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
Algorithmic number theory
Signature schemes based on the strong RSA assumption
CCS '99 Proceedings of the 6th ACM conference on Computer and communications security
An Improved Pseudo-random Generator Based on Discrete Log
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
On the Unpredictability of Bits of the Elliptic Curve Diffie--Hellman Scheme
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Secure hash-and-sign signatures without the random oracle
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
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
Quantum noisy rational function reconstruction
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On the modular inversion hidden number problem
Journal of Symbolic Computation
Efficient identity-based encryption without pairings and key escrow for mobile devices
WASA'13 Proceedings of the 8th international conference on Wireless Algorithms, Systems, and Applications
Limits of a conjecture on a leakage-resilient cryptosystem
Information Processing Letters
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We study a class of problems called Modular Inverse Hidden Number Problems (MIHNPs). The basic problem in this class is the following: Given many pairs 〈xi, MSBk((α + xi)-1 mod p)〉 for random xi ∈ Zp the problem is to find α ∈ Zp (here MSBk(x) refers to the k most significant bits of x). We describe an algorithm for this problem when k (log2 p)/3 and conjecture that the problem is hard whenever k 2 p)/3. We show that assuming hardness of some variants of this MIHNP problem leads to very efficient algebraic PRNGs and MACs.