International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Length-Based Attacks for Certain Group Based Encryption Rewriting Systems

J. Hughes
A. Tannenbaum
Search ePrint
Search Google
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.
  title={Length-Based Attacks for Certain Group Based Encryption Rewriting Systems},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Braid Group, Length attack, Conjugacy Search Problem AAG AAFG},
  note={Workshop SECI02 SEcurit? de la Communication sur Intenet , September, 2002, Tunis, Tunisa. 12196 received 23 May 2003},
  author={J. Hughes and A. Tannenbaum},