How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Synthesizers and their application to the parallel construction of pseudo-random functions
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Word Processing in Groups
New Public-Key Cryptosystem Using Braid Groups
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Efficient cryptographic schemes provably as secure as subset sum
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
An efficient pseudo-random generator provably as secure as syndrome decoding
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
An Efficient Implementation of Braid Groups
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Security Analysis of the MOR Cryptosystem
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
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Recently the braid groups were introduced as a new source for cryptography. The group operations are performed efficiently and the features are quite different from those of other cryptographically popular groups. As the first step to put the braid groups into the area of pseudorandomness, this article presents some cryptographic primitives under two related assumptions in braid groups. First, assuming that the conjugacy problem is a one-way function, say f, we show which particular bit of the argument x is pseudorandom given f(x). Next, under the decision Ko-Lee assumption, we construct two provably secure pseudorandom schemes: a pseudorandom generator and a pseudorandom synthesizer.