# Differential Analysis of a Cryptographic Hashing Algorithm HBC-256
## 1 Introduction
Let us consider the approaches applied to the analysis of the strength of the Keccak hash calculation algorithm. Error injection attacks [7; 8] consist in generating a message containing an error using the Keccak algorithm to extract secure hash data. Paper [8] presents a new error detection scheme based on a modification of the Keccak architecture, where the Keccak round was subdivided into two blocks. The attack simulation results showed that the proposed attack scheme achieves 99.995% of the expected error generation. Also, the proposed attack scheme was evaluated from the point of view of hardware implementation on the FPGA. In the paper [8], an efficient error detection scheme based on the architecture of the Keccak algorithm was proposed. The round of the Keccak algorithm is divided into two sub-rounds and a pipeline register is implemented between them. The proposed scheme does not depend on the Keccak implementation method, so the method can be applied to both pipelined and iterative architectures. The article [9] describes the use of power analysis attacks that use the correlation power analysis (CPA) technique to extract the MAC-Keccak secret key. The proposed attack methodology uses simulated power signal traces and is applied to the design of the high-speed Keccak core given in the SHA-3 competition. A 1-bit, 2-bit, 4-bit, 8-bit, and 16-bit CPA selection function with key size guessing was investigated to analyze the computational complexity of successful MAC-Keccak key extraction. The experiments performed confirmed that the larger the size of the proposed key of the selection function, the fewer traces are required to extract the key, but with a subsequent increase in computation time. The work [10] is devoted to the study of differential error analysis of the family of SHA-3 algorithms, namely the SHA3-224 and SHA3-256 algorithms. The authors have developed an error injection model and increased the realism of the attack for various SHA-3 implementation architectures. The propagation of errors in the SHA-3 algorithm within the framework of one-byte error models was analyzed and the use of the error signature on the output value to extract secret information was proposed. The results of the study showed that the proposed method can effectively detect introduced single-byte errors and then restore all internal states of the last round operation for both SHA3-224 and SHA3-256. Later authors extended the application of the developed approach to an attack based on error injection and in the article [11] conducted a study of algebraic analysis of errors, which made it possible to detect injected failures with a much greater speed and restore the full internal state of the penultimate round with a smaller number of injected errors. The paper [12] explored practical attacks based on collision detection for the Keccak algorithm with a small number of rounds. The following main results were obtained in the work: a collision search attack against a 5-round Keccak-224 was described and a description of the collision search problem for a 6-round Keccak was presented. The attacks were implemented by carefully studying the algebraic properties of the nonlinear layer in the basic Keccak permutation and applying the linearization method. The authors proposed using methods of partial linearization of the output bits of the nonlinear layer, which significantly reduced the computational complexity of the attack. Cubic attacks on the Keccak algorithm and its variants (Keccak-MAC, KMAC, Keyak, and Ketje) were presented in [13]. In paper [14], when attacking Keccak-384/512 with a reduced number of rounds, the authors found that the revealed linear dependencies are not fully used. In order to maximize the use of all 448 and 320 linear dependencies identified for the Keccak-512 and Keccak-384 algorithms, respectively, the authors proposed a special algebraic attack based on the expression of output values in the form of a system of quadratic logical equations.