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19
Lengthbased conjugacy search in the braid group
"... Several key agreement protocols are based on the following Generalized Conjugacy Search Problem: Find, given elements b1,..., bn and xb1x −1,..., xbnx −1 in a nonabelian group G, the conjugator x. In the case of subgroups of the braid group BN, Hughes and Tannenbaum suggested a lengthbased approac ..."
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Cited by 17 (3 self)
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Several key agreement protocols are based on the following Generalized Conjugacy Search Problem: Find, given elements b1,..., bn and xb1x −1,..., xbnx −1 in a nonabelian group G, the conjugator x. In the case of subgroups of the braid group BN, Hughes and Tannenbaum suggested a lengthbased approach to finding x. Since the introduction of this approach, its effectiveness and successfulness were debated. We introduce several effective realizations of this approach. In particular, a length function is defined on BN which possesses significantly better properties than the natural length associated to the Garside normal form. We give experimental results concerning the success probability of this approach, which suggest that an unfeasible computational power is required for this method to successfully solve the Generalized Conjugacy Search Problem when its parameters are as in existing protocols.
Quasigroups in cryptology
, 2009
"... We give a review of some known published applications of quasigroups in cryptology. ..."
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Cited by 4 (2 self)
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We give a review of some known published applications of quasigroups in cryptology.
Towards Provably Secure Group Key Agreement Building on Group Theory
, 2006
"... Known proposals for key establishment schemes basing on combinatorial group theory are often formulated in a rather informal manner. Typically, issues like the choice of a session identifier and parallel protocol executions are not addressed, and no security proof in an established model is prov ..."
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Known proposals for key establishment schemes basing on combinatorial group theory are often formulated in a rather informal manner. Typically, issues like the choice of a session identifier and parallel protocol executions are not addressed, and no security proof in an established model is provided. Successful attacks against proposed parameter sets for braid groups further decreased the attractivity of combinatorial group theory as a candidate platform for cryptography.
Decision and Search in NonAbelian CramerShoup Public Key Cryptosystem
, 2009
"... A method for nonabelian CramerShoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable / polycyclic group is suggested. In the process we review recent progress in nonabelian cryptography and post some open problems that naturally arise from this ..."
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A method for nonabelian CramerShoup cryptosystem is presented. The role of decision and search is explored, and the platform of solvable / polycyclic group is suggested. In the process we review recent progress in nonabelian cryptography and post some open problems that naturally arise from this path of research.
A Zeroknowledge Undeniable Signature Scheme in Nonabelian Group Setting
, 2008
"... Recently nonabelian groups have attracted the attention of cryptographers for constructing publickey cryptographic protocols. In this paper we use the conjugacy problem in nonabelian groups to construct a zeroknowledge undeniable signature scheme. ..."
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Recently nonabelian groups have attracted the attention of cryptographers for constructing publickey cryptographic protocols. In this paper we use the conjugacy problem in nonabelian groups to construct a zeroknowledge undeniable signature scheme.
Braid Compression
, 2004
"... In this paper, we describe the braid group, first mentioned in [2]. We give applications to cryptography mentioned in [1] and [8]. We then describe an apparently new method for shortening braid descriptions which could be useful for transmitting braids over a limited bandwidth channel. 1 ..."
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In this paper, we describe the braid group, first mentioned in [2]. We give applications to cryptography mentioned in [1] and [8]. We then describe an apparently new method for shortening braid descriptions which could be useful for transmitting braids over a limited bandwidth channel. 1
New PublicKey Cryptography Using Polynomials over NonCommutative Rings
, 2007
"... In this paper, we propose a new method for designing public key cryptosystems based on general noncommutative rings. The key idea of our proposal is that for a given noncommutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement ..."
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In this paper, we propose a new method for designing public key cryptosystems based on general noncommutative rings. The key idea of our proposal is that for a given noncommutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement DiffieHelmanlike key exchange protocol. And consequently, ElGamallike cryptosystems can be derived immediately. Moreover, we show how to extend our method to noncommutative groups (or semigroups).
Polynomial time solutions of computational problems in noncommutativealgebraic cryptography
, 2013
"... By introducing extra shields on Shpilrain and Ushakov’s KoLeelike protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly, if ..."
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By introducing extra shields on Shpilrain and Ushakov’s KoLeelike protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly, if the entities taking part in our protocols create their private keys composed by the generators of the Mihailova subgroups of Bn, we show that the safety of our protocols are very highly guarantied by the insolvability of subgroup membership problem of the Mihailova subgroups.
The Conjugacy Problem in Amalgamated Products I: Regular Elements and Black Holes
, 2009
"... We discuss the time complexity of the word and conjugacy search problems for free products G = A⋆C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the ..."
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We discuss the time complexity of the word and conjugacy search problems for free products G = A⋆C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups A,B, C.
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"... Abstract. We discuss the time complexity of the word and conjugacy problems for free products G = A ⋆C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum ..."
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Abstract. We discuss the time complexity of the word and conjugacy problems for free products G = A ⋆C B of groups A and B with amalgamation over a subgroup C. We stratify the set of elements of G with respect to the complexity of the word and conjugacy problems and show that for the generic stratum the conjugacy search problem is decidable under some reasonable assumptions about groups A, B, C. Moreover, the decision algorithm is fast on the generic stratum.