RU2325766C2 - Information protection method - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: said utility invention relates to information storage and transmission protection and may be used at both software and hardware implementation levels in communication systems, computer and information systems for cryptographic protection of text, voice, audio, and video information in the digital form, as well as for the protection of goods against falsification. It is achieved due to the discovery of prime number laws, according to which a sequence containing only prime numbers running is a strictly theoretical unidirectional function of four variables, which made it possible to create a linear algorithm of generation of only prime numbers running, and allowed to transfer the gamma generation at the finite machines into a non-periodic operating mode.

EFFECT: increased reliability.

2 cl, 2 dwg, 1 tbl

Description

The invention relates to the field of protection of storage and transmission of information by publicly available means of communication and can be used both at the software and hardware levels of implementation in communication systems, computing and information systems for cryptographic closure of text, speech, audio and video information in digital form.

Two information security systems are known: symmetric and public key (asymmetric). In practice, they use both systems, the so-called mixed (hybrid) cryptosystems, which are designed to balance the advantages and disadvantages of both systems (1. B. Schneier. Applied cryptography. TRIUMPH publishing house. Moscow. 2002, p. 18-19, 46-48 , 221-261).

In addition, there are two main types of symmetric algorithms for protection in the transmission of information: block ciphers and stream ciphers. Block ciphers have greater reliability, which you have to pay for by reducing the speed of information transfer. Stream ciphers, providing maximum performance, have insufficient reliability due to the fact that the gamma generator (running key generator) produces a stream of bits implemented on a state machine (computer, chip), which determines the gamma repeatability [1]. "Achilles heel" of stream encryption - periodicity due to the lack of rigorous mathematical evidence for the existence or possibility of constructing unidirectional functions [2. G. Brassard, "A Note on the Complexity of Cryptography", IEEE Transactions on Information Theory, v. IT-25, n.2. Mar. 1979, pp. 232-233, 3. J. Grollman and ALSelman, "Complexity Measures for Public-Key Cryptosystems", Proceedings of 25 ^th IEEE Symposium on the Foundations of Computer Science, 1984, pp. 495-503, 4. RPBrent , "Parallel Algorithms for Integer Factorization", Research Report CMA-R49-89, Computer Science Laboratory, The Australian National University, Oct. 1989, 5. S. Even and Y. Yacobi, "Cryptography and NP-Completeness", Proceedings of the 7th International Colloquium on Automata, Languages and Programming, Springer-Veriag, 1980, pp. 195-207, 6. MRGarey and DSJohnson , Computers and Intractability: A Guide to the Theory of NP-Completeness, WH Freeman and Co., 1979].

The disadvantages of all modern information protection and transmission systems are reliability, which is far from theoretically maximum, insufficient speed and problems associated with the great complexity of computing true primes, as well as the need to store, transmit keys to legitimate users and destroy keys.

To protect the transmission of information, the most widely used are block encryption systems DES, GOST 28147-89, Verba-0 and others (US 4232194, Н04К 1/06, 1980), of which Gamma-4, protected by the RU patent, has the best parameters. 2099885, H04K 1/06, 96.

The closest prototype of the claimed invention is a synchronous streaming encryption system [1, p.234-235]. The lack of patents for direct analogues is explained by the low reliability of the protection of stream encryption, taken on the basis of features as an analog.

The aim of the invention is to eliminate the above disadvantages and increase reliability.

The present invention can be used in the following two situations.

1. Encryption of information when entering it into the database.

2. Encryption of information during its transmission over open communication systems.

The goals are achieved by the fact that the function of arithmetic progression K = a · n + b is used as the initial sequence, which meets the requirements of the Dirichlet theorem on the mutual simplicity of the constant terms a and b, which after “decimation” and division by mod (the number of language characters), using the XOR operation, impose on the plaintext after "thinning", where:

- K is a sequence of candidates for simplicity, that is, either a prime or a composite number;

- a - "step" or the difference of arithmetic progression;

- n is a sequence of natural numbers;

- b is a constant.

The operation of “decimation” consists in eliminating compound numbers from the initial sequence of primes and compound numbers distributed within the RAM.

The original sequence K undergoes decimation by distributed exclusion of additive composite numbers, which stops at the moment the feedback signal arrives, due to which the sequence is constantly modified and, due to the random nature of the feedback signal, is deterministically random.

Achieving this goal becomes possible in connection with the discovery of the laws of prime numbers ("Primes Numbers"), according to which a sequence of only prime numbers in a row is a strictly theoretical unidirectional function of four variables, which made it possible to create a linear algorithm for generating only prime numbers in a row and it became possible to create aperiodic gamma generation on a finite state machine.

Improving the reliability of protection, reducing costs, increasing the speed of encoding and / or decoding digital information and improving ease of use (eliminating the need to obtain, know, remember or secretly record secret parameters and use) is achieved by using the linear function K = to generate the original numerical sequence f (n), where K is a sequence of candidates for simplicity, that is, either a prime or a composite number, for example, the arithmetic progression K = 210n + 1 = 211, 421, 631, 841 = 29 * 29, 1051, 1261 = 13 * 97, 1 471, 1681 = 41 * 41, ... to _i . The obtained first sequence is “thinned out” by distributed exclusion of sequences of additive composite numbers in a limited RAM range, which stops at the moment the “recall” signal arrives, due to which the sequence is constantly modified and, due to the random nature of the “recall” signal, is deterministically random . Additive composite numbers are formed by sequential addition to the base of the arithmetic progression of multiple quantities of this base. Such sequences are called spectrally additive sequences, the spectrum of which is given by the "base of the arithmetic sequence" b. Spectrally additive sequences are generated only by the addition operation of its “step” a, due to which a sequence of only composite numbers is formed with the smallest divisor equal to the base of such a sequence, for example, with base 3: C = 3 + 2n · 3 = {3, 9, 15, 21 , 27, 33 ...}. Thus, each addition operation gives a new composite number of one spectrum defined by the base 3: {3 * 3, 3 * 5, 3 * 7, 3 * 3, 3 * 11 ...}. After thinning the initial sequence with spectrally additive sequences without time limitation, a strictly determinate sequence of only primes P would be obtained. However, the duration of the thinning operation is selected by correlating RAM with the clock frequency so that it significantly exceeds the time period between the sync (initialization vector - The recipient’s IP number) and the acceptance of a “feedback” signal that disables the “thinning” operation. For the encryption of very large plaintexts, 2 alternately working RAMs can be used, discrete continuous generation of the original sequence and "thinning" to infinity. The second randomly obtained sequence of many digit numbers A thus obtained is subjected to the bitwise operation of comparing the digits of different numbers of this sequence and eliminating the same digits, after which the twice-deterministic random third sequence of differently digit numbers C is divided by mod (the number of characters of the language of communication) a randomly determined sequence of Ш, which is superimposed on the plaintext by the XOR operation and transmitted to the public communication system, g de it is perceived by the second transponder (dongie), performing XOR operation with encrypted text and synchronously generated by exactly the same three times randomly determined random sequence W, or stored in the user’s long-term memory during offline storage of information. Due to the fact that the identification uses the individual IP-code number (for example, phone number) of the sender, and for the start-up state of the generator, the individual IP-code number (for example, phone number) is used, all problems associated with the manufacture, storage, distribution and occasional key replacement, and the small bit depth of the sequence numbers and the minimum number of simple mathematical operations allows you to transfer protected "one-time tape" information at a speed slightly inferior transmission speed of open information. Thus, there is an objective possibility of generation that does not have a period of one-time encryption tape on finite state machines, which was previously considered an almost impossible task. The discovery of the laws of prime numbers and spectral additive sequences made this task practically feasible.

It is possible to further increase the reliability of protection through the use of a priori agreements (AS) between the recipient and the sender of information by increasing the capacity of the individual number of the sender and / or blocking some divisors and / or changing the "step" (difference of arithmetic progression) of the generator of the original sequence and / or preservation of some identical digits and / or exclusion of some different digits in the process of bitwise comparison of the digits of the members of the "thinned" sequence, which provides the maximum cryptographic reliability to this security system.

Thus, the proposed device provides a sharp reduction in cost and operating costs, and the difficulty of using this system by users is comparable to the skills of using cellular telephone communications.

The device is illustrated by drawings.

Figure 1 presents a block diagram of the invention when entering information into the database.

Figure 2 presents a block diagram of the encryption of information during its transmission over open communication systems.

At the end of the description is a comparative table of parameters of known analogues and the present invention "Method of protecting information with a disposable tape of infinite length on finite state machines in the" on-line "mode and a device for its implementation, which is recommended to be included in the abstract, as the most informative illustration.

Information confirming the possibility of implementing the invention.

In the process of encrypting information when entering it into the database, the device operates as follows (see figure 1). The operator, on block 1, dials an IP code (only a telephone number known to him, for example, the CONTINENT Academy number from the Moscow telephone directory 2005 - 107.38.75) of the starting position of the arithmetic progression generator 2.

The set of the 7th digit includes the generator 2 of the arithmetic sequence K = a · n + b. Suppose that the generation algorithm is based on the generation of arithmetic progression K = 210n + 1 = {211, 421, 631, 841, ... k}. Generator 2 is set to the initial generation value (K _H ) by dividing 107.38.75 modulo 210 (dividing by mod gives the remainder 145), subtracting the remainder from 107.38.75 and adding the number 211 by the formula K _H = 107 · 38 · 75-145 + 211 = 1073941 sets generator 2 to the starting current value of the function K _H.

A sequential addition of 210 to _KH generates a sequence of K primes and composite numbers: 1073941, 1074151, 1074361 , 1074571, 1074781, 1074991 , 1075201 , 1075411, 1075621 , 1075831, 1076041 , 1076251, 1076461, 1076681, 1076891, ....

Thus, the first sequence strictly determined by the formula 210n + 1 arises, which, in accordance with the Dirichlet theorem, contains both primes (underlined) and compound numbers, namely К = {1073941 = 11 * 97631, 1074151 = 13 * 82627, 1074361 , 1074571 = 349 * 3079, 1074781 = 673 * 1597, 1074991 , 1075201 , 1075411 = 23 * 46757, 1075621 , 1075831 = 769 * 1399, 1076041 = 31 * 34711, 1076251 = 11 * 97841, 1076461, 1076681 = 557 * 1933, 1076891 = 67 * 16073, ... p _i }. In this sequence, composite numbers are formed with the smallest divisors (prime numbers in a row) from 11, 13, 17, ... to p _i ≤n _RAM ^½ , where n _RAM is the maximum number of the sequence {210n + 1}, limited by the RAM size, if the amount of information does not exceed RAM, if it exceeds - generation continues with repeated use of RAM.

Then, any three-digit number (for example, the first 3 digits of "107" or the last 3 "875" digits of the same phone number) is dialed on the delay unit for the shutdown of the "thinning" 7 mode, corresponding, for example, to the number of milliseconds of the delay delay for the spectral additive sequence generator 3 only composite numbers, whose job is to generate spectrally additive sequences of only composite numbers, starting with the smallest divisor 11 according to the formula C ₁₁ = 1073941 + 11 * 210m = 97631 * 11 + 210m * 11 = {1073941, 1076251, 1078561, 1080871, 1083181 etc.}, where m = {1, 2, 3, ... m _RAM }, m _RAM - multiplicity of the "step" 210 * 11 of the sequence 97631 * 11 + 210m * 11 within the RAM. Spectrally additive sequences are formed by sequentially attaching to its base (prime) a multiple of its bases, so that a sequence of compound numbers with the smallest divisor equal to the base of the sequence is formed using only the addition operation. In spectrally additive sequences, the term of arithmetic progression, which is usually called the difference (11 * 210) or the "step", consists of a multiple of (210) bases (11) of the sequence, and the "spectrum" of the sequence defines its base (11), which is always prime number (11). In block 4, the “decimation” of the sequence K coming from the generator 2 of arithmetic progression occurs, with the exception of the numbers of sequences C ₁₁ , C ₁₃ , C ₁₇ , ... that is, with the exception of the sequence K, the sequence with the smallest divisor 11 C ₁₁ = { 1073941, 1076251, 1078561, 1080871, 1083181, etc.}, then - the sequence with the smallest divisor 13 according to the formula C ₁₃ = 1074151 (13 * 82627) + 13 * 210m = {1074151, 1076881, 1079611, 1082341, etc. etc.} and so on.

Suppose that for a given time of 107 ms, all composite numbers with the smallest divisors 11, 13, 17, 19, and 23 were excluded from the sequence K, after which the "decimation" of the sequence K ends and the second deterministic random sequence A = { 1074361 , 1074571, 1074781, 1074991 , 1075201 , 1075621 , 1075831, 1076041, 1076461 , 1076681, 1076891, ...}, which enters block 5 of the bitwise comparison of digits of this sequence, where the bitwise digits, for example of the next number, are compared with the digits of the number of the previous one, thanks to which there are twice determinants Anno-random sequence of different bit numbers C = {36, 57, 78, 499, 20, 62, 583, 4, 46, 68, 89, ...}. The sequence C enters the dividing unit modulo the number of characters of the adopted language 6. For example, for UNICS this is the number 256, the mod of which performs the operation of dividing the sequence C, so that at the output of block 6 we get a three-time-determined random sequence W = {36, 57, 78, 243, 20, 62, 71, 4, 46, 68, 89, ...}, which, using the XOR operation, is superimposed on the plaintext 8 and goes to the data storage database 9. To decrypt this file, type the same vector initialization 1073875 with the same "delay" off generator 3 sp ktralno addition sequences only composite numbers, resulting once again in the XOR operator will do the same three-deterministic random sequence W, which is superimposed on a closed text, so that there is the same plaintext. To approximate the parameters of sequence III to the parameters of a truly random sequence, it suffices to increase the bit depth of the difference of the arithmetic progression (210n) to a bit close to the bit of the IP code, for example, to 510510n + 1. In order not to overload the description, as a convenient example for checking, the sequence 210n + 1 is given.

If thinning is performed by monotonically increasing divisors {11, 13, 17, ...}, then the change in the density ratio of primes and composite numbers will have an exponential character (at first very frequent, rare towards the end, but at the end of thinning) only prime numbers). To eliminate this effect, the sequence-generating algorithm for spectral-additive sequences can specify an arbitrary given program for alternating spectrally-additive sequences. For the given example, in order to give an almost linear character to the change in the density ratio of primes and composite numbers, the alternation of the divisors may look like this: 11, p _i≤ n _RAM ^½ , 13, p _i-1 , 17, p _i-2 ....

When protecting information during the transmission (see figure 2) blocks 1-6 work in a similar way. The difference lies in the fact that for simultaneous encryption-decryption of information during its transmission, the device includes a synchronization unit 10 and a transceiver of the communication signal 11, and the input of the “thinning” off delay unit 7 is connected to the feedback signal receiver, providing a sequence change C in accordance with the current value of the time period between the clock transmission and the acceptance of the feedback signal, and the input of block 1 through the synchronization block 10 is connected to another output of the transceiver 11, which ensures simultaneous ennuyu synchronous operation of the transceiver 13a-public information of the sender information and classified information transceiver 13b recipient information.

In this use case, the operation is as follows:

- the sender of information, typing the IP-code of the recipient of information, sets the starting value of his arithmetic progression generator by the recipient's sync number (in the initial position, the starting value of the arithmetic progression generator is always set by the number of the owner-sender, that is, it is always ready to receive closed information);

- when dialing the last digit of the information recipient’s number from transponder 13a to transponder 12b, a synchronization signal is sent, which with a fixed delay is returned to transponder 13a and sent again to transponder 13b to start the operation of its generators 2, 3 and with a delay equal to half the delay of the sync return start the generators 2 and 3 of the transponder 13a, thereby ensuring their synchronous operation to generate identical sequences,

- at the time of connecting the transponder of the recipient of information 13b, a clock signal is sent from it to turn off the generator 3 of the transponder of the sender of information 13a and with a delay equal to half the delay in returning the clock to the generator 3, the transponder of the recipient of information 13b receives similar commands, while the clock signal to turn off the generator 3 includes blocks 5, 6, 7 and the XOR operator, due to which identical disposable encryption tapes are simultaneously synchronously generated on transponders 13a and 13b for simultaneous encryption of open text and decryption of the received closed text,

- the disposability of the tape is ensured by the random nature of the distribution of time between the arrival of the call signal and the appearance of the response signal, as well as the presence of blocks of a priori agreements, thanks to which it is possible to modify the encryption tape over wide ranges.

The transponders 13a and 13b can operate both without a block of a priori agreements 12 between the sender and the recipient of information, and with a block of a priori agreements 12. Assume, for example, that the block of a priori agreements contains an algorithm for increasing the IP code of the recipient of information. Assume that the a priori agreement (condition) for the recipient of information is determined by increasing the bit depth of the IP code by attaching the digit 3 at the beginning of the IP code. Then, the original IP code is transformed into 3.107.38.75.

The generator 2 is set to the initial value generation (K _N) by dividing 3.107.38.75 modulo 210 (division by mod 175 yields a residue) residue from 3.107.38.75 subtraction and addition of numbers 211 from the formula K = _H + 211 31073875-175 = 31073911 .

A sequential addition of 210 to K _N generates a sequence of K primes and composite numbers: 31074121, 31074331, 31074541, 31074751, 31074961, 31075171, 31075381, 31075591, 31075801, 31076011, 31076221, 31076431, 31076641, 31076851, 31077061, ... within RAM .

Thus, the first sequence strictly determined by the formula 210n + 1 arises that contains both primes and compound numbers, namely K '= {31073911 = 11 * 2824901, 31074121 = 13 * 2390317, 31074331, 31074541 = 23 * 1351067, 31074751 , 31074961, 31075171, 31075381, 31075591, 31075801, 31076011, 31076221 = 11 * 2825111, 31076431, 31076641, 31076851 = 13 * 2390527, 31077061 ... p _i }. In this sequence, as before (with K _H = 1073941), composite numbers are formed with the smallest divisors from 11, 13, 17, ... to p _i ≤n _RAM ^½ , where n _RAM is the maximum number of the sequence {210n +1} limited by RAM.

Suppose that the recall signal arrived with the same “delay” of 107 ms as before, due to which, as before, all composite numbers with the smallest divisors 11, 13, 17, 19, and 23 were excluded from the sequence K ' , after which we get the second, deterministic random sequence A '= {31074331, 31074751, 31074961, 31075171, 31075381, 31075591, 31075801, 31076011, 31076431, 31076641, 31077061 ... p _i }, which goes to block 5 of the bitwise comparison of digits of this sequence, where the bitwise digits, for example the next number, are compared with the digits of the number of the previous one, or according to another algorithm selection of combinations of numbers to be compared, due to which there arises a twice-determined random sequence of different-bit numbers C '= {33, 75, 496, 17, 38, 59, 580, 1, 43, 664,}.

The sequence C 'arrives at block 6 dividing modulo the number of characters of the received language, for example, this is the number 256 (. At the output of block 6, a thrice-determined random sequence W '= {33, 75, 240, 17, 38, 59, 58, 1, 43, 152, ...} is obtained, which is fundamentally different from the sequence W = {36, 57 , 78, 243, 20, 62, 71, 4, 46, 68, 89, ...}. Accordingly, the same text with the same “delay” (107 ms), but with an a priori agreement to increase the bit capacity by adding the number 3 in front of the IP code, after the XOR operation will have a completely different look, which can only be decrypted by synchronous operation a generator with the same mathematical function for generating the primary sequence, thinning and bitwise elimination blocks of identical digits, and with a priori block agreeing to increase the bit capacity by adding (for example, number 3) in front of the IP code.

In the mode of transmitting classified information to several recipients at the same time (supervisory briefing), the starting values of the generator 2 of all information recipients are set by the IP number of the information sender, and the time period of the delay of the thinning mode is set by a priori agreement between the participants.

The table below shows the advantages that are provided by the foregoing, based on the new mathematical foundation proposed by the invention, in comparison with the well-known technical solutions to the problem of protection in the transmission of information.

Name "Willow-0" DES Gamma 4 Invention Installation Is required Is required Is required NO Authentication Is required Is required Is required NO User accounting Is required Is required Is required NO Performance Delay depending on the amount of information Delay depending on the amount of information Delay according to key length 1 ms slower than "online" Key Length, Binary 256 56 30.60, 120, 240, 480, 960 determined by the number of excluded dividers

Claims (2)

1. A method of protecting information by generating an initial sequence of numbers and its subsequent processing to create a key superimposed on plain text, characterized in that as a function of generating the original sequence, use the arithmetic progression function, which provides an infinite sequence of primes and compound numbers, which is thinned out, excluding compound numbers with arbitrarily given divisors, carry out the launch of the generator of the original sequence, the initial state of which is set, and the generator of composite numbers, thinning is carried out in the period between the moment of simultaneous start and the given moment of arrival of the signal to turn off these generators, the sequence of numbers obtained at the moment of stopping thinning is compared in pairs and bitwise, removing the same numbers, modulo divide the number of characters of the plaintext language and serves for overlay on plaintext intended for entering into the database. 2. A method of protecting information by generating an initial sequence of numbers and its subsequent processing to create a key superimposed on plain text, characterized in that as a function of generating the original sequence, use the arithmetic progression function, which provides an infinite sequence of primes and compound numbers, which is thinned out, excluding compound numbers with arbitrarily given divisors, carry out the simultaneous start on the sender and receiver side of the generators of the initial sequence and generators of composite numbers from the same initial state by sending the recipient a message with the sender's identification number, receiving a confirmation message from him and starting the generators on the sender side after half the delay time between sending the message with sender’s identification number and receipt of a confirmation message, after receiving a confirmation message about t of the receiver, the sender sends the receiver a signal to turn on the generators, moreover, on the sender’s side, thinning is carried out between the moment of simultaneous start-up and the moment of arrival of the signal to turn off these generators from the receiver’s side, and on the recipient side, decimation is carried out, starting from the specified moment of simultaneous start and ending with the moment, which is calculated by summing the moment of simultaneous start of the generators with half the delay time between sending a confirmation message and the moment the signal comes on to turn on the generators, the sequence of numbers obtained at the time of thinning stop is compared in pairs and bitwise, removing the same numbers, modulo divide the number of characters of the plaintext language and on the sender side serves for overlay on the plaintext, and on the recipient side for overlay on the closed text.

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