Advanced code-based electronic digital signature scheme

Abstract

The article is devoted to the study and research of the properties of code-based cryptosystems. They provide a high level of security even in the conditions of quantum cryptographic analysis, i.e. belong to the new generation of cryptosystems for post-quantum application. The main disadvantage of the known code-based digital signature schemes is the long time to generate a signature. This is due to the large number of attempts to decode a randomly generated vector (which is interpreted as a syndrome vector). The high complexity of such a procedure requires the search for new mechanisms and algorithms that would accelerate the formation of code-base electronic signatures. The article presents the results of two research vectors. First, we propose a new code-based digital signature scheme on the use of a one-way function from the classical McEliece cryptosystem and not only provides a proper level of resistance to classical cryptanalysis and cryptanalysis using quantum computers, but also, compared to known alternatives, provides protection against special types of attacks, such as simultaneous counterfeit attacks. Quantitative estimates of the reliability and speed of the new cryptographic algorithm, which were obtained by experimental verification on the BCH codes, are also given. The second vector of research concerns the study of a new direction, which is associated with the modification of the decoder by artificially increasing the corrective code ability. Thanks to the improved decoder scheme, we can significantly reduce the generation time of signatures. The paper confirms the effectiveness of the proposed decoder modification in the implementation of a new digital signature scheme in comparison with the classic Peterson-Gorenstein-Zierler decoder in the context of comparing the speed of signature formation and the number of required decoding attempts.