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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2020, Number 2, Pages 3–10
(Mi basm528)
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This article is cited in 2 scientific papers (total in 2 papers)
Research articles
New form of the hidden logarithm problem and its algebraic support
D. N. Moldovyan St. Petersburg Institute for Informatics and Automation
of Russian Academy of Sciences,
14-th line 39, 199178, St. Petersburg,
Russia
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.
Keywords and phrases:
finite associative algebra, non-commutative algebra, right-sided unit, left-sided unit, local units, discrete logarithm problem, hidden logarithm problem, post-quantum cryptography, digital signature.
Received: 08.02.2019
Citation:
D. N. Moldovyan, “New form of the hidden logarithm problem and its algebraic support”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 2, 3–10
Linking options:
https://www.mathnet.ru/eng/basm528 https://www.mathnet.ru/eng/basm/y2020/i2/p3
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Abstract page: | 160 | Full-text PDF : | 34 | References: | 9 |
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