Public-key cryptosystem based on invariants of diagonalizable groups

František Marko; Alexandr N. Zubkov; Martin Juráš

doi:10.1515/gcc-2017-0003

Public-key cryptosystem based on invariants of diagonalizable groups

František Marko, Alexandr N. Zubkov, Martin Juráš

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).

Original language	English
Pages (from-to)	31-54
Number of pages	24
Journal	Groups, Complexity, Cryptology
Volume	9
Issue number	1
DOIs	https://doi.org/10.1515/gcc-2017-0003
Publication status	Published - May 1 2017
Externally published	Yes

Keywords

Cryptosystem
diagonalizable group
invariants
number field
supergroup

ASJC Scopus subject areas

Computer Networks and Communications
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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abstract = "We develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).",

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AB - We develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).

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KW - diagonalizable group

KW - invariants

KW - number field

KW - supergroup

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Public-key cryptosystem based on invariants of diagonalizable groups

Abstract

Keywords

ASJC Scopus subject areas

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