Abstract
We propose the first polynomial time algorithm for the braid Diffie-Hellman conjugacy problem (DHCP) on which the braid key exchange scheme and the braid encryption scheme are based [9]. We show the proposed method solves the DHCP for the image of braids under the Lawrence-Krammer representation and the solutions play the equivalent role of the original key for the DHCP of braids. Given a braid index n and a canonical length l, the complexity is about O(n 14.4 l 3.2) or O(n 4τ + 2ε l 2ε) bit operations for τ = log2 7 ≈ 2.8 and ε> log2 3 ≈ 1.57.
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Cheon, J.H., Jun, B. (2003). A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem. In: Boneh, D. (eds) Advances in Cryptology - CRYPTO 2003. CRYPTO 2003. Lecture Notes in Computer Science, vol 2729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45146-4_13
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DOI: https://doi.org/10.1007/978-3-540-45146-4_13
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