An enhanced version of the hidden discrete logarithm problem and its algebraic support
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MOLDOVYAN, Dmitriy; MOLDOVYAN, Alexandr; MOLDOVYAN, Nikolay. An enhanced version of the hidden discrete logarithm problem and its algebraic support. In: Quasigroups and Related Systems. 2020, nr. 2(28), pp. 269-284. ISSN 1561-2848.
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Quasigroups and Related Systems
Numărul 2(28) / 2020 / ISSN 1561-2848

An enhanced version of the hidden discrete logarithm problem and its algebraic support

CZU: 512.548.2+519.7+519.246

Pag. 269-284

Moldovyan Dmitriy, Moldovyan Alexandr, Moldovyan Nikolay
 
St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences
 
Disponibil în IBN: 21 ianuarie 2021


Rezumat

A new approach is proposed to the development of the signature schemes based on the computational difficulty of the hidden discrete logarithm problem, which is characterized in the adoption of the criterion of elimination of periodicity associated with the value of the discrete logarithm in the construction of periodic functions based on the public parameters of the signature scheme. In line with the approach, a new signature scheme is proposed as candidate for post-quantum public-key cryptoscheme. Its algebraic support represents a 6-dimensional finite non-commutative associative algebra set over the field GF(p); which contains p2 global right-sided units. Every one of the lasts is the unit of one of p2 isomorphic finite non-commutative groups contained in the algebra. Every of the said groups contains commutative subgroups possessing 2-dimensional cyclicity and this feature is exploited to implement the enhanced criterion of providing security to the known and potential future quantum attacks.