Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
On zero-testing and interpolation of k -sparse multivariate polynomials over finite fields
Theoretical Computer Science
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Local randomness in polynomial random number and random function generators
SIAM Journal on Computing
Computational Complexity of Sparse Rational Interpolation
SIAM Journal on Computing
Sparse Polynomial Interpolation in Nonstandard Bases
SIAM Journal on Computing
Finite fields
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Reconstructing Algebraic Functions from Mixed Data
SIAM Journal on Computing
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Reconstructing randomly sampled multivariate polynomials from highly noisy data
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
On The Correlation Of Binary M-sequences
Designs, Codes and Cryptography
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
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Security of the most significant bits of the Shamir message passing scheme
Mathematics of Computation
On the hardness of the shortest vector problem
On the hardness of the shortest vector problem
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
List decoding of algebraic-geometric codes
IEEE Transactions on Information Theory
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
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
The Hidden Number Problem in Extension Fields and Its Applications
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
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
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation
Mathematics of Computation
Polynomial interpolation from multiples
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On the hardness of approximating the permanent of structured matrices
Computational Complexity
Noisy Chinese remaindering in the Lee norm
Journal of Complexity - Special issue on coding and cryptography
On reducing a system of equations to a single equation
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Noisy Interpolation of Multivariate Sparse Polynomials in Finite Fields
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Quantum noisy rational function reconstruction
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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We consider a polynomial analogue of the hidden number problem which has recently been introduced by Boneh and Venkatesan. Namely we consider the sparse polynomial approximation problem of recovering an unknown polynomial f(X) \in \F_p[X] with at most $m$ non-zero terms from approximate values of f(t) at polynomially many points t \in \F_p selected uniformly at random. The case of a polynomial f(X) = &agr; X corresponds to the hidden number problem. The above problem is related to the noisy polynomial interpolation problem and to the sparse polynomial interpolation problem which have recently been considered in the literature. Our results are based on a combination of some number theory tools such as bounds of exponential sums and the number of solutions of congruences with the lattice reduction technique.