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IMI/Publicaţii/BASM/Ediţii/BASM n.2(93), 2020/

New Form of the Hidden Logarithm Problem and its Algebraic Support

Authors: D. N. Moldovyan

Abstract

The paper introduces a new form of the hidden discrete logarithm problem defined over finite non-commutative associative algebras containing two-sided global unit and sets of local left-sided and right-sided units. The proposed form is characterized in using a new mechanism for masking the finite cyclic group in which the base exponentiation operation is performed. Local units act in frame of subsets of non-invertible vectors and are used as elements of the private key in the proposed post-quantum digital signature scheme. A new 4-dimensional algebra is introduced as algebraic support of the proposed cryptoscheme. Formulas describing units of different types are derived.

St. Petersburg Institute for Informatics and Automation
of Russian Academy of Sciences
14-th line 39, 199178, St. Petersburg
Russia
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