RU2811065C1 - Method for byte-by-byte transmission of information using stream encryption - Google Patents

Abstract

FIELD: data encryption.

SUBSTANCE: SQ state matrix is created by writing numbers in order from 0 to 255. The option of constructing a KQ auxiliary key matrix is selected. The KQ auxiliary key matrix is calculated. The resulting SQL state matrix is calculated using the formula: SQL = SQ ⊕ KQ mod 256. The numeric values of the SQL matrix elements acre converted into the binary number system corresponding to the ASCII character table. Plaintext characters are written using the ASCII character table yielding the value of character X_i corresponding to the plaintext character, written in the binary system. One byte of ASCII characters, and one byte of an SQL matrix element, and one byte of X_i characters are summed by modulo two to obtain the encrypted message Y_i. The encrypted message Y_i is transmitted.

EFFECT: reduced time of encryption and decryption of text.

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Description

The invention relates to cryptography, in particular to stream encryption methods that use byte-by-byte information transfer based on the ASCII character encoding table.

The following terms are used in the description.

ASCII – (English: American standard code for information interchange) - the name of a table (encoding, set) in which numeric codes are associated with some common printed and non-printable characters.

Encryption algorithms are divided into two groups: symmetric encryption algorithms and asymmetric encryption algorithms. In symmetric encryption algorithms, which are also divided into two large groups: stream and block, the sender of information and the recipient of information have the same keys, and in asymmetric encryption algorithms the sender of information and the recipient of information have two keys each - public and private.

In symmetric encryption algorithms, the transmission of encryption keys is a weak point. For example, if a company consists of t branches, including the head office, then t·(t-1)/2 is required to ensure the exchange of information between all branches, but from time to time old keys must be replaced with new keys, which complicates the work.

Currently, stream encryption algorithms are widely used for plaintext encryption, which, unlike block encryption, transform information coming from the message source either one bit at a time or one byte (8 bits). Thus, the stream encryption algorithm can transform incoming information at the moment it is received.

The disadvantage of stream encryption, as noted earlier, is the need to obtain a new key (gamma) to encrypt incoming information. It is possible, instead of transmitting a new key, to calculate it, both on the side of the sender and the recipient of information using the same algorithm by means of matrix transformations based on the transmitted coefficients.

That is, instead of transmitting the key, exchange coefficients between the sender and recipient of information and, based on them, using matrix transformations, calculate the keys.

The RC-4 encryption algorithm is known - a class of algorithms determined by the size of its block or word - the parameter n. In the case when n = 8 bits or 1 byte, then the internal state of RC-4 (S-box) consists of an array of 2 ⁸ words in size, that is, the internal state includes 256 elements (0,1,2,….255 ).

The closest analogue to the claimed invention is the encryption method known from patent RU 2783406, which considers bit-stream encryption using matrix transformations.

However, when using this technical solution, each plaintext character must be translated into a set of zeros and ones in accordance with the alphabet used and added modulo two with the set of zeros and ones of the SQL matrix and sent this information to the recipient.

The advantage of the claimed invention is the use of a standard ASCII character encoding table for stream encryption.

The technical result of the invention is to simplify the process of encrypting and decrypting text, reducing time and computational costs.

In the proposed application, there is no need to convert each plaintext character into a set of zeros and ones - each character corresponds to its own number in the binary number system, which will be summed modulo two with an element of the resulting SQL matrix, also presented in the appropriate form and sent to the recipient of the information.

The essence of the claimed invention lies in the fact that in the method of byte-by-byte information transfer using stream encryption, a state matrix SQ is created, writing numbers in order from 0 to 255; select the option of constructing an auxiliary key matrix KQ; calculating the auxiliary key matrix KQ; calculate the resulting matrix SQL using the formula: SQL = SQ ⊕ KQ mod 256. Elements of the resulting matrix SQL(sql_ij) and will be the gamma (key) used when adding with plaintext characters. The resulting numeric values of the SQL matrix elements are converted to the binary number system corresponding to the ASCII character table, the plaintext characters are written using the ASCII character table, obtaining the value of the character X_i, corresponding to the plaintext character, written in binary number system and then sum modulo two one byte of ASCII characters corresponding to the plaintext character X_i with sql matrix element_ij, receiving encrypted message Y_i, transmit an encrypted message Y_i.

The use of n = 8 makes it possible to use a character table, for example, ASCII, in which characters - letters of the alphabet, numbers, arithmetic operations, and other characters are also represented as 8 bit values, for example character A - 01000001, character B - 01000010, character C – 01000011 and so on.

On the other hand, using an approach based on matrix transformations [Dedov O.P. Application of the matrix approach to stream encryption. Electronic scientific journal “E-Scio.ru”, 2021.-5с, hereinafter referred to as Source 1] it is possible to form a resulting matrix, the elements of which are a gamma (key), also consisting of 256 numbers written as 8 bit character values: 0 – 00000000, 1 – 00000001, 2 – 00000010, etc., and summing the plaintext characters and the elements of the resulting matrix (gamma) calculated using matrix transformations, modulo two to produce byte-by-byte encryption of the plaintext.

The claimed invention is illustrated in figures 1-2, which show:

- fig. 1 – diagram of the stream encryption algorithm;

- fig. 2 – block diagram of the proposed stream encryption algorithm.

On the figure 1 X_ii-th byte of plaintext and sql_ij SQL matrix element, written as a single byte, located in cell – K_i, where 0 ≤ i<≤255.

SQL is the resulting matrix, the elements of which are sql _ij [Source 1, S.A. Beletsky, O.P. Dedov, S.I. Zhuravlev. Construction of multi-layer and infinite scale for stream encryption. Industrial automated control systems and controllers. DOI: 10.25791/ asu.10.2022.1392 pp. 39-43 – further Source 2] are calculated using the formula

SQL= SQ + KQ mod 2 ⁿ , (1)

where SQ is the state matrix;

KQ – key matrix;

SQL is the resulting matrix, the elements of which, converted to the binary number system, will act as a gamma.

Moreover, in Source 1 it was shown that for n = 4, the parameter N, which determines the size of the square matrices SQ, KQ and SQL, is calculated using formula (1).

N= 2 ^4/2 = 2 ² = 4, (2)

That is, the matrices SQ, KQ and SQL with n = 4 are square matrices of size 4x4, and with n = 8 N will be equal to 16, which means that the matrices SQ, KQ and SQL will be square matrices of size 16x16, and each of them contains 256 elements (numbers). Each element of the SQL matrix (sgl _ij ) can be represented as a sequence of eight zeros and ones, that is, one byte.

Thus, each plaintext character X _i using the ASCII character table, written as a sequence of 8 bits, that is, one byte, can be added modulo two with the elements of the SQL matrix (sgl _ij ), each of which is also written as an eight-bit sequence (one byte), and as a result of this addition, Y _i is obtained - the encrypted value X _i, which is received as input by the recipient of the information and is decrypted there in reverse order, that is, by adding modulo two with the elements of the resulting matrix SQL(sgl _ij ), calculated by similar algorithm.

Source 2 discussed the calculation of square matrices SQ, KQ and SQL for n=4 and therefore N= 2 ^4/2 = 2 ² = 4, and the matrices SQ, KQ, SQL are 4x4 in size, in various ways.

That is, at the first stage there is a state matrix S (in the RC 4 algorithm) and a matrix SQ in the proposed encryption algorithm (n = 4 and 2 ⁴ = 16), which includes 16 number elements – 0,1,2,….15, arranged in order. At the second stage, the key matrix KQ is calculated - an analogue of the key matrix K in the RC 4 encryption algorithm (in various ways [Source 2]). At the third stage, the resulting matrix SQL is calculated as the sum of matrices SQ and KQ. All matrices SQ, KQ and SQL in [Source 2] have the same size - 4x4.

The matrix approach allows you to calculate the key matrix KQ in various ways [Source 2], for example, as the product of a column matrix of size 4 × 1 by a row matrix of size 1 × 4 modulo 2 ⁿ , and the elements of the column matrix and row matrix can also be chosen in different ways methods, either using a random number sensor DNS (among numbers in the range from 1 to 2 ⁿ -1) or selected as the product of a column matrix by a row matrix (both matrices are obtained from the state matrix S(RC-4) or SQ [Sources 1, 2].

In Sources 1,2 and the closest analogue, the calculation of matrices SQ, KQ, SQL for n=4 is considered.

Since n = 4, all calculations will be performed modulo 2 ⁴ , that is, modulo 16.

For n = 4, the state matrix SQ consists of 2 ⁴ elements and has the form:

SQ=

Let us calculate the key matrix KQ using one of the methods discussed in Source 2, as the product of the second column of the matrix SQ by the third row of this matrix modulo 16, that is

KQ = ×(8 9 10 11) = mod 16 (3)

The elements of the resulting SQL matrix will be calculated as the sum of the corresponding elements of the SQ and KQ matrices modulo 16.

SQL = SQ ⊕ KQ = mod 16

We will call this resulting matrix SQL, obtained as a result of a single addition of matrices SQ and KQ, single-layer [Source 2] and denote it as SQL ₁ . Source 2 shows the calculation of two-, three-layer matrices and multi-layer matrices in various ways, including multiplying the key matrix KQ by the constant µ ( 1 < µ ≤ 15 ) n=4.

The SQL ₂ matrix will be calculated using formula (1) and is called a two-layer matrix.

SQL₂ = SQL₁⊕ KQ mod 16

SQL ₂ =

In the case when information is transferred one byte at a time, that is, when n = 8, all matrices under consideration: the state matrix SQ, the key matrix KQ and the resulting matrix SQL will have a dimension of 16 × 16 and consist of 256 elements each. The SQ state matrix, consisting of 256 elements written in order, will look like:

0 1 2 3 4 5 6 7 8 9 10 eleven 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 thirty 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 223 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

Let us assume that the matrix KQ (for n = 8) is calculated similarly to the calculation of KQ (for n = 4), as in the example considered earlier, that is, as the product of the second column of the matrix SQ - ST(2,1) by the third row STR(3, 1) of this matrix, but modulo 256 instead of 16 (for n = 4). That is

KQ= ST(2) * STR(3)= *[32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47] mod 256 (4)

Thus, the KQ matrix will look like:

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 32 49 66 83 100 117 134 151 168 185 202 219 236 253 14 31 32 65 98 131 164 197 230 7 40 73 106 139 172 205 238 15 32 81 130 179 228 21 70 119 168 217 10 59 108 157 206 255 32 97 162 227 36 101 166 231 40 105 170 235 44 109 174 239 32 113 194 19 100 181 6 87 168 249 74 155 236 61 142 223 32 129 226 67 164 5 102 199 40 137 234 75 172 13 110 207 32 145 2 115 228 85 198 55 168 25 138 251 108 221 78 191 32 161 34 163 36 165 38 167 40 169 42 171 44 173 46 175 32 177 66 211 100 245 134 23 168 57 202 91 236 125 14 159 32 193 98 3 164 69 230 135 40 201 106 eleven 172 77 238 143 32 209 130 51 228 149 70 247 168 89 10 187 108 29 206 127 32 225 162 99 36 229 166 103 40 233 170 107 44 237 174 111 32 241 194 147 100 53 6 215 168 121 74 27 236 189 142 95 32 1 226 195 164 133 102 71 40 9 234 203 172 141 110 79 32 17 2 243 228 213 198 183 168 153 138 123 108 93 78 63

Then the SQL matrix which is equal to the sum of the SQ and KQ matrices is calculated by the formula

SQL = SQ ⊕ KQ mod 256, (5)

will take the following form:

32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 48 66 84 102 120 138 156 174 192 210 228 246 8 26 44 62 64 98 132 166 200 234 12 46 80 114 148 182 216 250 28 62 80 130 180 230 24 74 124 174 224 18 68 118 168 218 12 62 96 162 228 38 104 170 236 46 112 178 244 54 120 186 252 62 112 194 20 102 184 10 92 174 0 82 164 246 72 154 236 62 128 226 68 166 8 106 204 46 144 242 84 182 24 122 220 62 144 2 116 230 88 202 60 174 32 146 4 118 232 90 204 62 160 34 164 38 168 42 172 46 176 50 180 54 184 58 188 62 176 66 212 102 248 138 28 174 64 210 100 246 136 26 172 62 192 98 4 166 72 234 140 46 208 114 20 182 88 250 156 62 208 130 52 230 152 74 252 174 96 18 196 118 40 218 140 62 224 162 100 38 232 170 108 46 240 178 116 54 248 186 124 62 240 194 148 102 56 10 220 174 128 82 36 246 200 154 108 62 0 226 196 166 136 106 76 46 16 232 212 182 152 122 92 62 16 2 244 230 216 202 188 174 160 146 132 118 104 90 76 62

In general, the SQL _i matrix is calculated using the formula:

SQL _i = SQL _i-1 + KQ mod 16, (6)

Each element of this matrix sql _ij , written in binary form using 8 bits, is supplied to the first input of the adder modulo two (Fig. 1), where it is added to the plaintext character X _i , which is also written in the form of 8 bits (when using ASCII ), and at the output of the adder the encrypted symbol Y _i is obtained, and decryption is performed in the reverse order on the side of the information recipient.

Thus, each character of the plaintext can be encrypted and transmitted to the recipient of the information.

Note that when encrypting, you can use the elements of the sql _ij matrix in order, that is, starting with the first sql ₁₁ (the first character of the plaintext will be summed modulo two with sql ₁₁ ) and ending with the last sql _255,255 or, as stated in Source 1, the elements of this matrix can be used in reverse order, that is, from sql _255,255 to sql ₁₁ .

In addition, when applying the matrix approach, it is possible to use a group of elements (40-100) of the SQL matrix ₁ to encrypt part of the plaintext, and then move on to the same elements of the SQL matrix ₂ to encrypt the second part of the plaintext, etc.

This algorithm can be implemented as follows. Firstly, you can exchange the values of SQL matrices in advance - for a certain period (day, month) between the sender and recipient of the information. Secondly, at the “Handshakes” stage (Fig. 2), an exchange of coefficients takes place between the sender and the recipient of information, for which numbers can be used, or elements generated with the help of the random number are selected from numbers from 1 to 255, corresponding elements of the column matrix (16 numbers) and the row matrix (16 numbers), and the KQ matrix is calculated as their product, or, as in the previously discussed examples, you can specify the column number (α1) and row number (α2), when multiplied modulo 256 the key matrix KQ is obtained, you can also indicate the value of the coefficient µ (α3), which can be used when calculating the KQ matrix [Source 2] (in this work it was equal to 5), and also indicate the number of elements (α4) used in encryption, if it was decided to use 40-100 characters of the SQL ₁ matrix when encrypting, and then move on to the SQL ₂ matrix and then to the SQL _i matrix, and in this case it is necessary to indicate the number of the element K _i (α5) from which the report begins. All these coefficients can be summarized in table No. 1.

Table No. 1.

Column number (α1) Line number (α2) Coefficient ( µ=5) (α3) Number of elements (α4) Element number K _i (α5) 2 3 5 40 100

Note that the numbers included in the column matrix (α1) or row matrix (α2) can be used as the coefficient µ.

Figure 2 shows a block diagram of the stream encryption algorithm, where:

- block No. 1 – SQ matrix initialization block;

- block No. 2 – program for calculating the KQ key matrix;

- block No. 3 – calculation of the resulting SQL state matrix;

- block No. 4 – counter of elements of the resulting SQL state matrix;

- block No. 5 – conversion from the decimal number system to the binary number system;

- block No. 6 – open text;

- block No. 7 – block for converting an open test into ASCII characters.

The method is carried out as follows.

The work cycle consists of several stages. At the first stage, the matrix SQ is initialized (block No. 1), that is, numbers are written into this matrix in order from 0 to 255 (with n = 8) and the key matrix KQ is calculated based on the coefficients from table No. 1 or in another way, for example , using the DNS, elements are selected from numbers from 1 to 255, corresponding to the elements of the column matrix (16 numbers) and the row matrix (16 numbers), and the KQ matrix is calculated as their product (3,4).

At the second stage, using formula (3), taking into account the calculated values of the KQ matrix and the values of the SQ matrix, the SQL matrix is calculated.

At the third stage, the numeric values of the SQL matrix elements are converted into the binary number system corresponding to the ASCII character table.

At the fourth stage, plaintext characters are written using the ASCII character table (block No. 6 and block No. 7), and at the output of block No. 7, the value of the character X _i is obtained, corresponding to the plaintext character, but written in the binary number system.

At the fifth stage, after modulo summation, two 8-bit symbols received from block No. 5 and 8 bits of symbols received from block No. 7 receive an encrypted message Y _i .

There is no problem arising from having out-of-range bytes. All bytes, both the plaintext character conversion and the encryption bytes (the elements of the SQL matrix) are in the range from 0 to 255, and after modulo two addition they will also be in this range. That is, a word of 8 bits (1 byte) corresponding to a plaintext character is added with an element of the matrix sql _ij , also consisting of 8 bits modulo two, and the result is a word of 8 bits (1 byte).

If the size of the plaintext, that is, the number of characters of the plaintext is 256, then the elements of the SQL matrix are sufficient to encrypt them₁(the number of which is 256), and if more than 256 , then upon command from the element counter a new SQL matrix will be generated₂(the number of elements of which is also 256) etc.

In addition, it is possible to use a certain number of characters (40-100) from the SQL matrix ₁ , and then from the SQL matrix ₂ , etc., which will make it impossible to decrypt the encrypted text.

In the proposed method, matrix operations are performed that do not require large computational and, as a consequence, time costs: matrices are not raised to a power and there is no calculation of inverse matrices (which may not exist), which greatly simplifies the use of this method in real practice.

Claims (11)

1. A method of byte-by-byte information transmission using stream encryption, characterized by the fact that: - create a state matrix SQ, writing numbers in order from 0 to 255; - choose the option of constructing an auxiliary key matrix KQ; - calculate the auxiliary key matrix KQ; - calculate the resulting SQL state matrix using the formula: SQL = SQ ⊕ KQ mod256; - convert the numeric values of the SQL matrix elements into the binary number system corresponding to the ASCII character table; - plaintext characters are written using an ASCII character table, obtaining the value of the character X _i corresponding to the plaintext character, written in the binary number system; - sum modulo two one byte of ASCII characters of the SQL matrix and one byte of X characters_i, receiving encrypted message Y_i. - transmit an encrypted message Y _i . 2. The method according to claim 1, characterized in that KQ is calculated using a random number sensor.

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