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BraidBased Cryptography
, 2004
"... We survey some of the recently developed cryptographic schemes involving Artin's braid groups, as well as the attacks against these schemes. ..."
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We survey some of the recently developed cryptographic schemes involving Artin's braid groups, as well as the attacks against these schemes.
Polynomial time solutions of computational problems in noncommutativealgebraic cryptography
"... ..."
TOWARDS GENERATING SECURE KEYS FOR BRAID CRYPTOGRAPHY
"... Abstract. Braid cryptosystem was proposed in CRYPTO 2000 as an alternate publickey cryptosystem. The security of this system is based upon the conjugacy problem in braid groups. Since then, there have been several attempts to break the braid cryptosystem by solving the conjugacy problem in braid gr ..."
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Abstract. Braid cryptosystem was proposed in CRYPTO 2000 as an alternate publickey cryptosystem. The security of this system is based upon the conjugacy problem in braid groups. Since then, there have been several attempts to break the braid cryptosystem by solving the conjugacy problem in braid groups. In this paper, we first survey all the major attacks on the braid cryptosystem and conclude that the attacks were successful because the current ways of random key generation almost always result in weaker instances of the conjugacy problem. We then propose several alternate ways of generating hard instances of the conjugacy problem for use braid cryptography. 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).
An Overview of Braid Group Cryptography
, 2004
"... The past several years have seen an explosion of interest in the cryptographic applications of noncommutative groups. Braid groups in particular are especially desirable, as they provide di#cult computational problems and can be implemented quite e#ciently. Several di#erent groups of researcher ..."
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The past several years have seen an explosion of interest in the cryptographic applications of noncommutative groups. Braid groups in particular are especially desirable, as they provide di#cult computational problems and can be implemented quite e#ciently. Several di#erent groups of researchers have proposed numerous cryptographic protocols that make use of braid groups, but unfortunately, flaws have been found in nearly every one.
Gröbner Basis Cryptosystems
 AAECC
, 2005
"... In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings. Over free monoids, we adapt the known theory for right ideals and prove versions of Macaulay’s basis theorem, the Buchberger criterion, and the Buchberger algorithm. Over monoid ..."
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In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings. Over free monoids, we adapt the known theory for right ideals and prove versions of Macaulay’s basis theorem, the Buchberger criterion, and the Buchberger algorithm. Over monoids presented by a finitely generated convergent string rewriting system we generalize Madlener’s Gröbner basis theory based on prefix reduction from right ideals to right modules. After showing how these Gröbner basis theories relate to classical grouptheoretic problems, we use them as a basis for a new class of cryptosystems that are generalizations of the cryptosystems described in [2] and [8]. Well known cryptosystems such as RSA, ElGamal, Polly Cracker, Polly Two and a braid group cryptosystem are shown to be special cases. We also discuss issues related to the security of these Gröbner basis cryptosystems.
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.
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.
Key Agreement and Authentication Scheme Using NonCommutative Semigroups
, 2007
"... We give a new twopass authentication scheme, which is a generalisation of an authentication scheme of SibertDehornoyGirault based on the DiffieHellman conjugacy problem. Compared to the above scheme, for some parameters it is more efficient with respect to multiplications. We sketch a proof that ..."
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We give a new twopass authentication scheme, which is a generalisation of an authentication scheme of SibertDehornoyGirault based on the DiffieHellman conjugacy problem. Compared to the above scheme, for some parameters it is more efficient with respect to multiplications. We sketch a proof that our authentication scheme is secure.