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Paper 2003/102

Length-Based Attacks for Certain Group Based Encryption Rewriting Systems

J. Hughes, and A. Tannenbaum

Abstract

In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of the property that in the given group the word problem has a polynomial time solution, while the conjugacy problem has no known polynomial solution. An example is the braid group from topology in which the word problem is solvable in polynomial time while the only known solutions to the conjugacy problem are exponential. The attack in this paper is based on having a canonical representative of each string relative to which a length function may be computed. Hence the term length attack. Such canonical representatives are known to exist for the braid group.

Note: Updated since the proceedings.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Workshop SECI02 SEcurité de la Communication sur Intenet , September, 2002, Tunis, Tunisa.
Keywords
Braid GroupLength attackConjugacy Search Problem AAG AAFG
Contact author(s)
james_hughes @ StorageTek com
History
2003-05-29: received
Short URL
https://ia.cr/2003/102
License
Creative Commons Attribution
CC BY
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