Random subgroups and analysis of the length-based and quotient attacks
In this paper we discuss generic properties of “random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they “sit” inside G in a very particular way. This gives a strong mathematical foundation...
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2008-04-01
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Online Access: | https://doi.org/10.1515/JMC.2008.003 |
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doaj-1238887c957d484ea3b7c40ad62a6d032021-09-06T19:39:35ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842008-04-0121296110.1515/JMC.2008.003Random subgroups and analysis of the length-based and quotient attacksMyasnikov Alexei G.Ushakov AlexanderIn this paper we discuss generic properties of “random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they “sit” inside G in a very particular way. This gives a strong mathematical foundation for cryptanalysis of several group-based cryptosystems and indicates on how to chose “strong keys”. To illustrate our technique we analyze the Anshel-Anshel-Goldfeld (AAG) cryptosystem and give a mathematical explanation of recent success of some heuristic length-based attacks on it. Furthermore, we design and analyze a new type of attack, which we term the quotient attacks. Mathematical methods we develop here also indicate how one can try to choose “parameters” in AAG to foil the attacks.https://doi.org/10.1515/JMC.2008.003braid group cryptographyrandom subgroup of a braid grouplength-based attackquotient attackcommutator key-exchange |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Myasnikov Alexei G. Ushakov Alexander |
spellingShingle |
Myasnikov Alexei G. Ushakov Alexander Random subgroups and analysis of the length-based and quotient attacks Journal of Mathematical Cryptology braid group cryptography random subgroup of a braid group length-based attack quotient attack commutator key-exchange |
author_facet |
Myasnikov Alexei G. Ushakov Alexander |
author_sort |
Myasnikov Alexei G. |
title |
Random subgroups and analysis of the length-based and quotient attacks |
title_short |
Random subgroups and analysis of the length-based and quotient attacks |
title_full |
Random subgroups and analysis of the length-based and quotient attacks |
title_fullStr |
Random subgroups and analysis of the length-based and quotient attacks |
title_full_unstemmed |
Random subgroups and analysis of the length-based and quotient attacks |
title_sort |
random subgroups and analysis of the length-based and quotient attacks |
publisher |
De Gruyter |
series |
Journal of Mathematical Cryptology |
issn |
1862-2976 1862-2984 |
publishDate |
2008-04-01 |
description |
In this paper we discuss generic properties of “random subgroups” of a given group G. It turns out that in many groups G (even in most exotic of them) the random subgroups have a simple algebraic structure and they “sit” inside G in a very particular way. This gives a strong mathematical foundation for cryptanalysis of several group-based cryptosystems and indicates on how to chose “strong keys”. To illustrate our technique we analyze the Anshel-Anshel-Goldfeld (AAG) cryptosystem and give a mathematical explanation of recent success of some heuristic length-based attacks on it. Furthermore, we design and analyze a new type of attack, which we term the quotient attacks. Mathematical methods we develop here also indicate how one can try to choose “parameters” in AAG to foil the attacks. |
topic |
braid group cryptography random subgroup of a braid group length-based attack quotient attack commutator key-exchange |
url |
https://doi.org/10.1515/JMC.2008.003 |
work_keys_str_mv |
AT myasnikovalexeig randomsubgroupsandanalysisofthelengthbasedandquotientattacks AT ushakovalexander randomsubgroupsandanalysisofthelengthbasedandquotientattacks |
_version_ |
1717770415412084736 |