Today data confidentiality and privacy are ensured by various encryption algorithms (public key and secret key algorithms). There are no any universal encryption algorithms and different encryption algorithms are implemented to solve different security tasks. Many states have national standards of encryption but Kazakhstan hasn't it today. This paper presents an approach to the development of the Qalqan block symmetric encryption algorithm, taking into account complex cryptographic and operational requirements, as well as the cryptographic properties of the linear and nonlinear blocks of the algorithm that affect its cryptographic strength.
The Qalqan symmetric block encryption algorithm was developed by the team of the Information
Claude Shannon defined the basic principles of the reliability of ciphers, the principles of mixing (Confusion) and dispersion (Diffusion), and proposed to build strong cryptographic systems relatively using simple transformations.
Simple transformations make it possible to carry out cryptographic analysis of security with a high level of trust, as well as to guarantee the absence of “backdoors” of various kinds.
The development of the Qalqan block symmetric encryption algorithm was carried out taking into account all the principles of modern cryptography: 1. Using well-studied constructs and transformations.
2. Taking into account trends in the development of cryptography and cryptographic analysis of symmetric block encryption algorithms in order to ensure a “sufficient safety margin.” 3. Taking into account the trends in the development of computer technology to avoid the possibility of brute-force attacks and “rainbow tables.”
4. Taking into account the peculiarities of the implementation of the Qalqan block symmetric encryption algorithm in the software and hardware-software means of cryptographic information protection.
2022 Copyright for this paper by its authors. 3. Qalqan Block Symmetric Encryption Algorithm 3.1. Conventions
is the set of all binary strings of length s, where s is a natural number; numbering of substrings and string components is carried out from left to right, starting from zero; is inlet and outlet block length; is original encryption key length; is number of rounds of encryption algorithm; is source encryption key; ⨁ is modulo 2 addition; ⊞ is modulo 2128 addition; ⊟ is modulo 2128; ∔ is modulo 256 addition; ∸ is modulo 256 subtraction.
Algorithm architecture: LSX.
Block length: = 128 bit.
Key length: = 256. .1024 bit with 128 bit step. Number of rounds: = 17 + ⌊ 128 −256⌋ ∗ 2 (from 17 to 29 rounds).
Nonlinear bijective transformation : 128 → 128 is specified by substitution following order (0), . . , (255)): : 8 → 8 (in the
Byte 00 is replaced with eb, 01 with 89, ff with fa (values are in hexadecimal). Substitution is applied to all bytes of the processed block
Linear function : 128 → 128 converts an 16 byte input block B into an output block R of the same size as follows (bytes are numbered from high to low): 0 = 0 ∔ 1 ∔ 2 ∔ 3 4 = 4 ∔ 0 8 = 8 ∔ 0 12 = 12 ∔ 0 5 = 4 ∔ 5 ∔ 6 ∔ 7 1 = 1 ∔ 5 9 = 9 ∔ 5 13 = 13 ∔ 5 10 = 8 ∔ 9 ∔ 10 ∔ 11 2 = 2 ∔ 10 6 = 6 ∔ 10 14 = 14 ∔ 10 15 = 12 ∔ 13 ∔ 14 ∔ 15 3 = 3 ∔ 15 7 = 7 ∔ 15 11 = 11 ∔ 15
and ⨁ in the last).
Round keys are superimposed by modulo 2128adding with the processed data block (operation ⊞, where i – round number).
The keys of the first and last rounds are superimposed modulo 2 (operation in the first round ⨁
Each round of the algorithm except for the last one, includes sequentially key addition, nonlinear transformation and linear transformation, thus ( ) = ( ( ⊞( ))).
The last round contains only a modulo 2 key overlay operation.
The bytes of the key (starting with the least significant one) are fed in turn to the byte shift registers L0 and L1, starting from L0. Register L0 is 17 bytes long, L1 is 15 bytes long. Thus, a 256-bit key consisting of bytes { 0.. 31} fills the registers as follows: 0 = { 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 31}
1 = { 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29} The feedback of the shift registers is set as follows: 0 = { 01.. 016, ( 00)∔ 01 ∔ ( 03)∔ 07 ∔ ( 012)∔ 016}
1 = { 11.. 113, ( 10)∔ 13 ∔ ( 19)∔ 112 ∔ ( 114)}
The registers move uniformly, after the 17th step each value 015 ∔ 14 is filled into the byte of the next round key starting from the least significant.
For keys consisting of more than 256 bits, subsequent bytes in order from least significant to most significant are loaded into shift registers after the 17th step of operation by adding registers modulo 256 to the feedback function starting from register L1. Thus, at each even step of the registers, starting from the 18th, the value of the next byte of the key is superimposed on the feedback value of the L1 register, and at odd steps starting from the 19th - on the feedback value of the L0 register.
The encryption function consists of three parts and has the form: 1( ) = ( ( ⨁ ( ))) 2( ) = −1 (… 2 ( 1 ( 1( ( ) = ⨁ ( 2( )) The encryption algorithm schematically represented as follows: ))))
For decryption, functions opposite to those described above are used.
Non-linear function InvS is defined by substitution : 8 → 8 of the following kind (in the following order (0), . . , (255)):
Inverse linear operation : 128 → 128 converts 16 byte input block B to output block R of the same size as follows (bytes are numbered in ascending order): 1 = 1 ∸ 5 2 = 2 ∸ 10 3 = 3 ∸ 15 4 = 4 ∸ 0 6 = 6 ∸ 10 7 = 7 ∸ 15 8 = 8 ∸ 0 9 = 9 ∸ 5 11 = 11 ∸ 15 12 = 12 ∸ 0 14 = 14 ∸ 0 0 = 0 ∸ 1 ∸ 2 ∸ 3 5 = 5 ∸ 4 ∸ 6 ∸ 7 10 = 10 ∸ 8 ∸ 9 ∸ 11 15 = 15 ∸ 12 ∸ 13 ∸ 14
The round keys ⊟ are superimposed by modulo 2128subtraction. The keys of the first and last rounds are superimposed by modulo 2 operation.
One round of the decryption algorithm includes sequentially linear, non-linear transformations and key addition, thus ( ℎ ) = ⊟( ( ( ℎ )).
The decrypting operation of the Cipher ciphertext on round keys Key is represented as follows: 1( ℎ ) = ⨁ ( ℎ )
The correct choice of the characteristics of vector Boolean functions is the main factor in ensuring security, since they are the only non-linear node of the symmetric block encryption algorithm.
In this paper, the main cryptographic properties of the nonlinear node of the Qalqan symmetric block encryption algorithm, implemented as a vector Boolean function of 8 variables are investigated.
Due to the existence of serious claims to the secret internal structure of the nonlinear node of the
block symmetric encryption algorithm Kuznechik and the hash function Stribog [
For this, a similar to that used in the AES block symmetric encryption algorithm, the generation of
a replacement table according to proposed by K. Nyberg in 1991 [
As part of the research of the main cryptographic properties, the following properties shown in Table 1 were established.
The linear transformation of the Qalqan symmetric block cipher algorithm is built on a SQUARElike architecture and is a series of modulo 256 addition operations that propagate the influence of the bytes on each line of the intermediate state to the corresponding column. If we represent the state of the processed block in the form of a 4x4 byte matrix, then during the conversion to a byte located on the main diagonal (let's call it a diagonal byte), the remaining three bytes of this row are modulo 256summed, then the resulting sum is superimposed by adding modulo 256 to the rest three bytes located on the same column as the diagonal byte. Row and column additions occur independently of each other's results, i.e. changes in the state of the processing block are made immediately after all operations (figure 5).
To conclude about the effectiveness of the transformation, a comparison of the main characteristics with similar transformations of the symmetric block encryption algorithms AES [22] and Kuznechik [23] was made. Both algorithms are widely used and well enough studied to be considered as cryptographically strong, and are similar in main parameters to the Qalqan algorithm.
The difference between the Qalqan block symmetric encryption algorithm from most of the known algorithms is key overlay with bit transfer, i.e. instead of the XOR operation, modulo 2128 addition is used in the middle rounds of the algorithm. This operation has a positive effect on the complication of the relationship between the bits of encrypted data and increases the resistance to a number of modern attacks.
In this work, for the sake of purity of comparison, this feature of the algorithm will not be taken into account, since in the compared algorithms the key is overlaid by means of the XOR operation.
According to the principles of K. Shannon [
Ideally, when one bit of the key or data changes, half (on average) of the remaining bits of the block being processed after the linear operation should change. It is possible to construct such a block in practice (for example, using a linear shift register), but this is rarely used due to the high computational complexity of such transformation. In general, bit operations in modern processors and microcontrollers are relatively difficult to implement [20] in comparison with byte operations; therefore, it is advisable to consider byte-oriented transformations, which, nevertheless, are capable of ensuring the mutual influence of bits.
To provide the required avalanche effect, each byte must have an effect on the remaining bytes, while it is desirable to be different for bytes in different positions. The operations used in this case should also be significantly efficient in terms of memory and computational complexity, as well as being possible to implement on the maximum number of modern hardware platforms.
Measurement of the avalanche effect of linear transformations of the Qalqan, AES and Kuznechik algorithms for one, two and three rounds of the algorithm simulating the operation of an SP-network showed the following results:
To simulate the operation of several rounds of the symmetric block encryption algorithm an overlay of fixed bytes obtained using the standard pseudo-random number generator of the stdlib.h library between linear operations and byte substitution used in the Qalqan algorithm were added.
The measurement of the execution time of linear operations for the algorithms Qalqan, AES and Kuznechik has been carried out. For this, linear transformations of these algorithms are implemented and their speed is compared. Since each individual transformation is performed quickly, the measurement was made for large (on the order of hundreds of thousands) series of transformations separately with enabled and disabled optimization. Results are presented in the following tables:
The linear transformation of the Kuznechik algorithm for time optimization requires preliminary initialization of 9 tables of 256 bytes each.
Thus, it has been proven that the speed of linear transformation is significantly higher than world analogues. Moreover, as in the AES algorithm, there is a possibility of parallel implementation of the conversion into four threads, as well as implementation in single (one) clock cycle on FPGA [21].
It should be noted the simplicity of the implementation of the linear transformation of the Qalqan algorithm, since it contains only modulo 256 addition operations. Thus, when operating with 8-bit variables, the programmer uses only the addition operation. 7. References