How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
RSA and Rabin functions: certain parts are as hard as the whole
SIAM Journal on Computing - Special issue on cryptography
Paillier's cryptosystem revisited
CCS '01 Proceedings of the 8th ACM conference on Computer and Communications Security
An Efficient Discrete Log Pseudo Random Generator
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
The Modular Inversion Hidden Number Problem
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Finding Small Solutions to Small Degree Polynomials
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
On the cryptographic security of single RSA bits
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
Foundations of Cryptography: Volume 1
Foundations of Cryptography: Volume 1
Reconstructing noisy polynomial evaluation in residue rings
Journal of Algorithms
Why and how to establish a private code on a public network
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Efficient And Secure Pseudo-Random Number Generation
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
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
Concrete security of the blum-blum-shub pseudorandom generator
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
QUAD: A multivariate stream cipher with provable security
Journal of Symbolic Computation
Attacking Power Generators Using Unravelled Linearization: When Do We Output Too Much?
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
More efficient DDH pseudorandom generators
Designs, Codes and Cryptography
On the power generator and its multivariate analogue
Journal of Complexity
Adaptive trapdoor functions and chosen-ciphertext security
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Pseudorandom generators based on subcovers for finite groups
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
Predicting masked linear pseudorandom number generators over finite fields
Designs, Codes and Cryptography
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Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most O(logn) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(logn) bits per multiply at the cost of a reasonable assumption on RSA inversion.