Cryptanalysis of group-based key agreement protocols using subgroup distance functions

Authors:
Dima Ruinskiy;Adi Shamir;Boaz Tsaban
Affiliations:
The Weizmann Institute of Science, Rehovot, Israel;The Weizmann Institute of Science, Rehovot, Israel;The Weizmann Institute of Science, Rehovot, Israel
Venue:
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Year:
2007

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Abstract

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. Our approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompson's group F, and show that it can break about half the keys within a few seconds on a single PC.