Cryptanalysis of the Public-Key Encryption Based on Braid Groups

Lee, Eon-Kyung; Park, Je Hong

doi:10.1007/3-540-39200-9_30

Cited by 26 publications

(14 citation statements)

References 14 publications

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“…Lee and Park also proposed solutions to CSP and DHCP using Burau representation by proposing two improvements to Hughes algorithm [24]. They showed that the private-key could be recovered from the public-key for several parameters with significant probability in a reasonable time.…”

Section: Using Representations Of Braid Groupsmentioning

confidence: 97%

Towards generating secure keys for braid cryptography

Lee

Thomas

2007

Des. Codes Cryptogr.

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Braid cryptosystem was proposed in CRYPTO 2000 as an alternate public-key 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 article, 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.

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Section: Using Representations Of Braid Groupsmentioning

confidence: 97%

Towards generating secure keys for braid cryptography

Lee

Thomas

2007

Des. Codes Cryptogr.

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“…The second one is some attacks based on length or complexity, see [11,14,16,20]. The third one uses linear representations, see [5,15,20,21]. The choice of the random generator play a part in the security of braid based schemes.…”

Section: Introductionmentioning

confidence: 99%

A Weak Key Test for Braid Based Cryptography

Maffre

2006

Des Codes Crypt

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This work emphasizes an important problem of braid based cryptography: the random generation of good keys. We present a deterministic, polynomial algorithm that reduces the conjugacy search problem in braid group. The algorithm is based on the decomposition of braids into products of canonical factors and gives a partial factorization of the secret: a divisor and a multiple. The tests we performed on different keys of existing protocols showed that many protocols in their current form are broken and that the efficiency of our attack depends on the random generator used to create the key. Therefore, this method gives new critera for testing weak keys. We also propose a new random generator of key which is secure against our attack and the one of Hofheinz and Steinwandt.

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“…Recently, several heuristic algorithms were proposed using Burau representation. Though they may be implemented in quite efficient way, they do not solve the whole problem (their methods do not work for some parameters), so no theoretical bounds have been written yet [6,14].…”

Section: Introductionmentioning

confidence: 99%

A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem

Cheon

Jun

2003

Advances in Cryptology - CRYPTO 2003

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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 , the complexity is about O(n 14.4 3.2 ) or O(n 4τ +2 2 ) bit operations for τ = log 2 7 ≈ 2.8 and > log 2 3 ≈ 1.57.

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Cryptanalysis of the Public-Key Encryption Based on Braid Groups

Cited by 26 publications

References 14 publications

Towards generating secure keys for braid cryptography

Towards generating secure keys for braid cryptography

A Weak Key Test for Braid Based Cryptography

A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem

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