RU2140713C1 - Method for cryptographic conversion of binary data blocks - Google Patents

Abstract

FIELD: electrical communications and computer engineering. SUBSTANCE: method intended to increase number of various operations depending on block being converted involves division of binary data code into N≥1 data blocks and sequential conversion of data blocks; in addition, control code V is generated; during conversion of data block the latter undergoes at least one exchange control operation depending on value of control code V which is generated according to secret key; control code V is also generated according to current value of converted data block; control code V is likewise shaped according to secret key and to current value of data block. In addition, control code V is generated according to additional binary data. EFFECT: improved stability of code. 5 cl, 15 dwg

Description

 The invention relates to the field of telecommunications and computer technology, and more particularly to the field of cryptographic methods and devices for encrypting messages (information).

In the aggregate of the features of the proposed method, the following terms are used:
- the secret key is binary information known only to a legitimate user;
- cryptographic conversion is the conversion of digital information that provides the influence of one bit of the source data on many bits of the output data, for example, to protect information from unauthorized reading, the formation of a digital signature, and the generation of a modification detection code; One of the important types of cryptographic transformations is one-way conversion, hashing and encryption;
- hashing information is some way of generating a so-called hash code, the size of which is fixed (usually 128 bits) for messages of any size; Hash procedures ensure that the hash code is dependent on each bit of the message.

- encryption is a process of converting information that depends on the secret key and converts the source text into ciphertext (cryptogram), which is a pseudo-random sequence of characters from which obtaining information without knowing the secret key is practically impossible;
- decryption is the reverse process of encryption; decryption provides recovery of information from the cryptogram with the knowledge of the secret key;
- the cipher is a set of elementary steps for converting input data using a secret key; the cipher can be implemented as a computer program or as a separate device;
- a binary vector is a sequence of zero and one bits, for example (101101011); the specific structure of the binary vector can be interpreted as a binary number, if we assume that the position of each bit corresponds to a binary digit, i.e. a binary vector can be associated with a numerical value, which is determined uniquely by the structure of the binary vector;
- cryptanalysis - a method of calculating a secret key to obtain unauthorized access to encrypted information or developing a method that provides access to encrypted information without calculating a secret key;
- one-way conversion is the conversion of an m-bit input data block into an m-bit output data block, which makes it easy to calculate the output block from the input block, and calculating the input block, which would be converted to a randomly selected output block, is an almost impossible task;
- a one-way function is a function whose value is easily calculated by a given argument, however, calculating an argument from a given function value is a computationally difficult task; one-way functions are implemented as a sequence of procedures for one-way conversion of some input block (argument), the output value of which is taken as the value of the function;
- cryptographic strength is a measure of the reliability of encrypted information protection and represents the complexity, measured in the number of elementary operations that must be performed to recover information from a cryptogram with knowledge of the conversion algorithm, but without knowledge of the secret key; in the case of one-sided transformations, cryptographic strength is understood as the complexity of calculating the input value of a block from its output value;
- cyclic shift operations depending on the converted sub-blocks or depending on the binary vector — these are cyclic shift operations by the number of bits specified by the value of the sub-block or the value of the binary vector; operations of cyclic shift to the left (right) are indicated by the sign "<<<"(">>>"), for example, the entry B ₁ <<< B ₂ indicates the operation of cyclic left shift of the sub-block B ₁ by the number of bits equal to the value of the binary vector B ₂ ; similar operations are basic for the RC5 cipher;
- a single operation is an operation performed on one operand (data block or binary vector); the value of a subblock after performing some given unary operation depends only on its initial value; examples of single operations are cyclic shift operations;
- two-place operation is an operation performed on two operands; the result of some given two-place operation depends on the value of each operand; examples of double operations are the operations of addition, subtraction, multiplication, etc.

- the concatenation operation is the operation of combining several binary vectors, as a result of which a new binary vector is formed, including all the bits of each of the combined binary vectors, and the relative position of the bits corresponding to the original binary vectors does not change; for example, the concatenation of binary vectors W ₁ = (101101011) and W ₂ = (011101010) is written as W ₁ / W ₂ = (101101011011101010); these binary vectors can be combined by the concatenation operation in yet another way: W ₂ / W ₁ = (01110101010101101011).

 Known methods for block data encryption, see, for example, the DES cipher [B. Schneier, "Applied Cryptography", Second Eddition, John Wiley & Sons, Inc., New York, 1966, pp. 270-277]. In this method, the encryption of data blocks is performed by generating a secret key, dividing the converted data block into two subunits L and R and alternating the latter by performing bitwise summing operations modulo two over the subunit L and the binary vector, which is formed as the output value of some function F from the values of the sub-block R. After that, the sub-blocks are rearranged. The function F in the specified method is implemented by performing permutation and substitution operations performed on the sub-block R. This method has a high conversion speed when implemented in the form of specialized electronic circuits. However, the known analogue method uses a small secret key (56 bits), which makes it vulnerable to cryptanalysis based on key selection. The latter is associated with the high computing power of modern computers.

Closest in technical essence to the claimed method of block cryptographic conversion of binary information is the method implemented in the RC5 cipher described in the monograph [B. Schneier, "Applied Cryptography", Second Eddition, Jhn Wiley & Sons, Inc., New York, 1966 , pp. 344-346]. The prototype method includes the formation of a secret key in the form of a set of subkeys, a split of the binary information code into m-bit information blocks and the alternate conversion of m-bit blocks. The conversion of m-bit blocks is carried out by splitting the m-bit data block into n-bit subblocks A and B, and alternately converting the subblocks. Subblocks are converted by performing single and double operations on them. As two-place operations, the modulo 2 ⁿ addition operations are used, where n = m / 2 = 8, 16, 32, 64, and the bitwise summing operation is modulo 2. The cyclic left shift operation is used as the unary operation, and the number of bits by which the converted subblock is shifted depends on the value of the other subblock, which determines the dependence of the cyclic shift operation at the current step of transforming the subblock on the initial value of the input data block. Double operation is performed on a sub-block and a sub-block, as well as on two sub-blocks. Typical of the prototype method is the use of a cyclic shift operation, depending on the value of the input block. A subunit, for example subunit B, is transformed in the following way. The bitwise summing operation is performed modulo 2 over subunit A and B and the value obtained after performing this operation is assigned to subunit B. This is written as the ratio B: = B ⊕ A, where the “: =” sign indicates the assignment operation and the “⊕” sign denotes the operation of bitwise summing modulo 2. After this, the operation of cyclic left shift is performed on subblock B by the number of bits equal to the value of subblock A: B: = B <<< A. Then, modulo summation is performed on subblock B and one of the connections S 2 ^n, where n - the length knocked eye in bits: B: = (B + S ) mod 2 ^n. After that, subunit A is similarly converted. Several such steps are taken to convert both subunits.

 This method provides a high encryption speed when implemented in the form of a computer program. However, the prototype method has drawbacks, namely, with a software implementation for a computer with a 32-bit microprocessor, it does not provide high resistance of cryptographic data conversion to differential and linear cryptanalysis [Kaliski B. S., Yin Y.L. On Differential and Linear Cryptanalysis of the RC5 Encryption Algorithm. Advances in Cryptology - CRYPTO '95 Proceedings, Springer-Verlag, 1995, pp. 171-184]. This drawback is due to the fact that the efficiency of using operations that depend on the converted data in order to complicate the known cryptanalysis methods is reduced by the fact that the number of possible cyclic shift operations is equal to the number of binary bits of the n subunit and does not exceed 64.

 The basis of the invention is to develop a method for block cryptographic conversion of binary information in which the input data is converted in such a way as to increase the number of different operation options depending on the block being transformed, thereby increasing the resistance to differential and linear cryptanalysis.

 The problem is achieved in that in a method of block cryptographic conversion of binary information, including splitting a binary code of information into N ≥ 1 information blocks and alternating conversion of information blocks, new according to the invention is that the control code V is additionally generated when converting the information block over the information the unit performs at least one controlled permutation operation, depending on the value of the control code V.

 Thanks to this solution, an increase in the number of possible operation options depending on the block being transformed is ensured, which provides an increase in the resistance of the cryptographic transformation to differential and linear cryptanalysis.

 Also new is that the control code V is generated by the value of the secret key.

 Thanks to this solution, an additional increase in resistance to differential and linear cryptanalysis is provided.

 Also new is the fact that the control code V is generated by the current value of the converted block.

 Thanks to this solution, an additional increase in cryptographic resistance to attacks based on failures of the encryption device is provided.

 Also new is that the control code V is generated by the secret key and by the current value of the block being transformed.

 Thanks to this solution, an increase in cryptographic resistance to differential cryptanalysis based on failures of the encryption device is provided.

 Also new is the fact that the control code V is generated from additional binary information.

 Thanks to this solution, an additional increase in the hash strength is provided.

 Below the essence of the claimed invention is explained in more detail by examples of its implementation with reference to the accompanying drawings.

 In FIG. 1 presents a generalized scheme of cryptographic conversion according to the claimed method.

 In FIG. 2 shows possible types of information block conversion procedures.

 In FIG. 3 shows a block diagram of an elementary switch, which is the basic element of a managed operational permutation unit.

 In FIG. 4 schematically shows the structure of a managed operational permutation unit.

 In FIG. 5 schematically illustrates specific embodiments of a controlled permutation operation that differ in the method of generating the control code V. FIG. 5e shows a special case of a controlled permutation operation that does not change the position of bits in a certain sub-block of the information block.

 In FIG. 6 is a conversion diagram illustrating Example 3.

 In FIG. 7 is a conversion diagram illustrating Example 4.

The invention is illustrated by a generalized scheme of cryptographic conversion of data blocks based on the proposed method, which is presented in FIG. 1, where: P ₁ , P ₂ , ..., P _x - managed operational permutation blocks; T - convertible information block; V ₁ , V ₂ , ..., V _x are the values of the control code V at the corresponding steps of the transformation of the information block, x is a natural number. The controlled operational permutation unit performs the controlled permutation operation, which is understood as the implementation of the permutation of bits of the input block depending on any variable parameter involved in the transformation. Such variable parameters can be plug-ins, subblocks of the information block, or specially generated values that change with a change in the initial value of the information block. As a variable parameter that controls the permutation operation, values generated from random or pseudo-random data can also be used. In the general case, the value that controls the permutation operation will be called the control code V. By the formation of the control code V, we mean the formation of signals at the control input of the controlled operational permutation block. A controlled operation block of permutations is a transformation device having an n-bit information input, an n-bit output, and a g-bit control input. The controlled operational permutation unit (P-block) performs the operation of permuting bits of the information block supplied to the information input of the P-block, depending on the value of the signals at the g-bit control input. The set of all signals at the control input is the control code V, the value of which sets a specific option for the permutation of the bits of the converted information block.

где π_V - фиксированные перестановки длины n, которые в общем случае являются различными, V - значение управляющего кода, g - разрядность управляющего кода. Могут быть сконструированы управляемые операционные блоки перестановок со значением g, удовлетворяющим следующим условиям: 1) g < n, 2) g = n и 3) g > n. Для практического построения устройств криптографического преобразования наибольший интерес представляют P-блоки со значением n = 32, 64, 128 и 256 и значением g, в два и более раз превышающем значение n. В этих случаях формируется управляющий код, имеющий соответствующую длину. Например, управляющий код может быть сформирован путем:
1) повторения информационного блока: V =

2) дополнительного преобразования управляющего кода, сформированного в соответствии с пунктом 1,
3) объединения нескольких подключений: V =

где ω - натуральное число,
4) дополнительного преобразования управляющего кода, сформированного в соответствии с пунктом 3,
5) объединения подключей и информационного блока: V =

причем после такого объединения управляющий код может быть подвергнут дополнительному преобразованию, например, над ним может быть осуществлена операция фиксированной перестановки в соответствии с формулой: V: = π (V).The specific form (or type) of a controlled permutation operation P of length n is characterized by an ordered set

where π _V are fixed permutations of length n, which are generally different, V is the value of the control code, g is the bit depth of the control code. Managed operational permutation blocks can be constructed with a value g satisfying the following conditions: 1) g <n, 2) g = n, and 3) g> n. For practical construction of cryptographic conversion devices, P-blocks with a value of n = 32, 64, 128 and 256 and a value of g two or more times the value of n are of most interest. In these cases, a control code having an appropriate length is generated. For example, a control code may be generated by:
1) repetition of the information block: V =

2) additional conversion of the control code generated in accordance with paragraph 1,
3) combining multiple connections: V =

where ω is a natural number,
4) additional conversion of the control code generated in accordance with paragraph 3,
5) combining subkeys and information block: V =

moreover, after such a combination, the control code can be subjected to additional transformation, for example, a fixed permutation operation can be performed on it in accordance with the formula: V: = π (V).

6) conversion of the secret key or one or more subkeys,
7) additional conversion of the information block or one or more information subblocks.

The controlled permutation acts on the information block T as follows. As a control code value V is selected modification π _V, according to a fixed permutation π _V permutation is performed of the information block of bits T, which is formed as a result of the value of P _V (T).

 FIG. 1 shows a general transformation scheme using controlled permutation operations. This scheme of cryptographic conversion procedures can be used for encryption and for one-way conversions. As the control code V, (1) encryption subkeys generated by the secret key, (2) information block subblocks, (3) additional control information generated during the cryptographic conversion depending on the additional binary information can be used. As additional control information, a message can be used for which a hash code needs to be generated. In the case of one-way conversions, the secret key may not be used, and the current value of the information block can be used as the control code V, or the control code V can be generated from the current value of the information block by additional transformation of the information block. A special case of the formation of the control code V is the use of a subblock of the converted information block as the control code V to perform the controlled operation of the permutation of bits of the converted information block. The entire information block can be used as the control code V. The control input of the block P receives the signals of the control code V. Due to this, the permutation operation performed on the information block depends on the controlled code V.

и др. При этом в результате выполнения процедуры типа E над текущим значением информационного блока его размер может остаться неизменным, может увеличиться или может уменьшиться. Под размером информационного блока мы понимаем количество битов, содержащихся в информационном блоке. Под текущим значением преобразуемого информационного блока мы понимаем совокупность битов, получаемую (после выполнения некоторой процедуры преобразования) на выходе соответствующего операционного блока. Текущее значение преобразуемого информационного блока в общем случае меняется после выполнения каждой операции преобразования.In accordance with the cryptographic conversion scheme of FIG. 1 above the information block, two types of conversion procedures are performed: (1) the procedures shown by the operation blocks E ₁ , E ₂ , ..., E _x and (2) the procedures shown by the operation blocks P ₁ , P ₂ , ..., P _x . Procedures of type P represent a controlled permutation operation, that is, the operation block P permutes all bits of the information block or some part of it depending on the value of the control code V. Procedures of type E represent a certain set of known conversion operations: modulo two-bit addition (⊕ ) modulo 2 ⁿ addition, where n ≥ 8 (+), multiplication, division, cyclic shift operation, fixed permutation (π), table expansion operation, concatenation operation

etc. In this case, as a result of the execution of a procedure of type E on the current value of the information block, its size may remain unchanged, may increase or may decrease. By the size of the information block, we mean the number of bits contained in the information block. By the current value of the information block being transformed, we mean the set of bits obtained (after performing some conversion procedure) at the output of the corresponding operational block. The current value of the converted information block generally changes after each conversion operation.

где знак

обозначает конкатенацию значений T_вх и K. Фиг. 2в показывает вариант преобразования информационного блока с уменьшением размера информационного блока. Вариант на фиг. 2в описывается формулой T_вых = T_вх" ⊕ T_вх", где входной блок разбивается на два подблока одинакового размера, то есть представляется в виде конкатенации подблоков T_вх" и T_вх': T_вх =

Над подблоками T_вх" и T_вх" выполняется операция поразрядного суммирования по модулю два, в результате чего размер выходного блока уменьшается вдвое по сравнению с размером входного блока.In FIG. 2 schematically shows the main options for a Type E procedure. FIG. 2a shows an embodiment of converting an information block without changing its size. This option is described, for example, by the formula T _o = T _I ⊕ K, where sub K is the same size as the current value of the information block being transformed, designated as T _I. The value of the information block after the conversion is indicated by T _o . FIG. 2b shows a conversion option of an information block with an increase in the size of the information block. The embodiment of FIG. 2b is described, for example, by the formula T _o =

where is the sign

denotes the concatenation of the values of T _I and K. FIG. 2c shows an embodiment of converting an information block with decreasing information block size. The embodiment of FIG. 2c is described by the formula T _out = T _in "⊕ T _in ", where the input block is divided into two subblocks of the same size, that is, it is represented as the concatenation of the subunits T _in "and T _in ': T _in =

The bitwise summation modulo two operation is performed on the T _in and T _in subblocks, as a result of which the size of the output block is halved compared to the size of the input block.

Затем осуществляется фиксированная перестановка битов расширенного информационного блока

в результате чего вырабатывается информационный блок со значением R =

(Под фиксированной перестановкой π здесь понимается перестановка, которая не зависит от каких-либо параметров, участвующих в преобразовании. Такая перестановка легко реализуется в электронных схемах, например, как простое переплетение проводников. ) Полученное значение R может быть представлено в виде конкатенации двоичных векторов меньшей длины: R =

В качестве выходного блока может быть взят двоичный вектор R' (т.е. в этом случае имеем T_вых = R'), в качестве управляющего кода - двоичный вектор V=R". Возможны варианты передачи на вход следующего операционного блока (типа E или типа P) расширенных информационных блоков, например, в соответствии со следующими вариантами:
(1) T_вых = R и V = R",
(2) T_вых = R и V = R.FIG. 2d shows the conversion option of the information block combined with the formation of the control code V. The bitwise summing operation is performed modulo two over the input information block T _I and the plug-in, the resulting value is combined with the initial value of the input block, resulting in the formation of an extended information block equal to

Then, a fixed permutation of bits of the extended information block is performed

as a result, an information block is generated with the value R =

(A fixed permutation π here means a permutation that does not depend on any parameters involved in the transformation. Such a permutation is easily implemented in electronic circuits, for example, as a simple interlacing of conductors.) The obtained value of R can be represented as a concatenation of binary vectors smaller lengths: R =

The binary vector R 'can be taken as the output block (that is, in this case we have T _o = R'), the binary vector V = R "as the control code. Transmission to the input of the next operation block (type E or type P) extended information blocks, for example, in accordance with the following options:
(1) T _o = R and V = R ",
(2) T _o = R and V = R.

(3) объединения текущего значения информационного блока с подключом: T_вых =

Управляемые операционные блоки перестановок могут быть легко реализованы в виде несложных быстродействующих комбинационных электронных схем, использующих в качестве базового узла элементарный переключатель. На фиг. 3 показана блок-схема элементарного переключателя, где u - управляющий сигнал, a и b - входные сигналы данных, c и d - выходные сигналы данных. При u = 1 линия a коммутируется с линией c, а линия b - с линией d. При u = 0 линия a коммутируется с линией d, а линия b - c линией c. Таким образом, при значении управляющего бита u = 0 осуществляется перестановка двух входных битов, а при u = 1 входные биты не переставляются.There are other options for generating an expanded binary vector, for example, (1) by performing the multiplication operation on the current information block and subkey, (2) by repeatedly repeating the information block: T _o =

(3) combining the current value of the information unit with subkey: T _out =

Controlled operational permutation units can be easily implemented in the form of simple high-speed combinational electronic circuits using an elementary switch as a base unit. In FIG. Figure 3 shows a block diagram of an elementary switch, where u is the control signal, a and b are the input data signals, c and d are the output data signals. For u = 1, line a commutes with line c, and line b commutes with line d. For u = 0, line a commutes with line d, and line b connects with line c. Thus, with the value of the control bit u = 0, two input bits are permuted, and with u = 1, the input bits are not rearranged.

При n = 64 имеем 64! ≈ 2³²⁰, т.е. для реализации всех возможных перестановок потребуется использовать управляющий код длиной не менее 320 бит. Однако на практике достаточно использовать сравнительно малую долю из этого числа перестановок, например, 2²⁵⁶ перестановок, что соответствует 8-каскадному управляемому блоку перестановок с 64-битовым входом. Управляемые операционные блоки перестановок с такой структурой для значений n = 32,64,128 легко могут быть изготовлены с помощью современной микроэлектронной технологии.In FIG. 4 schematically shows the structure of a controlled operational permutation block with an n-bit input. The managed operational permutation block consists of several stages. Each cascade consists of a line of elementary switches S, which perform the switching of two adjacent bits of the information block, and the operation block of a fixed permutation π, which is a simple interweaving of conductors. The number of elementary switches in one cascade is n / 2. The number of stages can be selected depending on the specific conditions for the inclusion of a controlled permutation block in the encryption device. Obviously, the number of single-bit control inputs u of such a controlled permutation block is g = zn / 2, where z is the number of cascades. The number of possible permutations of n bits is the approximate Stirling formula

For n = 64 we have 64! ≈ 2 ³²⁰ , i.e. to implement all possible permutations, it is required to use a control code with a length of at least 320 bits. However, in practice, it is enough to use a relatively small fraction of this number of permutations, for example, ^2,256 permutations, which corresponds to an 8-stage controlled permutation block with a 64-bit input. Controlled operational permutation blocks with such a structure for n = 32.64.128 can easily be manufactured using modern microelectronic technology.

 In FIG. 5 shows possible options for controlled operations of permutations performed on the information block. In FIG. 5a shows a controlled bit-swapping operation of the information block T, performed depending on the value of T. In this case, a control code V equal to T. is generated.

Fig. 5b shows a controlled permutation operation performed on an m - bit information block T, depending on the value of the l least significant bits of the information block. In this case, the control code V = T mod 2 ^l , where l <m, is generated.

 In FIG. 5c shows a controlled permutation operation performed on the information block T depending on the value of the control code V, which is generated by the current value of the information block by performing a 7-bit cyclic left shift operation on the information block.

 In FIG. 5d shows a controlled permutation operation performed on the information block T depending on the value of the subkey K, i.e. the value of the round subkey K is taken as the control code V

а управляемая операция перестановки выполняется над блоком t₁ в зависимости от значения управляющего кода V, в качестве которого используется подблок t₂.By controlled permutation operation we also mean such a controlled permutation operation that permutes the bits of a certain sub-block of an information block or permutes several bits of an information block, leaving the positions of the remaining bits unchanged. This case is shown in FIG. 4e, where the information block T is represented as the concatenation of two blocks t ₁ and t ₂ : E =

and a controlled permutation operation is performed on the block t ₁ depending on the value of the control code V, which is used as a subblock t ₂ .

Рассмотрим конкретные примеры реализации заявляемого способа криптографических преобразований блоков двоичных данных.In FIG. 5e shows a controlled permutation operation performed on the information block T, depending on the value of the control code V, which is generated by the current value of the information block and by subkey K by combining the current value of the information block and subkey: V =

Consider specific examples of the implementation of the proposed method of cryptographic transformations of binary data blocks.

 Example 1

Секретный ключ представлен в виде совокупности восьми подключей K₁, K₂,..., K₈. Шифрование осуществляется в виде поочередного преобразования информационных блоков. Преобразование каждого информационного блока описывается следующей последовательностью процедур:
1. Установить счетчик числа раундов преобразования r = 1.This example relates to the use of the proposed method for data encryption. The binary information code is divided into 64-bit information blocks, represented as a concatenation of sixteen 4-bit subblocks: T =

The secret key is represented as a combination of eight subkeys K ₁ , K ₂ , ..., K ₈ . Encryption is carried out in the form of alternate conversion of information blocks. The transformation of each information block is described by the following sequence of procedures:
1. Set the counter for the number of rounds of conversion r = 1.

где ":=" - обозначение операции присваивания и

обозначение управляемой операции перестановки, где в нижнем индексе указано значение двоичного вектора, от которого зависит конкретный вид перестановки, выполняемой на текущем шаге.2. Convert the information block T in accordance with the expression:
T: =

where ": =" is the designation of the assignment operation and

designation of the controlled permutation operation, where the value of the binary vector is indicated in the subscript, on which the specific type of permutation performed at the current step depends.

где "S(t_i)" - обозначение операции подстановки, выполняемой над подблоком t_i, где i = 1, 2, ..., 16, по следующей таблице:

Выполнение операции подстановки состоит в следующем. Вычисляется значение j = i mod 4. Вместо подблока со значением t_i подставляется двоичный вектор со значением стоящим на пересечении j -ой строки и t_i-го столбца.3. Convert the information block T in accordance with the expression:

where "S (t _i )" is the designation of the substitution operation performed on the subunit t _i , where i = 1, 2, ..., 16, according to the following table:

The implementation of the substitution operation is as follows. Calculated value j = i mod 4. Instead subblock with the value t _i is substituted with the binary vector value at the intersection of row and j th t _i th column.

 4. If r <8, then increment the counter (r: = r + 1) and go to step 2, otherwise Stop.

 In Example 1, step 3 describes the conversion procedure indicated by operation block E in FIG. 1. There are options for using other options of encryption procedures as procedure E, given in the following examples.

 Example 2

Секретный ключ представлен в виде шестнадцати 32-битовых подключей K₁, K₂, . .., K₁₆. Шифрование осуществляется в виде поочередного преобразования информационных блоков. Преобразование каждого информационного блока описываются следующей последовательностью шагов преобразования:
1. Установить счетчик числа раундов преобразования r = 1.This example relates to the use of the proposed method for data encryption. The binary information code is divided into 64-bit information blocks, presented in the form of concatenation of two 32-bit subblocks: T =

The private key is represented as sixteen 32-bit subkeys K ₁ , K ₂ ,. .., K ₁₆ . Encryption is carried out in the form of alternate conversion of information blocks. The conversion of each information block is described by the following sequence of conversion steps:
1. Set the counter for the number of rounds of conversion r = 1.

3. Преобразовать информационный блок T в соответствии с формулами:

где совокупность битов информационного блока, соответствующих подблоку t₂, сохраняется неизменной, а значение t₂ берется в качестве управляющего двоичного вектора, а управляемая операция перестановки над информационным блоком выполняется путем перестановки битов подблока t₁ в зависимости от подблока t₂.2. Convert the information block T in accordance with the expressions:
t ₁ : = t ₁ ⊕ K _2r-1 ,
T: =

3. Convert the information block T in accordance with the formulas:

where the set of bits of the information block corresponding to the subblock t ₂ remains unchanged, and the value of t ₂ is taken as a control binary vector, and the controlled permutation operation on the information block is performed by rearranging the bits of the subblock t ₁ depending on the subblock t ₂ .

5. Преобразовать информационный блок T в соответствии с выражениями:
t₂:= t₂ ⊕ K_2r,
T: =

6. Преобразовать информационный блок T в соответствии с выражением:

T:=

где совокупность битов информационного блока, соответствующих подблоку t₁, сохраняется неизменной, а значение t₁берется в качестве управляющего двоичного вектора, а управляемая операция перестановки над информационным блоком выполняется путем перестановки битов подблока t₂ в зависимости от подблока t₁.4. Convert the information block T in accordance with the expressions:
t ₁ : = t ₁ ⊕ t ₂ ,
T: =

5. Transform the information block T in accordance with the expressions:
t ₂ : = t ₂ ⊕ K _2r ,
T: =

6. Convert the information block T in accordance with the expression:

T: =

where the set of bits of the information block corresponding to the subblock t ₁ is kept unchanged, and the value t ₁ is taken as a control binary vector, and the controlled permutation operation on the information block is performed by rearranging the bits of the sub block t ₂ depending on the sub block t ₁ .

8. Если r < 8, то прирастить счетчик (r:= r+1) и перейти к шагу 2, в противном случае Стоп.7. Convert the information block T in accordance with the expression:
t ₂ : = t ₂ ⊕ t ₁ ,
T: =

8. If r <8, then increment the counter (r: = r + 1) and go to step 2, otherwise Stop.

 In the second example, steps 2, 4, 5, and 7 describe the conversion procedures performed on the information block and are particular versions of the procedures designated as operation blocks E in FIG. 1.

 Example 3

Схема преобразований поясняется на фиг. 6. Процедура вычисления хэш-функции описывается следующей последовательностью шагов преобразования:
1. Установить счетчик числа преобразуемых информационных блоков j = 1 и исходное значение хэш-функции H₀ = 0.This example relates to the use of the proposed method for computing a hash function of binary information M, which is divided into N information blocks T _j , where j = 1, 2, ..., N. The calculation of the hash function is carried out by sequentially performing one-way conversion over 128-bit T _j . 128-bit information blocks T _j are represented as concatenation of 64-bit subblocks: T ^j =

The transformation scheme is illustrated in FIG. 6. The hash function calculation procedure is described by the following sequence of conversion steps:
1. Set the counter of the number of converted information blocks j = 1 and the initial value of the hash function H ₀ = 0.

где v" = t_j" и v' = t_j'.2. Generate a control code V: V: =

where v "= t _j " and v '= t _j '.

4. Преобразовать информационный блок T_j в соответствии с выражением:

5. Присвоить хэш-функции значение H_j: = T_j ⊕ H_j-1.3. Convert the information block T _j in accordance with the expression:

4. Convert the information block T _j in accordance with the expression:

5. Assign the hash functions to H _j : = T _j ⊕ H _j-1 .

 6. If j <N, then increment the counter (j: = j +1) and go to step 2, otherwise Stop.

The value of H _N is the value of the hash function of the message M.

 Example 4

Секретный ключ представлен в виде восьми 32-битовых подключей K₁, K₂,..., K₈. Шифрование осуществляется в виде восьмикратного повторения совокупности процедур, образующихся один раунд преобразования и схематично показанных на фиг.7. Раунд преобразования в данном примере представляет собой последовательное выполнение расширяющей процедуры E₁, управляемой операции перестановки P₁ и сужающей процедуры E₂.This example relates to the use of the proposed method to build a data encryption algorithm. The binary information code is divided into 64-bit information blocks, presented in the form of concatenation of two 32-bit subblocks: T =

The secret key is presented in the form of eight 32-bit subkeys K ₁ , K ₂ , ..., K ₈ . Encryption is carried out in the form of eight-fold repetition of the set of procedures that form one round of transformation and are schematically shown in Fig.7. The transformation round in this example is the sequential execution of the expanding procedure E ₁ , the controlled operation of the permutation P ₁ and the narrowing procedure E ₂ .

2. Над 64-битовым двоичным вектором B₀ осуществить (фиксированную) операцию перестановки π: B₁:= π (B₀).At the input of procedure E ₁ , a 64-bit information block is presented, presented in the form of two 32-bit data subblocks t ₁ and t ₂ , which are converted into an expanded output data block, presented in the form of three subblocks t ₂ , B ₂ and t ₁ . Subblock B _{2 is} generated in accordance with the following sequence of operations:
1. Combine the current round subkey K _r and the subblock t ₂ into a 64-bit binary vector B ₀ : =

2. Over the 64-bit binary vector B _0, perform the (fixed) permutation operation π: B ₁ : = π (B ₀ ).

3. Calculate the 64-bit binary vector B ₂ in accordance with the formula: B ₂ : = (B ₁ + t ₂ ) mod 2 ⁶⁴ .

The information input of the operating unit of permutations P ₁ serves subblocks t ₂ , B ₂ and t ₁ , and a round subkey K _r is fed to the control input of block P ₁ . The controlled operational permutation block P ₁ transfers information subblocks t ₂ and t ₁ without rearranging the bits of these two subblocks and permutes the bits of the information subblock B ₂ supplied to the input of the managed operational block P, which is part of the operational block P ₁ .

Управляемая операция перестановки осуществляется как перестановка битов подблока B₂ в зависимости от подблока данных t₂ и текущего раундового подключа K_r: B₃ = P_V(B₂), где управляющий код V зависит от информационного подблока t₂ и от подключа K_r: V =

На выходе управляемого операционного блока перестановок выводятся подблоки t₂, B₃ и t₁, которые составляют входной информационный блок для процедуры E₂.The information sub-block B ₂ is fed to the information input of the controlled operational permutation block P, and the control code V is the control input of block P, which is the combination of the information sub-block t ₂ and the round subkey K _r : V =

The controlled permutation operation is carried out as the permutation of the bits of subblock B ₂ depending on the data subblock t ₂ and the current round subkey K _r : B ₃ = P _V (B ₂ ), where the control code V depends on the information subblock t ₂ and on the subkey K _r : V =

At the output of the controlled operational permutation block, subblocks t ₂ , B ₃ and t ₁ are output, which make up the input information block for procedure E ₂ .

2. Сложить по модулю 2³² подблоки b" и b': b''':= (b"+b')mod 2³².Procedure E ₂ performs a narrowing transformation and generates two 32-bit data subblocks t "and t 'at the output, with t' = t ₂ , and the subblock t" is formed using the following steps:
1. Represent the 64-bit subblock B ₃ as the concatenation of two 32-bit subblocks b "and b ': B ₃ =

2. Add modulo 2 ³² subblocks b "and b ': b"'': = (b "+ b') mod 2 ³² .

3. Generate a subunit t ": = t ₁ ⊕ b '''.

Пример 5.In total, 8 such conversion rounds are performed. The values of t "and t 'generated in the rth round, where r ≤ 7, are taken as the input data information block (represented as two subunits t ₂ and t ₁ ) for the subsequent (r + 1) th round. Concatenation the values of t "and t 'generated in the eighth round are taken as an encrypted data block C =

Example 5

Блочное криптографическое преобразование значения H₀ выполняется в виде N-раундового преобразования в соответствии со следующим алгоритмом :
1. Установить счетчик числа раундов преобразования j = 1.This example relates to the use of the proposed method for constructing an algorithm for computing the hash function of a message M. The binary vector H ₀ having a length of 128 bits is taken as additional binary information. Message M is represented as a concatenation of 128-bit blocks M _i , where i = 1, 2, ..., N: M =

Block cryptographic conversion of the value of H ₀ is performed as an N-round conversion in accordance with the following algorithm:
1. Set the counter for the number of rounds of transformation j = 1.

где M_j - соответствующий блок сообщения M.2. Generate a control code V by the value of M: V: =

where M _j is the corresponding message block M.

3. Calculate the information block H _j in accordance with the expression:
H _j : = P _V (H _j-1 ) ⊕ M _j
4. If j <N, then increment the counter (j: = j + 1) and go to step 2; otherwise, take the value of H _N as the value of the hash function of message M.

 5. STOP.

 The above examples show that the proposed method of cryptographic transformations of binary data blocks is technically feasible and allows us to solve the problem.

 Due to its simple structure, modern silicon planar technology makes it easy to manufacture cryptographic microprocessors containing controlled permutation blocks with input sizes of 32, 64 and 128 bits. The inventive method can be implemented, for example, in specialized cryptographic microprocessors, providing an encryption speed of about 500 Mbit / s, sufficient for real-time encryption of data transmitted via high-speed fiber-optic communication channels.

Claims (5)

 1. The method of block cryptographic conversion of binary information, including splitting the binary code of information into N ≥ 1 information blocks and sequentially converting information blocks, characterized in that they further form a control code V and, when converting the information block, at least one controlled operation is performed on the information block permutations depending on the value of the control code V.  2. The method according to claim 1, characterized in that the control code V is formed by a secret key.  3. The method according to claim 1, characterized in that the control code V is formed by the current value of the converted information block.  4. The method according to claim 1, characterized in that the control code V is generated by the secret key and by the current value of the converted information block.  5. The method according to claim 1, characterized in that the control code V is generated from additional binary information.

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