RU2277759C2 - Method for generation of encoding-decoding key - Google Patents

Abstract

FIELD: computer science and communications engineering, in particular, methods and devices for cryptographic transformation of data.

SUBSTANCE: method includes generating two binary vectors of numbers a and p, having certain parameters, transferred by means of unprotected communication channel to each user of network, and generation by network users independently from each other of secret keys and generation of open keys by network users by means of transformation of binary vectors of secret key and numbers a and p, to obstruct possible determining of secret keys, and also common secret sub-keys of network users, while for determining secret sub-keys K it is required to know binary checksum vector of transferred message ξ, which changes for each communication session in random fashion. Utilization of checksum for source message during generation of protection key allows to prevent imposing of false information and to determine errors in transferred message, while possibility of determining of secret keys and common secret sub-keys of network users is excluded even when using cryptanalysis method with known open text. Instead of generation of binary checksum vector for transferred message binary hash function vector may be generated for transferred message or a random binary vector, for example, by using random numbers generator in conjunction with timer indications.

EFFECT: increased speed of operation of encoding-decoding key generation process and increased message encoding speed.

1 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:

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

the encryption-decryption key (cipher key) is a combination of bits used in encrypting information data 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 transformation of data blocks using a cryptographic key, converting data into a cryptogram, which is a pseudo-random 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 of a number is a signal in the form of a sequence of zero and unit bits corresponding to the representation of a number in the binary system.

Known methods for generating an encryption-decryption key (see, for example, Russian standard encryption standard USSR standard GOST 28147-89 [1], British B-Grypt algorithm, US standard DES, Japanese FEAL data encryption algorithm [2], pp. 48-52 as well as the patent of the Russian Federation for the invention No. 2171012, IPC ⁷ H 04 L 9/08, 9/00, application No. 2000108296/09 of 04/03/2000).

In known methods, the encryption-decryption key is generated by using a random number generator with some unpredictable factor, for example, the choice of bits from the timer. The generated numerical key is transmitted by the network user and is used as the base (initial value) of the pseudo-random sequence of numbers generator. The output bit stream is added modulo 2 with the source text to form an encrypted message and vice versa.

However, the known methods analogous to the formation of an encryption-decryption key require the use of secure communication channels to transmit the generated key to network users.

The closest in technical essence to the claimed method of generating an encryption-decryption key is the method described by the protocol in the US standard DES [2], p. 71, and [3], p. 61.

обмен пользователями открытыми ключами и формирование каждым из них общего секретного подключа

К=K_AB=К_ВА и использование этого подключа в качестве базы для начального заполнения регистра сдвига, имеющего n разрядов и вырабатывающего псевдослучайную последовательность символов максимальной длины.The prototype method includes the formation for all network users of two binary vectors of numbers a and p, with a prime number p≥2 ⁿ -1, users of the network independently choosing secret keys x _A , ..., x _B , such such that 1 <x _A <2 ⁿ , 1 <x _B <2 ⁿ , the formation of network keys by public users

exchange of public keys by users and the formation of a common secret subkey by each of them

K = K _AB = K _VA and the use of this subkey as the basis for the initial filling of the shift register, which has n digits and generates a pseudorandom sequence of characters of maximum length.

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. Modeling the operation of the shift register in the opposite direction, it is possible to determine its initial state, and, consequently, the keys used by network users for encryption-decryption of information.

If the structure of the shift register with n bits is unknown, then 2 n characters of known plaintext and 2 n characters of ciphertext corresponding to it are sufficient to quickly (within a few seconds of the operation of a computer) determine the state of the shift register and calculate the keys used (see ., for example, [4] p. 93).

Therefore, the keys generated for encryption-decryption of information can be used only once and during the next communication session should be determined in a new way. And this leads to a significant complication of the procedure for distributing keys in a computer network, because each time confirmation of the authenticity of the communication session and the authenticity of the network user is required by using electronic signatures or digital signatures. This reduces the speed of the process of generating the encryption-decryption key and the speed of information encryption.

The invention is aimed at increasing the speed of the process of generating the encryption-decryption key and increasing the speed of message encryption.

обмене пользователями сети открытыми ключами и формировании каждым из них для связи с другими пользователями сети общего секретного подключа

К=К_АВ=К_ВА, дополнительно пользователи сети формируют для связи с другими пользователями сети двоичный вектор обратного элемента общего секретного подключа между пользователями сети К₀ путем преобразования двоичного вектора общего секретного подключа между пользователями сети

и для передачи сообщения формируют случайный двоичный вектор ξ, формируют шифрключ β путем сложения по модулю два битов случайного двоичного вектора ξ с битами двоичного вектора общего секретного подключа К, закладывают его в шифрующее устройство, формирующее псевдослучайную последовательность символов максимальной длины 2ⁿ-1 для шифрования сообщения, формируют двоичный вектор α путем сложения по модулю два битов случайного двоичного вектора ξ с битами двоичного вектора обратного элемента общего секретного подключа между пользователями К₀ сети и передают его по каналу связи вместе с зашифрованным сообщением, а при приеме сообщения пользователи сети формируют случайный двоичный вектор ξ путем сложения по модулю два битов принимаемого двоичного вектора α с битами двоичного вектора обратного элемента общего секретного подключа между пользователями сети K₀, а затем формируют шифрключ β путем сложения по модулю два битов случайного двоичного вектора ξ с битами двоичного вектора общего секретного подключа К и закладывают его в шифрующее устройство для дешифрования сообщения.This is achieved by the fact that in the known method of generating an encryption-decryption key, which consists in generating for all network users binary vectors of two numbers a and p, while a prime number p≥2 ⁿ -1, in generating network users independently of each other secret keys x _A , ..., x _B , such that 1 <x _A <2 ⁿ , 1 <x _B <2 ⁿ , when the network users form public keys

exchange of network keys by public users and the formation of each of them for communication with other network users with a shared secret subkey

K = K _AB = K _VA , additionally, network users form for communication with other network users a binary vector of the inverse element of the shared secret subkey between users of the network K ₀ by converting the binary vector of the shared secret subkey between network users

and for transmitting the message, a random binary vector ξ is formed, a cipher key β is formed by modulo adding two bits of a random binary vector ξ with the bits of the binary vector of the shared secret subkey K, put it into an encryption device forming a pseudorandom sequence of characters of maximum length 2 ⁿ -1 for encryption messages form the binary vector α by modulo adding two bits of the random binary vector ξ with the bits of the binary vector of the inverse element of the common secret subkey between the user s K ₀ network and transmitting it over the communication channel together with the encrypted message, and upon receiving the message the network users form a random binary vector ξ by modulo-two bits of the received binary vector α with the bits of the binary vector inverse element shared secret is connected between the network users K ₀ and then form the encryption key β by modulo adding two bits of the random binary vector ξ with the bits of the binary vector of the shared secret subkey K and put it into an encryption device for decryption with bscheniya.

The listed set of essential features makes it difficult to determine the secret keys, as well as the general secret subkeys of network users. In this case, although the initial state of the shift register will be determined, knowledge of a random binary vector ξ is required to determine secret subkeys K, which varies randomly for each communication session.

A random binary vector can be generated, for example, by using a random number generator in combination with a timer. In this case, the possibility of determining private keys, as well as shared secret connections of network users, even when using the cryptanalysis method with known plaintext, is excluded. Despite the fact that in some communication session the initial state of the shift register will be determined, but to determine the secret subkeys K, knowledge of a random binary vector ξ is required, which is randomly selected for each communication session. Since the statistical methods of cryptanalysis are not applicable in this case, the secret subkeys K ₁ , K ₂ can be opened only by total enumeration of the entire set of keys. In accordance with the Russian standard GOST 28147-89 for a shift register with 256 memory cells, the power of the set of keys will be 10 ⁷⁷ . If the key is opened using a computer with a clock frequency of 100 GHz, the number of operations performed by this computer during the year will be 3 · 10 ²⁰ , and the key opening time will be 3 · 10 ⁵⁶ years.

The cryptanalyst’s knowledge of the public keys, as well as the numbers a and p transmitted through insecure communication channels, also does not allow one to find the values of secret keys x _A1 , x _A2 , ..., x _B1 , x _B2 and common secret connections of network users K ₁ and K ₂ since the procedure for finding them is reduced to calculating the discrete logarithm of an arbitrary element of a finite field F _p having a total number of elements 10 ⁷⁷ . Therefore, the solution to this problem is beyond the technological capabilities of modern computers.

Since the secret keys and subkeys are not opened in the considered method, there is no need to assign keys for communication of new sessions, and therefore, there is no need to confirm the authenticity of subscribers and communication sessions, which greatly simplifies the procedure for distributing keys in a computer network and eliminates the need for electronic signatures or digital signatures for each communication session, which leads to an increase in the speed of encryption-decryption key generation and increase encryption speed.

Despite the fact that there can be many users in a computer network, different secret subkeys inaccessible to other network users will be used with each of them for the proposed method of generating encryption-decryption keys.

The possibility of technical implementation of the proposed method is illustrated as follows. In the key distribution center, two numbers a and p are selected, which are communicated to all users of the network by generating binary vectors and transmitting them through insecure communication channels. The number a can be chosen within 1 <a <2 ⁿ , which is not a big problem, and the number p must be chosen simple. This number can be selected from Mersenne primes of type 2 ^k -1, where k is a prime number. For example, the US DES standard provides for the use of a shift register having 127 memory cells (key length 127 bits). In this case, the Mersenne number p = 2 ¹²⁷ -1 can be used as a prime number. For the Russian standard GOST 28147-89, you can use the number p = ^2,257 -1.

To generate public keys of the network y _А , ..., y _B , as well as shared secret subkeys K and reverse elements of shared secret subkeys K ₀ , the algorithm for quickly raising a power to a power in a finite field F _p can be used (see [4] p. 39) and for p = ^2,257 -1, on modern computers, keys can be generated in a few minutes. To generate a random binary vector, the algorithms presented in [5] can be used. The remaining procedures for generating the encryption-decryption key are implemented by known methods and are not in doubt.

The proposed method can be implemented using a computer or a computing device, represented by a block diagram in the drawing, where

block 1 - input-output device;

block 2 - a device for generating public keys;

block 3 - a device for generating secret subkeys for communication with a selected network user;

block 4 - device for generating a random binary vector;

block 5 - a device for generating a session encryption key;

block 6 is a device for generating a session decryption key.

For simplicity, the description of the operation of the device will use small numbers. We assume that network users use shift registers with 5 memory cells (key length 5 bits, n = 5). Then, in the center of the distribution of keys, two numbers a = 2 and p = 2 ⁵ -1 = 31 are determined and binary vectors of these numbers are generated

a = 00010 = 2

p = 11111 = 31

and over an insecure communication channel transmit them to all network users.

The network users fix the binary vectors of numbers a and p in block 1 and feed them to block 2. In block 2, network users generate secret keys (for example, user A generates secret keys x _A = 00011 = 3, and user B generates secret keys x _B = 00010 = 2), fix them and generate public keys (for example, user A generates a public key)

Y _А ≡2 ³ (mod 31) = 01000 = 8,

(and user B generates public keys)

y _B ≡2 ² (mod 31) = 00100 = 4.

The generated public keys are submitted to block 1, fixed there and transmitted via an unsecured communication channel through the key distribution center to other network users. Accepted open spikes of other users are fixed in block 1.

If user A wants to send an encrypted message to user B, he proceeds as follows.

In block 3, the user forms secret subkeys between users A and B, using the public key of user B (at _B ), which comes from block 1, and his private key (x _A ), coming from block 2, and also forms a binary vector the inverse of the shared secret subkey between users of the network K ₀

(mod р)≡4³(mod 31)=00010=2K _AB ≡

(mod p) ≡4 ³ (mod 31) = 00010 = 2

(mod р)≡2²⁹(mod 31)=10000=16K ₀ ≡

(mod p) ≡2 ²⁹ (mod 31) = 10000 = 16

In block 4, user A generates a random binary vector ξ (for example, by using a random number generator in combination with a timer, the number ξ = 10101 = 21 is obtained).

In block 5, user A generates a binary vector α by modulo addition of 2 bits of a random binary vector ξ with bits of a binary vector of a shared secret subkey K _AB coming from block 3

and also forms a binary vector β by adding modulo 2 bits of a random binary vector ξ with the bits of the binary vector of the shared secret subkey K _AB coming from block 3

User A places the binary vector β into the encryption device, which generates a pseudo-random sequence of characters using the shift register, and transmits the binary vector α and the encrypted text to user B.

Having received the binary vector α and the ciphertext from user A, user B proceeds as follows.

In block 3, user B forms a shared secret subkey between users B and A, using the public key of user A (at _A ) coming from block 1 and his private key (x _B ) coming from block 2, and also forms a binary vector of the inverse element of the common secret subkey between users of the network K ₀ .

In block 6, user B generates a random binary vector ξ by adding modulo 2 received bits of the binary vector α coming from block 1 with the bits of the binary vector of the inverse element of the common secret subkey K ₀ coming from block 3

and in block 5, a binary vector β is formed by modulo 2 addition of the 2 bits of the random binary vector ξ coming from block 6 with the bits of the binary vector of the shared secret subkey K _BA coming from block 3

The binary vector β, user B, places a pseudorandom sequence of characters used to decrypt the message using the shift register, using the shift register.

Information sources

1. The Russian encryption standard is the USSR standard GOST 28147-89 information processing system. Cryptographic protection. Cryptographic conversion algorithm.

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

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

4. V.I. Tupota. Adaptive means of information security in computer networks. - M .: Radio and communications, 2002, - 176 p.

5. GOST R 34.11-94. "Information technology. Cryptographic protection of information. Hashing function."

Claims (1)

A method of generating an encryption-decryption key based on the generation of two binary vectors of numbers a and p, where 1 <a <2 ⁿ , and p is a prime number and p≥2 ⁿ -1, where n is the key length in bits, transmitted over unprotected the communication channel of binary vectors of numbers a and p to each network user, network users generating secret keys x _A , ..., x _B independently from each other, where x _A is the secret key of user A, 1 <x _A <2 ⁿ , x _B - the secret key of user B, 1 <x _B <2 ⁿ , and the formation by users of the network of public keys by binary conversion x vectors of secret key and numbers a and p

where _A is the public key of user A, _B is the public key of user B, transmitting public keys via an insecure communication channel to all other network users and forming network users to communicate with another network user for a shared secret subkey K by converting the binary vectors of their private key and another user's public key

K = K _AB = K _BA , where K _AB is the common secret subkey between users A and B, K _wa is the common secret subkey between users B and A, K is the common secret subkey, and a random binary code is generated for each communication session vector ξ, form the binary vector β by modulo adding two bits of the random binary vector ξ with the bits of the binary vector of the shared secret subkey K, use the binary vector β as an encryption key for an encryption device forming a pseudorandom sequence of characters ma maximum DUTY length 2 ⁿ -1 to encrypt a message form binary vector α, which is transmitted through the communication channel together with the encrypted message, and upon receiving the message the network users form a random binary vector ξ, and then form a binary vector β by addition of two random bits modulo binary vector ξ with bits of the binary vector of the shared secret subkey K and the binary vector β are used in an encryption device forming a pseudorandom sequence of characters used to decrypt the message, characterized in that during transmission, network users independently form a binary vector of the inverse element of the common secret subkey between users of the network K ₀ for communication with another network user by converting the binary vector of the common secret subkey between network users

and form a binary vector α by modulo adding two bits of a random binary vector ξ with bits of a binary vector of the inverse element of the common secret subkey between users K ₀ , and when a message is received, a random binary vector ξ is formed by adding modulo two bits of the received binary vector α with bits binary vector of the inverse of the shared secret subkey between users K ₀ .