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14
Random subgroups and analysis of the lengthbased and quotient attacks
 Journal of Mathematical Cryptology
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Cryptanalysis of Shifted Conjugacy Authentication Protocol, ArXiv preprint
, 2006
"... Abstract. In this paper we present the first practical attack on the shifted conjugacybased authentication protocol proposed by P. Dehornoy in [5]. We discuss the weaknesses of that primitive and propose ways to improve the protocol. 1. ..."
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Abstract. In this paper we present the first practical attack on the shifted conjugacybased authentication protocol proposed by P. Dehornoy in [5]. We discuss the weaknesses of that primitive and propose ways to improve the protocol. 1.
Braid Group Cryptography
, 2008
"... In the last decade, a number of public key cryptosystems based on combinatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, ..."
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In the last decade, a number of public key cryptosystems based on combinatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts on braid groups and on the Garside normal form of its elements, some known algorithms for solving the word problem in the braid group, the major publickey cryptosystems based on the braid group, and some of the known attacks on these cryptosystems. We conclude with a discussion of future directions (which includes also a description of cryptosystems which are based on other noncommutative groups).
On the Security of the ChaKoLeeHanCheon Braid Group Publickey Cryptosystem, ArXiv preprint
, 2007
"... We show that a number of cryptographic protocols using noncommutative semigroups including the ChaKoLeeHanCheon braid group cryptosystem have security based on the MSCSP. We give two algorithms to solve the DP using the MSCSP. 2. ..."
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We show that a number of cryptographic protocols using noncommutative semigroups including the ChaKoLeeHanCheon braid group cryptosystem have security based on the MSCSP. We give two algorithms to solve the DP using the MSCSP. 2.
A note on the shifted conjugacy problem in braid groups, Groups  Complexity  Cryptology 1(2
, 2009
"... Abstract It is an open problem whether the shifted conjugacy (decision) problem in B∞ is solvable. We settle this problem by reduction to an instance of the simultaneous conjugacy problem in Bn for some n ∈ N. Recall Artin's presentation of the braid group B n with n ≥ 2 strands [1]: The group ..."
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Abstract It is an open problem whether the shifted conjugacy (decision) problem in B∞ is solvable. We settle this problem by reduction to an instance of the simultaneous conjugacy problem in Bn for some n ∈ N. Recall Artin's presentation of the braid group B n with n ≥ 2 strands [1]: The groups B n (n ≥ 2) build an inductive system of groups, which has a direct limit: the braid group on innitely many strands B ∞ is generated by {σ 1 , σ 2 , . . .} subject to the same relations. The shifted conjugacy operation * : where ∂ : σ i → σ i+1 denotes the shift operator, is an example for a leftselfdistributive operation other than classical conjugacy. The shifted conjugacy (decision) problem (ShCP) in B ∞ , i.e., given (x, y) ∈ B 2 ∞ , decide whether there exists c ∈ B ∞ such that y = c * x was introduced in [3] and its search version had been been proposed as a base problem for an authentication scheme. According to