A key distribution system equivalent to factoring
Journal of Cryptology
A probabilistic poly-time framework for protocol analysis
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Breaking generalized Diffie-Hellman modulo a composite is no easier than factoring
Information Processing Letters
Signature schemes based on the strong RSA assumption
ACM Transactions on Information and System Security (TISSEC)
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Complexity of Lattice Problems
Complexity of Lattice Problems
Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Discrete Logarithms and Factoring
Discrete Logarithms and Factoring
Logics for Reasoning about Cryptographic Constructions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A composable cryptographic library with nested operations
Proceedings of the 10th ACM conference on Computer and communications security
Completeness theorems for the Abadi-Rogaway language of encrypted expressions
Journal of Computer Security - Special issue on WITS'02
Collision-free accumulators and fail-stop signature schemes without trees
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Adaptive security of symbolic encryption
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Computationally sound implementations of equational theories against passive adversaries
Information and Computation
Breaking RSA Generically Is Equivalent to Factoring
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Secure mobile subscription of sensor-encrypted data
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Adaptive pseudo-free groups and applications
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
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We prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free abelian group generated by the symbols g1,...,gn, together with a solution modulo the product of two randomly chosen safe primes when g1,...,gn are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free abelian groups under a standard cryptographic assumption, and resolves a conjecture of Rivest (TCC 2004).