Algebraic and quantum attacks on two digital signature schemes

Vitaly Roman'kov; Alexander Ushakov; Vladimir Shpilrain

doi:10.1515/jmc-2022-0023

Algebraic and quantum attacks on two digital signature schemes

Vitaly Roman'kov
, Alexander Ushakov
, Vladimir Shpilrain

Department of Mathematical Sciences

RAS - Sobolev Institute of Mathematics, Siberian Branch
City University of New York

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

6 Scopus citations

Abstract

In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum safe. We also show that in many cases these schemes are, in fact, vulnerable to "classical"algebraic cryptanalysis.

Original language	English
Article number	20220023
Journal	Journal of Mathematical Cryptology
Volume	17
Issue number	1
DOIs	https://doi.org/10.1515/jmc-2022-0023
State	Published - 1 Jan 2023

Keywords

algebraic cryptanalysis
associative algebra
digital signature
hidden subgroup problem
noncommutative algebra
post-quantum cryptography
quantum attack

Access to Document

10.1515/jmc-2022-0023

Cite this

@article{d975b44f93354ca7bee0f992222e58ab,

title = "Algebraic and quantum attacks on two digital signature schemes",

abstract = "In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum safe. We also show that in many cases these schemes are, in fact, vulnerable to {"}classical{"}algebraic cryptanalysis.",

keywords = "algebraic cryptanalysis, associative algebra, digital signature, hidden subgroup problem, noncommutative algebra, post-quantum cryptography, quantum attack",

author = "Vitaly Roman'kov and Alexander Ushakov and Vladimir Shpilrain",

note = "Publisher Copyright: {\textcopyright} 2023 the author(s), published by De Gruyter.",

year = "2023",

month = jan,

day = "1",

doi = "10.1515/jmc-2022-0023",

language = "English",

volume = "17",

number = "1",

}

TY - JOUR

T1 - Algebraic and quantum attacks on two digital signature schemes

AU - Roman'kov, Vitaly

AU - Ushakov, Alexander

AU - Shpilrain, Vladimir

PY - 2023/1/1

Y1 - 2023/1/1

N2 - In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum safe. We also show that in many cases these schemes are, in fact, vulnerable to "classical"algebraic cryptanalysis.

AB - In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum safe. We also show that in many cases these schemes are, in fact, vulnerable to "classical"algebraic cryptanalysis.

KW - algebraic cryptanalysis

KW - associative algebra

KW - digital signature

KW - hidden subgroup problem

KW - noncommutative algebra

KW - post-quantum cryptography

KW - quantum attack

UR - https://www.scopus.com/pages/publications/85148725807

UR - https://www.scopus.com/pages/publications/85148725807#tab=citedBy

U2 - 10.1515/jmc-2022-0023

DO - 10.1515/jmc-2022-0023

M3 - Article

AN - SCOPUS:85148725807

SN - 1862-2976

VL - 17

JO - Journal of Mathematical Cryptology

JF - Journal of Mathematical Cryptology

IS - 1

M1 - 20220023

ER -

Algebraic and quantum attacks on two digital signature schemes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this