Abstract:The aim of the research was to conduct a cryptographic analysis of an encryption scheme developed on the basis of nonpositional polynomial notations to estimate the algorithm strength. Nonpositional polynomial notations (NPNs) are residue number systems (RNSs) based on irreducible polynomials over GF(2). To evaluate if the algorithms developed on the basis of NPNs are secure, mathematical models of cryptanalysis involving algebraic, linear and differential methods have been designed. The cryptanalysis is as follows. A system of nonlinear equations is obtained from a function transforming plaintext into ciphertext with a key. Next, a possibility of transition of the nonlinear system to a linear one is considered. The cryptanalysis was conducted for the cases with known: 1) ciphertext; 2) plaintext and the related ciphertext; 3) plaintext file format; and 4) ASCII-encoded plaintext.
This paper proposes the new hash algorithm HBC-256 (Hash based on Block Cipher) based on the symmetric block cipher of the CF (Compression Function). The algorithm is based on the wipe-pipe construct, a modified version of the Merkle-Damgard construct. To transform the block cipher CF into a one-way compression function, the Davis-Meyer scheme is used, which, according to the results of research, is recognized as a strong and secure scheme for constructing hash functions based on block ciphers. The symmetric CF block cipher algorithm used consists of three transformations (Stage-1, Stage-2, and Stage-3), which include modulo two addition, circular shift, and substitution box (four-bit S-boxes). The four substitution boxes are selected from the “golden” set of S-boxes, which have ideal cryptographic properties.
The HBC-256 scheme is designed to strike an effective balance between computational speed and protection against a preimage attack. The CF algorithm uses an AES-like primitive as an internal transformation.
The hash image was tested for randomness using the NIST (National Institute of Standards and Technology) statistical test suite, the results were examined for the presence of an avalanche effect in the CF encryption algorithm and the HBC-256 hash algorithm itself. The resistance of HBC-256 to near collisions has been practically tested.
Since the classical block cipher key expansion algorithms slow down the hash function, the proposed algorithm is adapted for hardware and software implementation by applying parallel computing. A hashing algorithm was developed that has a sufficiently large freedom to select the sizes of the input blocks and the output hash digest. This will make it possible to create an almost universal hashing algorithm and use it in any cryptographic protocols and electronic digital signature algorithms
This paper addresses to structures and properties of the cryptographic information protection algorithm model based on NPNs and constructed on an SPnetwork. The main task of the research is to increase the cryptostrength of the algorithm. In the paper, the transformation resulting in the improvement of the cryptographic strength of the algorithm is described in detail. The proposed model is based on an SP-network. The reasons for using the SP-network in this model are the conversion properties used in these networks. In the encryption process, transformations based on S-boxes and P-boxes are used. It is known that these transformations can withstand cryptanalysis. In addition, in the proposed model, transformations that satisfy the requirements of the "avalanche e ect" are used. As a result of this work, a computer program that implements an encryption algorithm model based on the SP-network has been developed.
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