Simultaneous security of bits in the discrete log
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
How to predict congruential generators
CRYPTO '89 Proceedings on Advances in cryptology
The Bit Security of Modular Squaring Given Partial Factorization of the Modulos
CRYPTO '85 Advances in Cryptology
Cryptographic Computation: Secure Faut-Tolerant Protocols and the Public-Key Model
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
All Bits ax+b mod p are Hard (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Practical Construction and Analysis of Pseudo-Randomness Primitives
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On Formal Verification of Arithmetic-Based Cryptographic Primitives
Information Security and Cryptology --- ICISC 2008
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
Stronger security proofs for RSA and rabin bits
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Universal hash functions & hard core bits
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Dial C for cipher: le chiffrement était presque parfait
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Three XOR-lemmas - an exposition
Studies in complexity and cryptography
On the provable security of an efficient RSA-Based pseudorandom generator
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Another look at “provable security”. II
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Efficient primitives from exponentiation in Zp
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
Concrete security of the blum-blum-shub pseudorandom generator
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Information Sciences: an International Journal
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Cryptographically secure pseudo-random number generators known so far suffer from the handicap of being inefficient; the most efficient ones can generate only one bit on each modular multiplication (n/sup 2/ steps). Blum, Blum and Shub ask the open problem of outputting even two bits securely. We state a simple condition, the XOR-Condition, and show that any generator satisfying this condition can output logn bits on each multiplication. We also show that the logn least significant bits of RSA, Rabin's Scheme, and the x/sup 2/ mod N generator satisfy boolean predicates of these bits are secure. Furthermore, we strengthen the security of the x/sup 2/ mod N generator, which being a Trapdoor Generator, has several applications, by proving it as hard as Factoring.