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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

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A linear decomposition attack

Alexei Myasnikov / Vitaliĭ Roman'kov
  • Institute of Mathematics and Information Technologies, Omsk F. M. Dostoevsky State University, Mira, 55-A, Omsk 644077, Russia
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Published Online: 2015-04-18 | DOI: https://doi.org/10.1515/gcc-2015-0007


We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in all the schemes under consideration. Furthermore, we show that in this case, contrary to the common opinion, the typical computational security assumptions are not very relevant to the security of the schemes, i.e., one can break the schemes without solving the algorithmic problems on which the assumptions are based.

Keywords: Algebraic cryptography; Diffie–Hellman scheme; cryptanalysis; linear decomposition; linear representation

MSC: 94A60; 20F10

About the article

Received: 2015-01-08

Published Online: 2015-04-18

Published in Print: 2015-05-01

Funding Source: NSF

Award identifier / Grant number: DMS-1318716

Funding Source: RFBR

Award identifier / Grant number: 13-01-00239a

Funding Source: Russian Research Fund

Award identifier / Grant number: 14-11-00085

Citation Information: Groups Complexity Cryptology, Volume 7, Issue 1, Pages 81–94, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2015-0007.

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