How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
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
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Discrete Log Pseudo Random Generator
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
How discreet is the discrete log?
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
An Improved Pseudo-Random Generator Based on the Discrete Logarithm Problem
Journal of Cryptology
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key encryption in a multi-user setting: security proofs and improvements
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient pseudorandom generators based on the DDH assumption
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key 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
QUAD: a practical stream cipher with provable security
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
How to turn loaded dice into fair coins
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Pseudorandom generators based on subcovers for finite groups
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
Hi-index | 0.00 |
In this paper, we first show a DDH Lemma, which states that a multi-variable version of the decisional Diffie---Hellman problem is hard under the standard DDH assumption, where the group size is not necessarily known. Our proof, based on a self-reducibility technique, has a small reduction complexity. Using DDH Lemma, we extend the FSS pseudorandom generator of Farashahi et al. to a new one. The new generator is almost twice faster than FSS while still provably secure under the DDH assumption. Using the similar technique for the RSA modulus, we improve the Goldreich---Rosen generator. The new generator is provably secure under the factoring assumption and DDH assumption over $${\mathbb{Z}_N^*}$$ . Evidently, to achieve the same security level, different generators may have different security parameters (e.g., distinct length of modulus). We compare our generators with other generators under the same security level. For simplicity, we make comparisons without any pre-computation. As a result, our first generator is the most efficient among all generators that are provably secure under standard assumptions. It has the similar efficiency as Gennaro generator, where the latter is proven secure under a non-standard assumption. Our second generator is more efficient than Goldreich---Rosen generator.