Code-based schemes for digital signatures

Abstract

This article is devoted to the features of construction and use of electronic digital signature schemes based on the use of error-correcting codes, namely the most common scheme, which is based on this approach, CFS and the new proposed scheme. A functioning of these schemes directly depends on used code cryptosystem: the first basically contains principles of Niederreiter code cryptosystem, the second involves use of McEliece cryptosystem, which until recently was considered impossible. Algorithms for generating and verifying signatures according to both schemes, described step by step, are considered in detail. The article studies the efficiency of algorithms in terms of volume of required keys and the length of generated signature, the results of which are presented using analytical ratios and in graphical form for specific examples. The resistance of the considered schemes to classical and quantum cryptanalysis was also analyzed, the latter of which is a actual topic in the era of the rapid development of the sphere of post-quantum cryptography. Both schemes have provable resistance to both types of cryptanalysis, but when using quantum computers it is necessary to significantly increase the key lengths, which is a great shortcoming. It has been revealed that the proposed scheme has an indisputable advantage over the used CFS scheme - protection from specific attacks such as a simultaneous replacement of two signature elements and rapid falsification, by adding an additional element to the generated signature. During the study, the advantages, disadvantages and prospects of using the proposed scheme and the CFS scheme in terms of use of quantum computers are highlighted.