R. G. Biyashev, S. E. Nyssanbayeva

In the work the systems of the electronic digital signature (EDS) developed on the basis of not resulted polynomial over the field of item polynomial notations (FIPN) are considered. FIPN Bases are GF (2). Application of FIPN by the development of algorithms of symmetric enciphering and EDS formation allows us to raise essentially their crypto stability. Cryptographic algorithms at which creation FIPN are applied, are called not conventional. Known approaches to construction of systems of the digital signature can be divided into three groups: 1) schemes on the basis of dissymmetric systems of enciphering; 2) schemes with specially developed procedures of formation and check of EDS; 3) schemes on the basis of symmetric systems of enciphering. Used by development of algorithms of EDS formation the not conventional approach belongs to the second group. At the not conventional approach to creation of cryptosystems substantial increase of efficiency of algorithms, reduction of lengths of hash-value and EDS, and also paralleling operations are possible. The increase of crypto stability about five orders is received. Dependence of crypto stability on length of the message is more linear than in the first algorithm of EDS formation on modules of the several superfluous bases. It is caused by presence of restrictions on a choice of the superfluous basis and on formation of a full key. Algorithms of the formation of an electronic digital signature in the non-positional polynomial notation are considered. Digital signatures are created on the modulo surplus bases. The cryptostability of created algorithms is investigated.