Introduction to algorithms
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
A Linear Algebraic Attack on the AAFG1 Braid Group Cryptosystem
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
New Key Agreement Protocols in Braid Group Cryptography
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Analysis and Improvements of NTRU Encryption Paddings
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Potential Weaknesses of the Commutator Key Agreement Protocol Based on Braid Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of a Pseudorandom Generator Based on Braid Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
A Practical Attack on Some Braid Group Based Cryptographic Primitives
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Complexity of the generalized conjugacy problem
Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
A Weak Key Test for Braid Based Cryptography
Designs, Codes and Cryptography
Towards generating secure keys for braid cryptography
Designs, Codes and Cryptography
A new hard problem over non-commutative finite groups for cryptographic protocols
MMM-ACNS'10 Proceedings of the 5th international conference on Mathematical methods, models and architectures for computer network security
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At CRYPTO 2000, a new public-key encryption based on braid groups was introduced. This paper demonstrates how to solve its underlying problem using the Burau representation. By this method, we show that the private-key can be recovered from the public-key for several parameters with significant probability in a reasonable time. Our attack can be mounted directly on the revised scheme mentioned at ASIACRYPT 2001 as well. On the other hand, we give a new requirement for secure parameters against our attack, which more or less conflicts with that against brute force attack.