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arXiv · 1305.0548

Length-based attacks in polycyclic groups

David Garber·Delaram Kahrobaei·Ha T. Lam
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Abstract

After the Anshel-Anshel-Goldfeld (AAG) key-exchange protocol was introduced in 1999, it was implemented and studied with braid groups and with the Thompson group as its underlying platforms. The length-based attack, introduced by Hughes and Tannenbaum, has been used to extensively study AAG with the braid group as the underlying platform. Meanwhile, a new platform, using polycyclic groups, was proposed by Eick and Kahrobaei. In this paper, we show that with a high enough Hirsch length, the polycyclic group as an underlying platform for AAG is resistant to the length-based attack. In particular, polycyclic groups could provide a secure platform for any cryptosystem based on conjugacy search problem such as non-commutative Diffie-Hellman, ElGamal and Cramer-Shoup key exchange protocols.

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David Garber, Delaram Kahrobaei, Ha T. Lam. 2013-05-02. Length-based attacks in polycyclic groups. https://arxiv.org/abs/1305.0548

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