A simple unpredictable pseudo random number generator
SIAM Journal on Computing
An efficient non-interactive statistical zero-knowledge proof system for quasi-safe prime products
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Separability and Efficiency for Generic Group Signature Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
On the Exact Security of Full Domain Hash
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Certifying Cryptographic Tools: The Case of Trapdoor Permutations
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Multiple non-interactive zero knowledge proofs based on a single random string
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Finding a small root of a univariate modular equation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Instantiability of RSA-OAEP under chosen-plaintext attack
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Basing non-interactive zero-knowledge on (enhanced) trapdoor permutations: the state of the art
Studies in complexity and cryptography
Round optimal blind signatures
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
More constructions of lossy and correlation-secure trapdoor functions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Chosen-Ciphertext security from slightly lossy trapdoor functions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Optimal security proofs for full domain hash, revisited
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Unrestricted aggregate signatures
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
DupLESS: server-aided encryption for deduplicated storage
SEC'13 Proceedings of the 22nd USENIX conference on Security
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We propose an algorithm that, given an arbitrary N of unknown factorization and prime e ≥ N1/4+ε, certifies whether the RSA function RSAN,e(x) :=xe mod N defines a permutation over ℤ*N or not. The algorithm uses Coppersmith's method to find small solutions of polynomial equations and runs in time O(ε−8 log2N). Previous certification techniques required eN.