Finite Non-commutative Associative Algebras for Setting the Hidden Discrete Logarithm Problem and Post-quantum Cryptoschemes on its Base
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MOLDOVYAN, Nikolay. Finite Non-commutative Associative Algebras for Setting the Hidden Discrete Logarithm Problem and Post-quantum Cryptoschemes on its Base. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, nr. 1(89), pp. 71-78. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1(89) / 2019 / ISSN 1024-7696 /ISSNe 2587-4322

Finite Non-commutative Associative Algebras for Setting the Hidden Discrete Logarithm Problem and Post-quantum Cryptoschemes on its Base

CZU: 512.552.18
MSC 2010: 94A60, 16Z05, 14G50, 11T71, 16S50.

Pag. 71-78

Moldovyan Nikolay
 
Institute for Informatics and Automation of Russian Academy of Sciences Sankt Petersburg
 
Disponibil în IBN: 16 august 2019


Rezumat

The paper considers finite non-commutative associative algebras every of which contains a large set of the global one-sided (right and left) units. Formulas describing all of the global units are derived for each of the algebras. Finite algebras of such type are introduced as carriers of the hidden discrete logarithm problem that is defined in three new forms. One of them is used to design the post-quantum cryptoscheme for public key-distribution. Two others are applied to design the postquantum digital signature schemes.

Cuvinte-cheie
finite associative algebra, non-commutative algebra, right unit, set of global units, discrete logarithm problem, Digital signature, post-quantum cryptography