The Security of All Bits Using List Decoding

Authors:
Paz Morillo;Carla Ràfols
Affiliations:
Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Spain E-08034;Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Barcelona, Spain E-08034
Venue:
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Year:
2009

Citing 8
Cited 0

RSA and Rabin functions: certain parts are as hard as the whole

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
Learning decision trees using the Fourier spectrum

STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Learning Polynomials with Queries: The Highly Noisy Case

SIAM Journal on Discrete Mathematics
All Bits ax+b mod p are Hard (Extended Abstract)

CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Proving Hard-Core Predicates Using List Decoding

FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The security of all RSA and discrete log bits

Journal of the ACM (JACM)
Public-key cryptosystems based on composite degree residuosity classes

EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques

Quantified Score

Hi-index	0.00

Visualization

Abstract

The relation between list decoding and hard-core predicates has provided a clean and easy methodology to prove the hardness of certain predicates. So far this methodology has only been used to prove that the O (loglogN ) least and most significant bits of any function with multiplicative access --which include the most common number theoretic trapdoor permutations-- are secure. In this paper we show that the method applies to all bits of any function defined on a cyclic group of order N with multiplicative access for cryptographically interesting N . As a result, in this paper we reprove the security of all bits of RSA, the discrete logarithm in a group of prime order or the Paillier encryption scheme.