RU2239290C2 - Data stream encryption method - Google Patents

Abstract

FIELD: electrical communications and computer engineering; cryptographic conversion.

SUBSTANCE: proposed method includes generation of encryption key in the form of binary vector; delivery of the latter for initial filling of feedback shift register shaping pseudorandom sequence of binary characters; conversion of data stream into encrypted message, and its transfer over communication line; novelty is that pseudorandom sequence of binary characters is shaped as pseudorandom sequence postamble Fp with characteristic of p = 257 in the form of eight-bit vectors by reading information off eight different places of shift register whose numbers are found by value of encryption key being entered, while skipping time steps of shift register where at least one of generated pseudorandom sequence characters of postamble Fp includes character "0"; data stream is converted into encrypted message by dividing source data stream into blocks in the form of eight-bit binary vectors, and blocks are alternately converted into binary vector using pseudorandom sequence characters of postamble Fp in compliance with chosen linear or nonlinear cryptographic conversions including character addition, multiplication, and exponentiation in preamble Fp.

EFFECT: enhanced attack stability of logical number based on known and selected source texts.

1 cl, 2 dwg

Description

The invention relates to the field of telecommunications and computing, and more particularly to the field of methods and devices for cryptographic data conversion.

In the aggregate of the features of the proposed method, the following terms are used:

the secret key (or password) is a combination of bits known only to a legitimate user;

encryption key - decryption (cipher key) is a combination of bits used in encrypting information signals; the cipher key is a removable cipher element and is used to convert a given message or a given set of messages; the cipher key is known only to the legitimate user or can be generated by deterministic password procedures;

a cipher is a set of elementary steps for converting input data using a cipher key; the cipher can be implemented as a computer program or as a separate device;

encryption is the process of cryptographic data conversion using a cryptographic key, translating data into a cryptogram, which is a pseudorandom sequence of characters from which obtaining information without knowing the key is practically impossible;

decryption is the opposite of encryption; decryption provides recovery of information from the cryptogram with knowledge of the cipher key;

a binary vector is a signal in the form of a sequence of zero and unit characters, corresponding to the representation of a number in the binary system.

Known methods for stream encryption of data (see, for example, the Russian standard encryption standard USSR ROST 28147-89 [1], the British algorithm B-Grypt, the US Standard DES, the Japanese data encryption algorithm FEAL [2] p. 48-52, as well patent of the Russian Federation for the invention No. 2106752, CL H 04 L 9/00).

In known methods, data encryption is carried out by generating an encryption key, generating a pseudo-random sequence of binary characters and block-wise conversion of the data stream, including modulo two symbol addition operations with symbol substitution and symbol permutation operations in the data blocks.

However, the known analogue methods of stream encryption of data have a small speed, since up to 32 rounds of mixing and scattering of characters in blocks are used to ensure the statistical uniformity of the characters of the ciphertext.

The closest in technical essence to the claimed method of streaming data encryption is the method presented in the US standard DES ([1] p. 126-127 and in [3] p. 50-51).

The prototype method includes generating an encryption key in the form of a binary vector with a length of n bits, supplying it for the initial filling of a shift register with feedback, having n bits and generating a pseudo-random sequence of maximum length containing 2 ⁿ -1 binary characters, generating a pseudo-random sequence of characters , transforming the data stream by modulo adding two characters of the source text with characters of the pseudo-random sequence and transmitting the encrypted message along the line communication to another network user.

However, the prototype method has a drawback. Despite the fact that a cipher based on the addition of a pseudo-random bit stream with source text bits modulo 2 is generally theoretically unrecognizable (see [2], p. 128), the cryptosystem itself is not durable and can be disclosed. If the structure of the shift register with n bits is known, then to find the initial state of the shift register, you need to know n characters of the known plaintext, which are added modulo 2 with the corresponding n characters of the ciphertext. The obtained n characters of the pseudo-random sequence determine the state of the shift register at some point in time. By modeling the operation of the shift register in the opposite direction, it is possible to determine its initial state, and therefore the keys used by network users in encrypting-decrypting information.

If the structure of a shift register having n-bits is unknown, then 2 · n characters of known plaintext and 2 · n characters of ciphertext corresponding to them are sufficient to quickly (within a few seconds of computer operation) determine the state of the shift register and calculate the keys (see, for example, [4] p. 93). And this leads not only to a decrease in the resistance of the cipher to attacks based on known and selected source texts, but also to a significant complication of the procedure for generating the encryption-decryption key in the computer network, since the cryptographic keys can be used only once and should be determined by the next communication session -new.

The invention is aimed at increasing the resistance of the cipher to attacks based on well-known and selected source texts.

This is achieved by the fact that in the known method of encrypting a data stream, which consists in generating an encryption key in the form of a binary vector with a length of n bits, supplying it for the initial filling of the shift register with feedback having n bits and generating a pseudorandom sequence of maximum length containing 2 ⁿ -1 characters, forming a pseudo-random sequence of characters, converting the data stream using a pseudo-random sequence of characters into an encrypted message and transmitting it through the communication line according to the invention further form one or more pseudo-random sequences, all pseudo-random sequence is formed as a pseudo-random sequence of finite field symbols F _p to the characteristic of p = 257 in the form of binary vectors of length 8 bits by removing information from eight different register bits shift and replacing the characters "0" with the characters "256", divide the data stream into blocks in the form of binary vectors 8 bits long and alternately transform the blocks using pseudo random ynyh sequences of symbols of a finite field, as well as linear or nonlinear cryptographic transformations, including operations of addition, multiplication or raising a degree of symbols in the finite field F _p.

The listed set of essential features excludes the possibility of defining encryption-decryption keys when using the cryptanalysis method with known plaintext and increases the resistance of the cipher to attacks based on known and selected source texts. In this case, the generated pseudo-random sequences of characters in the form of binary vectors with a length of 8 bits are a pseudo-random sequence of characters {0, 1, 2, ..., 255} of the final field F ₂₅₇ , have the same period N = 2 ⁿ -1 as the pseudo-random sequences of binary numbers and ensure the statistical uniformity of the characters used. When replacing the characters "0" with the characters "256", the formation of pseudo-random sequences of characters of the multiplicative group of the final field F ₂₅₇ {1, 2, ..., 255} is ensured. This allows you to create in the field F _{257 a} variety of functions for encrypting the characters of the source text α, including operations of adding characters modulo p, multiplying the characters modulo p, raising characters to the power modulo p and their various combinations, unlike the field F ₂ , in which to encrypt one binary character of the source text, modulo two addition will be the only way to build a reversible encryption function.

Since several pseudo-random sequences of symbols of the finite field {x, ..., y} can be removed from one shift register, each of which will not be cyclically shifted relative to other pseudorandom sequences, both linear and nonlinear cryptographic transformations can be implemented using several pseudo-random sequences of symbols of the final field F _p to obtain encrypted symbols β of the final field F _p

α x + y≡ β (mod p), α ^x + y≡ β (mod p), α ^x · y = β (mod p), ...,.

Since the symbols of the pseudo-random sequences x and y are elements of the multiplicative group of a finite field F _p , inverse quantities can be calculated

x ^-1 ≡ x ^p-2 (mod p), y ^-1 ≡ y ^p-2 (mod p), ...

and conjugated elements

x * = p-x, y * = p-y, ...

which allow you to implement cryptographic transformations to decrypt ciphertext characters

(β + y *) x ^-1 ≡ α (mod p), (β + y *) x ^-1 ≡ α (mod p),

(β · y ^-1 ) x ^-1 ≡ α (mod p), ...

The choice as the characteristic of the final field of the number p = 257 is due to the fact that modern computers use 256 characters to play multimedia data and the closest prime number to the number 256 is 257.

в то время как для поля F₂, с каких бы точек регистра сдвига не снимали бы информацию, псевдослучайная последовательность двоичных чисел будет лишь циклически сдвинутой относительно других псевдослучайных последовательностей двоичных чисел, снимаемых с других разрядов регистра сдвига.Since the pseudo-random sequences of symbols of the final field F _p are removed from eight bits of the shift register, one symbol of the final field F _{p is} not reproduced, since the maximum number represented by 8 binary digits is 255, so the pseudorandom sequences removed are not pseudorandom sequences of the maximum length in the final field F _p , and represent nonlinear pseudorandom sequences. The total number of possible pseudorandom sequences of characters of the final field will be determined by the number of possible combinations of eight bits of the shift register from which information can be taken, and the number of permutations within one combination, each of which determines the reading order of the information for the shift register consisting of n = 256 bits, the number of different pseudorandom sequences of characters of the final field F ₂₅₇ will be Q = 8!

while for the field F ₂ , from whatever points of the shift register the information would be taken, the pseudo-random sequence of binary numbers will only be cyclically shifted relative to other pseudorandom sequences of binary numbers taken from other bits of the shift register.

Since cryptographic transformations use two or more pseudorandom sequences of characters of the final field F ₂₅₇ , then, if there are any characters of the source and corresponding characters of the ciphertext, the possibility of determining the characters of pseudorandom sequences is excluded, since to determine them the number of equations will always be two times less than the number of unknowns. This ensures the resistance of the cipher to attacks based on known and selected source texts, since the opening of the state of the shift register in this case can be achieved only by total enumeration of the entire set of possible states of the shift register. Since the US standard for DES data encryption uses a shift register that has 128 bits (128 bit key length), the power of the many possible states of the shift register will be 10 ³⁸ . If the opening of the state of the shift register will be carried out using a computer with a clock frequency of 10 GHz, the number of operations performed by this computer during the year will be 3-10 ¹⁹ , and the opening time is 10 ¹⁸ years.

In accordance with the Russian standard GOST28147-89 for a shift register having 256 bits (key length 256 bits), the opening time of the state of the shift register will be 10 ⁵⁷ years.

The possibility of technical implementation of the claimed method of encrypting a data stream is explained as follows. The encryption key can be generated by entering a password from the keyboard or from a magnetic storage medium into a pseudo-random number generator, receiving an encryption key of the required size at the output (see, for example, [5] p. 87-89).

The formation of a pseudo-random sequence of maximum length containing 2 ⁿ -1 characters can be achieved by using a linear shift register with n digits, the feedback of which is determined by the form of the selected primitive polynomial of degree n. Finding primitive polynomials of degree n is described in [4] on pages 74–75.

The formation of pseudorandom sequences of characters of the final field F ₂₅₇ in the form of binary vectors 8 bits long can be accomplished by taking information from eight different bits of the shift register, numbers that can be determined by the value of the entered cipher key K. For example, by determining the generating element

L ₀ = K (mod q), if 1 ₀ <2, then 1 ₀ = 2,

and calculating the number of the discharge register shift according to the formula

1 ₁ = 1 ₀ , l _i ≡ l ₀ l _i-1 (mod q), i =

будут различны. В псевдослучайных последовательностях x и y двоичных векторов осуществляют замену символов "0" на "256".The value of q is selected from primes and for the shift register, which has 256 bits, q = 257, for the shift register, which has 128 bits, q = 127. In this case, by raising to the power of the generating number 1 ₀ we will pass from one element of the field F _q to another. Moreover, as shown in [4] p. 44, if 1 ₀ is an element of order k, then all elements

will be different. In the pseudo-random sequences of x and y binary vectors, the characters "0" are replaced by "256".

The formation of pseudo-random sequences of symbols of the final field F _p can also be carried out as a “compression generator” by taking information from eight bits of the shift register and skipping those clock cycles of the shift register for which at least one of the pseudo-random sequences contains the symbol “0”.

Conversion of the data stream into an encrypted message can be done by breaking the source data into blocks in the form of characters α of binary vectors 8 bits long, calculating in the final field F _p , (p = 257) the values of the characters β of the encrypted text in accordance with the selected encryption function, for example, α X + y = β (mod p), converting the resulting number β to a binary vector and transmitting it over the communication line.

Three more options for the formation of pseudo-random sequences of symbols of the final field in the form of binary vectors can be used.

1. Elements of one of the selected and generated pseudo-random sequences of symbols of the final field y in the form of binary vectors are used as generating elements y _n for an additional pseudo-random sequence z, elements of which at each clock cycle of the shift register are defined as generated elements of the field F _p : z≡ z · y _n (mod p)

If in the process of computing at some i clock cycle of the shift register it turns out that z = 1, then in this case the generating element y _{n of the} field F _p changes. Moreover, as the new generating element y _{n, we} take the element formed at a given cycle of the shift register of the selected pseudorandom sequence y of characters of the final field F _p , y _n = y, if y <2, then y _n = 2. The generated additional pseudorandom sequence of the final field z is used in cryptographic transformations when converting the data stream into an encrypted message, for example:

αx + y + z = β (mod p) or αx + z = β (mod p)

будут различны на интервале k тактов работы регистра сдвига. Поскольку порождающие элементы y_n могут быть разного порядка в конечном поле F_p, то смена порождающих элементов будет осуществляться по псевдослучайному закону. При этом обеспечивается статистическая равномерность символов зашифрованного текста на интервале, равном p-1 тактам работы регистра сдвига, что исключает применение статистических методов криптоанализа для определения состояния регистра сдвига.Since in the additional pseudorandom sequence of the finite field, the elements are formed by raising to the power a generating element y _n of order k, then all elements

will be different on the interval k cycles of the shift register. Since the generating elements y _n can be of different orders in the final field F _p , the change of the generating elements will be carried out according to the pseudo-random law. This ensures the statistical uniformity of the characters of the ciphertext on an interval equal to p-1 clock cycles of the shift register, which eliminates the use of statistical methods of cryptanalysis to determine the state of the shift register.

2. Change the numbers of bits of the shift register, from which information is removed for one of the pseudo-random sequences of characters of the final field in accordance with the change in the generating element of the additional pseudo-random sequence

l ₀ = y _n , l _i = y _n l _i-1 (mod q),

3. Change the reading order of information for one of the generated pseudo-random sequences of characters of the final field in accordance with the change of the striking element, an additional pseudo-random sequence of characters, for example, using the relations

l _i = l _k ,

k≡ i + y _n (mod 8),

The formation of pseudorandom sequences of characters of the final field according to claim 1, 2 and 3 increases the resistance of the cipher to attacks based on known and selected source texts when generating an encryption key of short length.

The proposed method can be implemented using a computer or device. Figure 1 presents the structural diagram of the device, where

block 1 - device for generating an encryption key;

block 2 - shift register;

block 3 - encryption device;

block 4 - transmitting device.

For simplicity, the description of the operation of the device will use small numbers. We assume that the shift register has 6 digits (the key length is 6 bits), and the entire alphabet of the source text contains 16 characters, then a binary vector 4 bits long can be used to transmit one character, and, as a characteristic of the final field, F _p can be the number p = 17 is selected.

To determine the structure of the shift register, choose a primitive polynomial of the sixth degree, for example, λ ⁶ + λ ⁵ +1.

For the selected primitive polynomial, the structural diagram of the feedback shift register will have the form shown in FIG. 2, where blocks 5-10 are bits 1-6 of the shift register, and block 11 is an adder modulo two.

Formed in block 1 of Fig. 1 using a random number generator, an encryption key of 6 bits in length

<λ ₆ , λ ₅ , λ ₄ , λ ₃ , λ ₂ , λ _l >,

where λ _I = 0, λ ₂ = 0, λ ₃ = 0, λ ₄ = 1, λ ₅ = 1, λ ₆ = 1;

enters the shift register and is used to initially fill the bits of the shift register. Binary symbols from the 5th and 6th bits of the shift register arrive at the input of the adder 11 modulo two in each clock cycle, and from the output of the adder modulo two symbols ε go to the input of the first bit of the shift register (block 5, Fig. 2). In this case, the state of the discharges for each cycle during the operation of the shift register is determined by the expression

λ ₁=ελ _I = λ _i-1 for

λ ₁ = ε

and are presented in the table.

If the characters will be removed from the sixth digit λ ₆ of the shift register (block 10, FIG. 2), then the binary pseudorandom sequence of the maximum period will be {1110000010000110001010011110100011100100101101110110011010101111}.

Note that during the period of this sequence, any nonzero set of six characters 0 and 1 occurs only once.

If we take binary numbers from the 1st, 2nd, 3rd and 4th digits of the shift register (blocks 5, 6, 7, 8, Fig. 2) and at each clock cycle of the shift register and with the set <λ ₁ , λ ₂ , λ ₃ , λ ₄ > we map the binary vector (number) x = λ ₁ + 2λ ₂ +2 ² λ $\genfrac{}{}{0ex}{}{}{\text{3}}$ + 2 ³ λ $\genfrac{}{}{0ex}{}{}{\text{4}}$ , then the sequence of binary numbers in the process of register operation can be considered as a sequence of x numbers (characters) {0, 1, 2, ..., 15} in the form

x = {8, 0, 0, 1, 2, 4, 8, 0, 1, 3, 6, 12, 8, 1, 2, 5, 10, 4, 9, 3, 7, 15, 14, 13 , 10, 4, 8, 1, 3, 7, 14, 12, 9, 2, 4, 9, 2, 5, 11, 6, 13, 11, 7, 14, 13, 11, 6, 12, 9 , 3, 6, 13, 10, 5, 10, 5, 11, 7, 15, 15, 15, 14, 12, ...}.

If we take binary numbers simultaneously from the 1st, 2nd, 5th, 6th digit, shift register (blocks 5, 6, 9, 10, Fig. 2) and at each clock cycle of the shift register with the set <λ ₆ , λ ₅ , λ ₂ , λ ₁ > we will compare the number in the form y = λ ₆ + 2λ ₅ +2 ² λ $\genfrac{}{}{0ex}{}{}{\text{2}}$ + 2 ³ λ $\genfrac{}{}{0ex}{}{}{\text{1}}$ , then the sequence of binary numbers in the process of the shift register can be considered as a sequence of characters

y {0, 1, 2, ..., 15} in the form

y = {3, 3, 1, 8, 4, 0, 0, 2, 9, 12, 4, 0, 2, 11, 5, 8, 4, 2, 9, 14, 13, 12, 6, 11 , 7, 3, 1, 10, 13, 12, 4, 2, 11, 7, 1, 8, 6, 9, 12, 6, 9, 14, 15, 5, 10, 15, 7, 1, 10 , 15, 5, 8, 6, 11, 5, 10, 13, 14, 13, 14, 15, 7, 3, ...}.

An analysis of the generated sequences x and y shows that on the interval corresponding to the period equal to 63 clock cycles of the shift register, each of the symbols {1, 2, ..., 15} occurs exactly four times. The symbol corresponding to zero in both sequences occurs exactly three times, while the sequences x and y cannot be obtained from each other as a result of a cyclic shift. In sequences x and y, there are no hidden periodicities and the statistical uniformity of the symbols used is ensured. Since one of the symbols of the pseudorandom sequences of the final field F _{17 is} not reproduced, the symbol "0" in both sequences is replaced by the symbol "16".

In addition to the pseudo-random sequences of symbols x, y of the final field F _p , Table 1 shows the formation of an additional pseudo-random sequence z by using the pseudo-random sequence y as generating elements of the characters, as well as the formation of a pseudo-random sequence of characters of the final field v by changing the reading order of the information for the pseudo-random sequence of characters of the final field x in accordance with the change in the generating element of the additional pseudo-case fine sequence z.

The generated pseudo-random sequences of symbols of the final field x and y in the form of binary vectors are sent to the encryption device 3 (Fig. 1), where the incoming data stream is converted into an encrypted message by using pseudo-random sequences of symbols x and y of the final field F ₁₇ in accordance with the selected cryptographic conversion in the final field F ₁₇ for example

Sources of information

1. Russian encryption standard USSR standard GOST 28147-89 Information processing systems. Cryptographic protection. Cryptographic conversion algorithm.

2. S. Maftik. Protection mechanisms in computer networks, M., 1993

3. V.I. Nechaev. Elements of cryptography. Fundamentals of information security theory. - M.: Higher school, 1999.

4. B.N. Voronkov, V.I. Stupid. Toolkit for the development of information security tools in computer networks. Voronezh: Voronezh State University, 2000.

5. E.F. Bickell, E.M. One by one. Cryptanalysis: A review of the latest results // TIIER, 1988, v. 16, No. 5.

Claims (4)

1. The method of stream encryption of data, which consists in generating an encryption key in the form of a binary vector, supplying a binary vector for the initial filling of the shift register with feedback, forming a pseudo-random sequence of binary characters, converting the data stream into an encrypted message and transmitting it over the communication line, characterized in that pseudo-random sequences of binary symbols are formed as pseudo-random sequences of symbols of the final field Fp with characteristic p = 257 in the form of binary vectors of length 8 bits by taking information from eight different bits of the shift register, the numbers of which are determined by the value of the entered encryption key, and the total number of possible pseudorandom sequences of characters of the final field is determined by the number of possible combinations of eight bits of the shift register from which the information is removed, and the number permutations within the framework of one combination, skip those steps of the shift register in which at least one of the generated pseudorandom sequences of characters of finite I Fp has the character 0, the data stream is converted into an encrypted message by splitting the source data stream into blocks in the form of binary vectors 8 bits long and alternately converting the blocks into a binary vector by using pseudorandom sequences of characters of the final field Fp in accordance with the selected linear or nonlinear cryptographic transformations, including addition, multiplication or exponentiation of symbols in the final field Fp. 2. The method according to claim 1, characterized in that the characters of one of the generated pseudo-random sequences of the final field are used as generating elements to form an additional pseudo-random sequence of characters, which are determined as generated elements of the final field Fp at each shift work step. 3. The method according to claim 2, characterized in that the numbers of the bits of the shift register are changed from which information for one of the generated pseudo-random sequences of symbols of the final field Fp is generated in accordance with the change in the generating element of the additional pseudo-random sequence. 4. The method according to claim 2, characterized in that the order of reading information for one of the generated pseudo-random sequences of characters is changed in accordance with a change in the generating element of the additional pseudo-random sequence.

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