of sequential decoding using arithmetic decoding of encoded sequences of the nth Ex the code block in accordance with the secret initial probability values of the decoded zero symbol and a single symbol are as follows. The arithmetic decoding input with established secret initial probabilities of the decoded zero symbol and a single symbol receives coded sequences of the nth Pr. code block, for example, KP of the first UDP KVK of the form 1011 0100 0100 1010 1111 0000 with a length of 24 binary symbols formed by arithmetic coding with the set probabilities of the encoded zero symbol and a single symbol. Arithmetic decoding on the read input data input of the first 16 bits of the coded sequences of the form 1011 0100 0100 1010, which corresponds to the decimal number 46154. The current value of the read encoded sequence is compared with the boundaries of the initial value decoding subslot ₀ DD [0] zero symbols from 0 to 46,259 and with the boundaries of the initial value of the decoding interval of the unit symbols DD ₁ [0] from 46259 to 65535. Depending on the limits within which the decoding interval of the symbols was the current value reading the encoded sequence, they decide to decode the next character of the ordered binary sequence of the KVK of the n-th received code block, etc. The state table of arithmetic decoding of encoded sequences of the nth received code block using arithmetic decoding by setting secret initial probabilities of decoded zero and single symbols is shown in FIG. twenty.

If the current decimal value of the input data becomes equal to the lower value of the decoding interval, then decoding the encoded sequence of the next UDP KVK n-th code block is completed. If the current value is greater than the lower value of the decoding interval, then decoding continues. For example, when decoding the sixth character, the current decimal value of the input data becomes equal to the lower value of the decoding interval (value 35166), as shown in FIG. 20 for t = 6. If each of the L calculated length values matches the previously calculated length of the ordered binary sequence of the wavelet coefficients of the code block, then the nth received code block is considered authentic.

To decode all six characters from the KP of the first UDP KVK of the form 1011 0100 0100 1010 1111 0000, the first 22 binary characters were required.

, а начальное значение вероятности декодируемых единичных символов равным $$p{p}_1[0]=\frac{200}{300}$$

, как показано на фиг. 21. На вход такого арифметического декодирования поступают кодированные последовательности n-го Пр. кодового блока, например, КП первой УДП КВК вида 1011 0100 0100 1010 1111 0000 длиной 24 двоичных символа, сформированной арифметическим кодированием с установленными по ДП СК секретными начальными значениями вероятностей кодируемых нулевых и единичных символов. На вход арифметического декодирования считывают входные данные из первых 16 бит данной кодированной последовательности вида 1011 0100 0100 1010, что соответствует десятичному числу 46154. В результате выполнения последовательных операций арифметического декодирования, показанных на фиг. 21, декодируют последовательность вида "1110001…" длиной более 7 двоичных символов, при этом декодирование кодированной последовательности очередной УДП КВК n-го Пр. кодового блока не закончено, так как текущее десятичное значение входных данных не равно нижнему значению интервала декодирования. В результате длина декодированной последовательности очередной УДП КВК n-го Пр. кодового блока не соответствует исходной длине этой кодированной последовательности и в результате значение данной длины не равно предварительно вычисленной длине упорядоченной двоичной последовательности вейвлет коэффициентов кодового блока и этот принятый кодовый блок не будет признан подлинным.The intruder intercepts the transmitted EI, divides it into coded sequences and attempts to decode the encoded sequences of the UDP KVK received blocks of EI. Arithmetic decoding is performed by the intruder in the same way as the receiver, with the exception of setting secret initial probabilities of decoded zero and single characters due to the lack of knowledge of the SC SK. The intruder randomly selects his initial probabilities of decoded zero and single characters, for example, sets the initial probability of decoded zero characters to $$p{p}_0[0]=\frac{\mathrm{one\; hundred}}{300}$$

, and the initial probability value of decoded unit symbols is equal to $$p{p}_{\mathrm{one}}[0]=\frac{200}{300}$$

as shown in FIG. 21. The input of such arithmetic decoding receives encoded sequences of the nth Pr. a code block, for example, the control gear of the first UDP KVK of the form 1011 0100 0100 1010 1111 0000 with a length of 24 binary symbols, formed by arithmetic coding with secret initial values of the probabilities of encoded zero and single characters established by the DC SC. The input from the first 16 bits of this encoded sequence of the form 1011 0100 0100 1010, which corresponds to the decimal number 46154, is read to the arithmetic decoding input. As a result of the sequential arithmetic decoding operations shown in FIG. 21, decode a sequence of the form "1110001 ..." with a length of more than 7 binary characters, while decoding the encoded sequence of the next UDP KVK n-th the code block is not finished, since the current decimal value of the input data is not equal to the lower value of the decoding interval. As a result, the length of the decoded sequence of the next UDP KVK n-th Pr. the code block does not correspond to the original length of this coded sequence and as a result, the value of this length is not equal to the previously calculated length of the ordered binary sequence of the wavelet coefficients of the code block and this received code block will not be recognized as genuine.

Verification of the theoretical premises of the claimed method of authentication EI (second option), using the installation of secret initial probabilities of encoded and decoded zero and single characters, was verified by its analytical studies.

In the second version of the claimed authentication method of EI, using the setting of secret initial probabilities of encoded and decoded zero and single characters, electronic images were encoded, each of which contained N = 15,480 code blocks each with a size of 32 × 32 quantized wavelet coefficients. The quantized wavelet coefficients of each code block were converted into L≤11 ordered binary sequences of quantized wavelet coefficients of the nth code block, which were encoded using arithmetic coding into the encoded sequences of this block. Before encoding the UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding, secret initial values of the probabilities of the encoded and decoded zero and single symbols were set in accordance with a pre-formed 8-bit DC SC. The size of the uncompressed EI and the size of the encoded EI in bytes were calculated. The compression coefficient of EI was also calculated in times by dividing the size of the uncompressed EI by the size of the encoded EI. The coding results of three different EIs in the second embodiment of the claimed EI authentication method using setting secret initial probabilities of encoded and decoded zero and single symbols are shown in the table in FIG. 22. In the prototype method, in order to provide security for attempts by an intruder to substitute authentic authenticated EI for non-authentic EI, the length of the binary CEH sequences of each code block should be at least 32 bits, which causes an increase in the length of the coded with authentication compared with the length of the coded without providing authentication EI . For comparison, the table shows the results of encoding the same EI using arithmetic coding without authentication. It is seen that providing authentication when encoding EI using arithmetic coding leads to an increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication by 7502 ... 7722 bytes, and causes a decrease in the value of the compression coefficient of EI by 0.26 ... 0.64 times. However, when using the prototype method, the increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication is 7920 bytes, which exceeds the achieved values in the second embodiment of the claimed method of authenticating EI, as shown in FIG. 22.

Thus, in the second embodiment of the claimed method of authentication EI, using the setting of secret initial probability values of the encoded and decoded zero and single characters, a reduction in the difference in the length of the encoded with the authentication of EI compared to the length of the encoded without providing authentication of EI is achieved.

The differences of the third variant of the authentication method of EI are in the secret key change of the boundaries of the encoding interval of the arithmetic coding and the decoding interval of the arithmetic decoding for each encoded and decoded bit.

The algorithm for generating authenticated EI when changing the secret key of the boundaries of the coding interval of the arithmetic coding for each encoded bit is shown in FIG. 23.

The sender before encoding the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding changes the boundaries of the coding interval of the arithmetic coding in accordance with the previously generated DP SK. For this, before encoding the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding, the boundaries of the coding interval of the arithmetic coding are changed in accordance with the next bit of the secret key. For example, with a single value of the next bit of the secret key, the upper limit of the arithmetic coding encoding interval H is reduced by a unit value, and at a value of the next bit of the secret key, the lower boundary of the arithmetic coding encoding interval L. is increased by a unit value.

An exemplary coding shown in FIG. 4 (e) of the first UDP DCC of the nth code block in the form of a binary sequence "011111" with a length of 6 binary symbols using arithmetic coding into coded sequences of the nth code block with changing the boundary of the coding interval of the arithmetic coding before encoding the next bit in accordance with the preliminary the formed DP SC is shown in FIG. 24. Let a binary sequence of a secret key of the form “010010” of the same length be used to encode this binary sequence of 6 binary characters in length. Before encoding the first bit of this UDP in accordance with equal initial probabilities of the encoded null characters p ₀ [0] and unit characters p ₁ [0], the initial upper H [0] = 65535 and lower L [0] = 0 values of the encoding interval are set arithmetic coding and the value Q = 32767 ,, as shown in FIG. 25 at t = 0. The first bit of the private key has a zero value, therefore, the lower boundary of the coding interval of the arithmetic coding L is increased by a unit value, therefore, L [0] = 1. Taking into account the effect of the first bit of the secret key, the state of arithmetic coding is specified, that is, when the boundaries of the coding interval are changed, the Q value is calculated, as shown in the second row of the table in FIG. 25.

Before encoding the second bit of this UDP, the second bit of the secret key has a single value, therefore, the current value of the upper boundary of the encoding interval H [1] = 65534 is reduced by a single value and the value of the upper boundary of the interval becomes equal to H [1] = 65533, etc.

The result of encoding this UDP KVK of the nth code block in the form of a binary sequence "011111" with a length of 6 binary symbols is a binary sequence of the form "01111" with an end coding combination of "0011 1100 1100 1100", as shown in FIG. 25, the last line.

The authentication algorithm of the nth received code block when changing the key of the boundaries of the decoding interval of the arithmetic decoding for each decoded bit is shown in FIG. 26.

Before decoding the next bit of the next encoded sequence of the n-th received code block, the receiver uses the arithmetic decoding to change the boundaries of the decoding interval of the arithmetic decoding in accordance with the previously generated DP SK.

For this, before decoding the next bit of the next encoded sequence of the nth received code block using arithmetic decoding, the boundaries of the decoding interval of the arithmetic decoding are changed in accordance with the next bit of the secret key. For example, at a single value of the next bit of the secret key, the upper limit of the arithmetic decoding decoding interval HH is reduced by a unit value, and at a value of the next bit of the secret key, the lower boundary of the arithmetic decoding decoding interval LL is increased by a unit value.

For example, the input of an arithmetic decoding receives the encoded sequence of the first UDP KVK of the form 0111 1001 1110 0110 0110 0 with a length of 21 binary symbols formed by arithmetic encoding with a change in the key of the boundaries of the encoding interval of the arithmetic encoding for each encoded bit. For arithmetic decoding, the binary secret key sequence “010010” is used, the same type as for arithmetic encoding.

An exemplary arithmetic decoding of the indicated encoded sequence with changing the boundary of the arithmetic decoding decoding interval before decoding the next bit in accordance with the pre-formed DP SC is shown in FIG. 27. The input data from the first 16 bits of the specified encoded sequence of the form 0111 1001 1110 0110, which corresponds to the decimal number 31206, is read to the arithmetic decoding input. Before decoding the first bit of this CP in accordance with equal initial probabilities of decoded zero characters pp ₀ [0] and single characters pp ₁ [0], set the initial upper HH [0] = 65535 and lower LL [0] = 0 values of the decoding interval of the arithmetic decoding and the value QQ = 32767, as shown in FIG. 28 at t = 0. The first bit of the secret key has a value of zero, so the lower limit of the arithmetic decoding decoding interval LL is increased by a single value, therefore LL [0] = 1. Taking into account the effect of the first bit of the secret key, the state of arithmetic decoding is specified, that is, when the boundaries of the decoding interval are changed, the QQ value is calculated, as shown on the second line of FIG. 28.

The current value of the read encoded sequence indicated in FIG. 27 by an arrow, compare with the current boundaries of the decoding subinterval interval DD ₀ [0] from 1 to 32767 and with the current boundaries of the decoding subinterval interval DD ₁ [0] from 32767 to 65535. Since the current value of the read encoded sequence lies within the current boundaries of the subinterval decoding of null characters, it is decided to decode the first character, which is a null character, etc.

Decoding the next encoded sequence UDP UDP KVK n-th the code block is terminated when the current decimal value of the input data numerically matches the lower value of the decoding interval. For example, when decoding the sixth character, the current decimal value of the input data becomes equal to the lower value of the decoding interval (value 40550), as shown in FIG. 28 at t = 6. As a result, from the KP of the first UDP KVK n-th Pr. 6 symbols are decoded in the code block, which coincides in length with the previously calculated length of the ordered binary sequence of wavelet coefficients of the code block. If each of the L calculated length values matches the previously calculated length of the ordered binary sequence of the wavelet coefficients of the code block, then the nth received code block is considered authentic.

The intruder intercepts the transmitted EI, divides it into coded sequences and attempts to decode the encoded sequences of the UDP KVK received blocks of EI. The violator performs the arithmetic decoding in the same way as the recipient, except for the correct change of the boundaries of the decoding interval of the arithmetic decoding before decoding the next bit due to the ignorance of the secret key. Let the intruder try to decode the intercepted EI without changing the key of the boundaries of the decoding interval of the arithmetic decoding for each decoded bit. For example, the input of such arithmetic decoding receives the encoded sequence of the first UDP KVK of the form 0111 1001 1110 0110 0110 0 with a length of 21 binary symbols formed by arithmetic encoding with a change in the key of the boundaries of the encoding interval of the arithmetic encoding for each encoded bit, as shown in FIG. 29. As a result of sequential arithmetic decoding operations shown in FIG. 29, decode a sequence of the form "0111101 ..." with a length of more than 7 binary characters, while decoding the encoded sequence of the next UDP KVK n-th the code block is not finished, because the current decimal value of the input data is not equal to the lower value of the decoding interval. As a result, the length of the decoded sequence of the next UDP KVK n-th Pr. the code block does not coincide in length with the pre-calculated length of the ordered binary sequence of wavelet coefficients of the code block and this code block will not be recognized as genuine.

Checking the theoretical background of the claimed method of authentication EI (third option), using a secret key to change the boundaries of the encoding interval of the arithmetic encoding and the decoding interval of the arithmetic decoding for each encoded and decoded bits, was checked by its analytical studies.

In the third version of the claimed method of authentication EI, using a secret key to change the boundaries of the encoding interval of the arithmetic coding and the decoding interval of the arithmetic decoding for each encoded and decoded bits, the encoding of the same electronic images was performed under the same conditions as for the first two versions of the claimed authentication method EI. The coding results of three different EIs in the third embodiment of the claimed method for authenticating EIs when changing the boundaries of the coding interval of the arithmetic coding by ± 1 and ± 2 are shown in the table in FIG. 30. It is seen that providing authentication when encoding EI using arithmetic coding when changing the boundaries of the encoding interval of the arithmetic coding by ± 1 and ± 2 leads to an increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication by 2708 ... 3812 bytes and by 4341 ... 4453 bytes, which is significantly less than the increase in the length of the encoded EI when using the prototype method of 7920 bytes.

Thus, in the third embodiment of the claimed method for authenticating an EI using a secret key of the boundaries of the encoding interval of the arithmetic coding and the decoding interval of the arithmetic decoding for each encoded and decoded bits, the difference in the length of the encoded one is ensured with the authentication of the EI compared to the length of the encoded one without the authentication of the EI .

The differences of the fourth variant of the authentication method of EI are in changing the probability values of the encoded and decoded zero and single characters for each encoded and decoded bits in accordance with a pre-formed DP SK.

An algorithm for generating an authenticated EI when changing the probability values of encoded zero and single symbols for each encoded bit with a secret key is shown in FIG. 31.

After the coding of the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using the arithmetic coding, the sender increases the probability of the coded zero characters after the next zero bit is encoded, otherwise the probability of the coded single characters increases, otherwise, with a single the value of the next bit of the preformed DP SC reduces the probability of encoded zero characters after the encoded Ania next zero bit, or reduce the likelihood of the encoded single character. For this, before encoding the next bit of the next UDP of the quantized wavelet coefficients of the nth code block using arithmetic coding, the probability of the encoded symbols is changed in accordance with the next bit of the secret key.

For example, at the next value of the next bit of the secret key, after encoding the next zero bit, the number of encoded zero characters N _{0 is} increased by a unit value, and after the encoding of the next unit bit, the number of encoded unit characters N _{1 is} increased by a unit value. Accordingly, with the unit value of the next bit of the secret key after encoding the next zero bit, the number of encoded zero characters N _{0 is} reduced by a unit value, and after the encoding of the next unit bit, the number of encoded unit characters N _{1 is} reduced by a unit value.

An exemplary coding shown in FIG. 4 (e) of the first UDP DCC of the nth code block in the form of a binary sequence "011111" with a length of 6 binary symbols using arithmetic coding into the coded sequence of the nth code block with the secret key changing the probability values of the encoded zero and single characters for each encoded the bit is shown in FIG. 32. Let us use a binary sequence of a secret key of the form "11001" with a length of 5 binary characters to encode this binary sequence of 6 binary characters in length. The initial number of encoded null characters N ₀ [0] is set equal to N ₀ [0] = 1, and the initial number of encoded single characters N ₁ [0] is set to N ₁ [0] = 1. Before encoding the first bit of this UDP in accordance with equal initial probabilities of the encoded null characters p ₀ [0] and unit characters p ₁ [0], the initial upper H [0] = 65535 and lower L [0] = 0 values of the encoding interval are set arithmetic coding and a value of Q = 32767, as shown in FIG. 33 at t = 0. After encoding the zero first bit of this UDP, the probabilities of the encoded null characters p ₀ [0] and single characters take the values p ₀ [0] = 2/3 and p ₁ [0] = 1/3, respectively. Since the first bit of the secret key has a single value, after encoding the zero first bit of this UDP, the number of encoded zero characters N _{0 is} reduced by a single value, that is, it becomes equal to N ₀ = 1 and the probabilities of the encoded zero characters p ₀ [0] and unit symbols take the values p ₀ [0] = 1/2 and p ₁ [0] = 1/2, as shown in FIG. 32 at t = 1. The arithmetic coding of the next bits of the next UDP of the quantized wavelet coefficients of the nth code block does not differ from the arithmetic coding method described in the prototype method.

For example, after encoding the third bit of the next UDP TAC of the n-th code block having a unit value, in accordance with the zero value of the third bit of the secret key, the number of encoded unit characters N ₁ is increased by a unit value, etc.

The result of encoding the first UDP KVK of the nth code block in the form of a binary sequence "011111" using arithmetic coding into the encoded sequence of the nth code block with the secret key changing the probability values of the encoded zero and single characters for each encoded bit is a binary sequence of the form " 011 "with the end coding combination" 0111 1010 1010 0011 ", as shown in FIG. 32.

The authentication algorithm of the nth received code block when the secret key changes the probability values of the decoded zero and one symbols for each decoded bit is shown in FIG. 34.

After decoding the next bit of the next coded sequence of the nth received code block using the arithmetic decoding, the receiver increases the probability of decoded zero characters after decoding the next zero bit, otherwise the probability of decoded single characters increases, and at a single value the next bit of the pre-formed DP SC reduce the probability of decoded zero characters s after decoding the next zero bit, otherwise reduce the probability of decoded single characters.

For this, after decoding the next bit of the next encoded sequence of the n-th received code block using arithmetic decoding, the probability value of the decoded symbols is changed in accordance with the next bit of the secret key. For example, if the next bit of the secret key is zero, after decoding the next zero bit, the number of decoded zero characters NN _{0 is} increased by a unit value, and after decoding the next single bit, the number of decoded unit characters NN _{1 is} increased by a unit value. Accordingly, at a single value of the next bit of the secret key after decoding the next zero bit, the number of decoded zero characters NN _{0 is} reduced by a unit value, and after decoding of the next single bit, the number of decoded unit characters NN _{1 is} reduced by a unit value.

For example, an arithmetic decoding input receives a coded sequence of the form 0110 1111 0101 0100 011 with a length of 19 binary symbols formed by arithmetic coding with a secret key changing the probability values of the encoded zero and one characters for each encoded bit. For arithmetic decoding, the binary secret key sequence "11001" is used in the same form as for arithmetic encoding.

An exemplary arithmetic decoding of the indicated encoded sequence with the secret key changing the probability values of the decoded zero and one symbols for each decoded bit is shown in FIG. 35. The input data from the first 16 bits of the specified encoded sequence of the form 0110 1111 0101 0100 is read to the arithmetic decoding input, which corresponds to the decimal number 28500. Before decoding the first bit of this CP in accordance with equal initial probabilities of the decoded zero characters pp ₀ [0] and single characters pp ₁ [0] set the initial upper HH [0] = 65535 and lower LL [0] = 0 values of the decoding interval of the arithmetic decoding and the value QQ = 32767, as shown in FIG. 36 at t = 0.

As a result of decoding the first bit of the specified coded sequence and subsequent normalization, the lower and upper boundaries of the decoding interval of the arithmetic decoding acquire the values LL [1] = 0 and HH [1] = 65534, respectively. Since the first decoded bit has a zero value, the probabilities of the decoded zero characters and single characters take the values pp ₀ [0] = 2/3 and pp ₁ [0] = 1/3, respectively. Since the first bit of the secret key has a unit value, after decoding the zero first bit of this UDP, the number of decoded zero characters NN _{0 is} reduced by a unit value, that is, it becomes equal to NN ₀ = 1 and the probabilities of decoded zero characters and unit characters take values pp ₀ [0] = 1/2 and pp ₁ [0] = 1/2, as shown in FIG. 36 at t = 1. The arithmetic decoding of the next bits of the next CP of the n-th received code block does not differ from the arithmetic decoding method described in the prototype method.

For example, after decoding the third bit of the next CP of the n-th received code block having a unit value, in accordance with the zero value of the third bit of the secret key, the number of decoded unit characters N ₁ is increased by a unit value, etc.

Decoding the next coded sequence of the nth Ave the code block is terminated when the current decimal value of the input data numerically matches the lower value of the decoding interval. For example, as a result of decoding the sixth bit, the current decimal value of the input data 31395 numerically coincides with the lower value of the decoding interval, as shown in FIG. 36 at t = 6, and on this decoding the given encoded sequence of the nth Ex code block finish.

The intruder intercepts the transmitted EI, splits it into encoded sequences and attempts to decode the encoded sequences of the received code blocks. Arithmetic decoding is performed by the intruder in the same way as the receiver, except for the correct key change of the probability values of the decoded zero and single characters for each decoded bit due to the ignorance of the secret key. Let the intruder try to decode the intercepted EI with a change in the probability of the decoded zero and one characters for each decoded bit over the intruder’s key, while the intruder’s key is different from the secret key. For example, the intruder key looks like "001 ...".

At the input of arithmetic decoding, the intruder receives the first encoded sequence of the nth Pr. a code block of the form 0110 1111 0101 0100 011, 19 binary characters long, formed by arithmetic coding with a secret key changing the probability values of the encoded zero and single characters for each encoded bit. As a result of the intruder performing the sequential arithmetic decoding operations shown in FIG. 37, using all the input bits, the intruder decodes a sequence of the form “0101 ...” with a length of 4 binary symbols or more, while decoding the next encoded sequence of the nth Pr. the code block is not completed, since the current decimal value of the input data 31395 is not equal to the lower value of the decoding interval 16378. As a result, the length of this decoded sequence of the nth Ex the code block is not equal to the pre-calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and the nth received code block is considered non-authentic.

Verification of the theoretical premises of the claimed method of authentication EI (fourth option), using a secret key to change the probability values of the encoded and decoded zero and single characters for each encoded and decoded bits, was checked by its analytical studies.

In the fourth embodiment of the claimed authentication method of EI, using a secret key change of the probability values of the encoded and decoded zero and single characters for each encoded and decoded bits, the encoding of the same electronic images was performed under the same conditions as for the first two variants of the claimed method Authentication EI. The coding results of three different EIs in the fourth embodiment of the claimed EI authentication method are shown in the table in FIG. 38. It is seen that providing authentication when encoding EI using arithmetic coding leads to an increase in the length of the encoded EI compared to the length of the encoded EI without providing authentication by 3033 ... 4278 bytes, which is significantly less than the increase in the length of the encoded EI when using the prototype method of 7920 byte.

Thus, in the fourth embodiment of the claimed authentication method of EI using a secret key change of the probability values of the encoded and decoded zero and single symbols for each encoded and decoded bit, a reduction in the difference in the length of the encoded with the provision of authentication of EI compared to the length of the coded without providing authentication of EI is achieved.

The studies confirm that when using the proposed options for the authentication method EI provides a decrease in the difference in the length of the coded with the authentication of EI compared to the length of the coded without providing authentication of EI.

Claims (8)

1. The method of authentication of an electronic image, which consists in the fact that a binary secret key sequence is formed for the sender and recipient, the sender performs wavelet transform on the electronic image, the resulting wavelet transform coefficients are quantized and divided into N≥2 code blocks of quantized wavelet coefficients each size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, the code block of quantized wavelet koe coefficients are converted into binary sequences of quantized wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, ordered binary sequences of quantized wavelet coefficients of the nth code block are encoded using arithmetic coding to encoded sequences of this block, at the end of arithmetic coding of ordered binary sequences of quantized wave the coefficients of the nth code block enter into the binary sequence of the coded electronic image the code block dividing marker is written, and the authentication steps from the sender of the code blocks are repeated until their receipt is completed, the encoded electronic image is transmitted to the recipient, where the authenticity of the electronic image received by the recipient is verified, for which they are divided binary sequence of the electronic image received by the recipient into binary sequences of its received blocks using the dividing marker of each code block, which are divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding in L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat actions to verify the authenticity of the received code blocks before completion of their reception, the received electronic image is considered genuine, e if N received code blocks turn out to be authentic, characterized in that the length of the ordered binary sequence of quantized wavelet coefficients of the code block is calculated for the sender and receiver, the sender sets the secret initial values before encoding the ordered binary sequences of quantized wavelet coefficients of the nth code block using arithmetic coding arithmetic coding interval limits in accordance with previously c formed by the binary secret key sequence, the recipient before decoding the encoded sequences of the nth received code block using arithmetic decoding sets the secret initial boundaries of the decoding interval of the arithmetic decoding in accordance with the pre-generated binary secret key sequence, and after decoding the ordered binary sequences of quantized wavelet coefficients n received code block by read the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block and compare the calculated values of this length values with the previously calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match for each of the L calculated values of length, the nth received code block is considered authentic. 2. The method according to p. 1, characterized in that the sender sets the secret initial boundaries of the encoding interval of the arithmetic coding in accordance with a pre-formed binary sequence of the secret key and the number of the nth code block, and the recipient sets the secret initial boundaries of the decoding interval of the arithmetic decoding in accordance with a pre-formed binary sequence of the secret key and the number of the n-th received code block. 3. A method of authenticating an electronic image, which consists of generating a binary secret key sequence for the sender and recipient, performing the wavelet transform on the electronic image, the resulting wavelet transform coefficients are quantized and divided into N≥2 code blocks of quantized wavelet coefficients each size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, the code block of quantized wavelet koe coefficients are converted into binary sequences of quantized wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, ordered binary sequences of quantized wavelet coefficients of the nth code block are encoded using arithmetic coding to encoded sequences of this block, at the end of arithmetic coding of ordered binary sequences of quantized wave the coefficients of the nth code block enter into the binary sequence of the coded electronic image the code block dividing marker is written, and the authentication steps from the sender of the code blocks are repeated until their receipt is completed, the encoded electronic image is transmitted to the recipient, where the authenticity of the electronic image received by the recipient is verified, for which they are divided binary sequence of the electronic image received by the recipient into binary sequences of its received locks using the separation marker of each code block, which is divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding in L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat actions to verify the authenticity of the received code blocks before the completion of their reception, the received electronic image is considered authentic, eu whether N received code blocks are genuine, characterized in that the length of the ordered binary sequence of quantized wavelet coefficients of the code block is calculated for the sender and receiver, the sender sets the secret initial values before encoding the ordered binary sequences of quantized wavelet coefficients of the nth code block using arithmetic coding probabilities of encoded null characters and single characters in accordance with With a randomly generated binary secret key sequence, the recipient, before decoding the encoded sequences of the nth received code block using arithmetic decoding, sets the secret initial probabilities of the decodable zero characters and unit characters in accordance with the preformed binary sequence of the secret key, and after decoding the ordered binary sequences quantized wavelet coefficients of the nth adopted of the code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length values are compared with the previously calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they coincide, for each of the L calculated values of length, the nth accepted The code block is considered genuine. 4. The method according to p. 3, characterized in that the sender sets the secret initial probability values of the encoded zero characters and single characters in accordance with a pre-formed binary sequence of the secret key and the number of the nth code block, and the recipient sets the secret initial probability values decoded null characters and single characters in accordance with a pre-formed binary sequence of the secret key and the number of the n-th received code block but. 5. The method of authentication of an electronic image, which consists in the fact that the binary sequence of the secret key is formed for the sender and recipient, the sender performs wavelet transform on the electronic image, the resulting wavelet transform coefficients are quantized and divided into N≥2 code blocks of quantized wavelet coefficients each size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, the code block of quantized wavelet koe coefficients are converted into binary sequences of quantized wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, ordered binary sequences of quantized wavelet coefficients of the nth code block are encoded using arithmetic coding to encoded sequences of this block, at the end of arithmetic coding of ordered binary sequences of quantized wave the coefficients of the nth code block enter into the binary sequence of the coded electronic image the code block dividing marker is written, and the authentication steps from the sender of the code blocks are repeated until their receipt is completed, the encoded electronic image is transmitted to the recipient, where the authenticity of the electronic image received by the recipient is verified, for which they are divided binary sequence of the electronic image received by the recipient into binary sequences of its received locks using the separation marker of each code block, which is divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding in L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat actions to verify the authenticity of the received code blocks before the completion of their reception, the received electronic image is considered authentic, eu whether N received code blocks turn out to be authentic, characterized in that the length of the ordered binary sequence of quantized wavelet coefficients of the code block is calculated for the sender and receiver before the sender before encoding the next bit of the next ordered binary sequence of quantized wavelet coefficients of the mth code block using arithmetic coding change the boundaries of the coding interval of the arithmetic coding in accordance with pre sf Before decoding the next bit of the next encoded sequence of the nth received code block using the arithmetic decoding, the recipient changes the boundaries of the decoding interval of the arithmetic decoding in accordance with the preformed binary sequence of the secret key, and after decoding the ordered binary sequences of quantized wavelet coefficients n-th received code block subs the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of these lengths are compared with the previously calculated length of the ordered binary sequence of quantized wavelet coefficients of the code block, and if they match for each of the L calculated values of length, the nth received code block is considered authentic. 6. The method according to claim 5, characterized in that the sender, before encoding the next bit of the next ordered binary sequence of wavelet coefficients of the nth code block using arithmetic coding, changes the boundaries of the coding interval of the arithmetic coding in accordance with the previously generated binary secret key sequence and number nth code block, and the receiver before decoding the next bit from the next encoded sequence of the nth received codes th block arithmetic decoding using decoding interval boundaries change arithmetic decoding in accordance with a predetermined binary sequence generated secret key number and n-th received code block. 7. A method of authenticating an electronic image, which consists of generating a binary sequence of a secret key for the sender and recipient, performing the wavelet transform on the electronic image, the resulting wavelet transform coefficients are quantized and divided into N≥2 code blocks of quantized wavelet coefficients each size n ₁ × n ₂ coefficients where n ₁ ≥2 ≥2 and n _2, the quantized wavelet coefficients of the n-th, where n = 1, 2, ..., N, the code block of quantized wavelet koe coefficients are converted into binary sequences of quantized wavelet coefficients of the nth code block, which are converted into L≥2 ordered binary sequences of quantized wavelet coefficients of the nth code block, ordered binary sequences of quantized wavelet coefficients of the nth code block are encoded using arithmetic coding to encoded sequences of this block, at the end of arithmetic coding of ordered binary sequences of quantized wave the coefficients of the nth code block enter into the binary sequence of the coded electronic image the code block dividing marker is written, and the authentication steps from the sender of the code blocks are repeated until their receipt is completed, the encoded electronic image is transmitted to the recipient, where the authenticity of the electronic image received by the recipient is verified, for which they are divided binary sequence of the electronic image received by the recipient into binary sequences of its received locks using the separation marker of each code block, which is divided into coded sequences of the nth received code block, decode the encoded sequences of the nth received code block using arithmetic decoding in L ordered binary sequences of quantized wavelet coefficients of the nth received code block, repeat actions to verify the authenticity of the received code blocks before the completion of their reception, the received electronic image is considered authentic, eu whether N received code blocks turn out to be authentic, characterized in that the length of the ordered binary sequence of quantized wavelet coefficients of the code block is calculated for the sender and receiver, after the coding of the next bit of the next ordered binary sequence of quantized wavelet coefficients of the nth code block using arithmetic coding when the next bit of the preformed binary sequence is secret, zero of the key increases the probability of encoded null characters after encoding the next null bit, otherwise it increases the likelihood of encoded single characters, and with a single value of the next bit of a preformed binary sequence of the secret key, they reduce the likelihood of encoded null characters after encoding the next null bit, otherwise they reduce the likelihood of encoded single characters, after decoding the next bit of the next encoded sequence n-g the received code block using arithmetic decoding at zero value of the next bit of the preformed binary sequence of the secret key increases the probability of decoded zero characters after decoding the next zero bit, otherwise the probability of decoded single characters increases, and at a single value of the next bit of the preformed binary sequence of the secret key, the probability decoded null characters after deco of the next zero bit, otherwise the probability of decoded single symbols is reduced, and after decoding the ordered binary sequences of quantized wavelet coefficients of the n-th received code block, the length of each decoded ordered binary sequence of quantized wavelet coefficients of this block is calculated and the calculated values of this length are compared with the previously calculated length ordered binary sequence of quantized wavelet code coefficients block, and if they coincide, for each of the L calculated lengths, the nth received code block is considered authentic. 8. The method according to claim 7, characterized in that the sender, before encoding the next bit of the next ordered binary sequence, the wavelet coefficients of the nth code block using arithmetic coding, change the probability of the encoded symbols in accordance with the value of the next bit of the pre-formed binary sequence of the secret key and numbers of the nth code block, and the receiver before decoding the next bit from the next encoded sequence of the nth received code of the th block using arithmetic decoding, the probability of the decoded symbols is changed in accordance with the value of the next bit of the preformed binary sequence of the secret key and the number of the nth received code block.

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