Article

# Conjugacy in Garside Groups III: Periodic braids

Journal of Algebra (Impact Factor: 0.6). 10/2006; DOI: 10.1016/j.jalgebra.2007.02.002

Source: arXiv

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**ABSTRACT:**In the last decade, a number of public key cryptosys-tems based on combinatorial group theoretic problems in braid groups have been proposed. Our tutorial is aimed at presenting these cryptosystems and some known attacks on them. We start with some basic facts on braid groups and on the Gar-side normal form of its elements. We then present some known algorithms for solving the word problem in the braid group. After that, we present the major public-key cryptosystems based on the braid group. We then discuss some of the known attacks on these cryptosystems. We finish with a discussion of future directions.12/2007; - [Show abstract] [Hide abstract]

**ABSTRACT:**We propose a new public-key cryptosystem named conjugacy search problem-based Diffie–Hellman integrated encryption scheme (CSP-DHIES), by using conjugation-related assumptions for a special monoid of matrices of truncated multi-variable polynomials over the ring ℤ12 where the CSP is assumed to be intractable. Our construction can be viewed as the first noncommunicative variant of the well-known DHIES cryptosystem. Under the assumptions of the intractability of the CSP-based hash Diffie–Hellman problem and the CSP-based oracle Diffie–Hellman problem, our scheme is provably secure against both chosen-plaintext attacks and secure against chosen-ciphertext attacks. Our proofs are constructed in the standard model. We also discuss the possibility of implementing our proposal using braid groups. Copyright © 2011 John Wiley & Sons, Ltd.Security and Communication Networks 10/2011; 5(7):809 - 822. · 0.43 Impact Factor -

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