How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Determinants and ranks of random matrices over :1Mm
Discrete Mathematics
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Constructing normal bases in finite fields
Journal of Symbolic Computation
Local randomness in polynomial random number and random function generators
SIAM Journal on Computing
On some approximation problems concerning sparse polynomials over finite fields
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
Finite fields
Modern computer algebra
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
On the Generalised Hidden Number Problem and Bit Security of XTR
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
All Bits ax+b mod p are Hard (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th 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
The Complexity of Computing Hard Core Predicates
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
The Insecurity of Nyberg-Rueppel and Other DSA-Like Signature Schemes with Partially Known Nonces
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Universal Hash Functions from Exponential Sums over Finite Fields and Galois Rings
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Security of the most significant bits of the Shamir message passing scheme
Mathematics of Computation
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Singularity Probabilities for Random Matrices over Finite Fields
Combinatorics, Probability and Computing
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Universal hash functions & hard core bits
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Finite Fields and Their Applications
On the Density of Normal Bases in Finite Fields
Finite Fields and Their Applications
Security of polynomial transformations of the Diffie-Hellman key
Finite Fields and Their Applications
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We present polynomial time algorithms for certain generalizations of the hidden number problem which has played an important role in gaining understanding of the security of commonly suggested one way functions.Namely, we consider an analogue of this problem for a certain class of polynomials over an extension of a finite field; recovering a hidden polynomial given the values of its trace at randomly selected points. Also, we give an algorithm for a variant of the problem in free finite dimensional modules. This result can be helpful for studying security of analogues of the RSA and Diffie-Hellman cryptosystems over such modules.The hidden number problem is also related to the so called black-box field model of computation. We show that simplified versions of the above recovery problems can be used to derive positive results on the computational power of this model.