Efficient quantum algorithm for identifying hidden polynomials

Authors:
Thomas Decker;Jan Draisma;Pawel Wocjan
Affiliations:
School of Computer Science, McGill University, Montreal, Quebec, Canada;Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands;School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL
Venue:
Quantum Information & Computation
Year:
2009

Citing 17
Cited 0

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

SIAM Journal on Computing
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum Computation and Lattice Problems

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)

CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Modern Computer Algebra

Modern Computer Algebra
Classical and quantum function reconstruction via character evaluation

Journal of Complexity - Special issue on coding and cryptography
Fast quantum algorithms for computing the unit group and class group of a number field

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Polynomial time quantum algorithm for the computation of the unit group of a number field

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups

FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Limitations of quantum coset states for graph isomorphism

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Quantum computation of zeta functions of curves

Computational Complexity
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Quantum Algorithms for Some Hidden Shift Problems

SIAM Journal on Computing
Quantum algorithm for a generalized hidden shift problem

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Algorithms for Hidden Nonlinear Structures

FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups

STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Quantum noisy rational function reconstruction

COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a natural generalization of an abelian Hidden Subgroup Problem where thesubgroups and their cosets correspond to graphs of linear functions over a finite field Fwith d elements. The hidden functions of the generalized problem are not restricted tobe linear but can also be m-variate polynomial functions of total degree n 2.The problem of identifying hidden m-variate polynomials of degree less or equalto n for fixed n and m is hard on a classical computer since Ω(√d) black-box queriesare required to guarantee a constant success probability. In contrast, we present aquantum algorithm that correctly identifies such hidden polynomials for all but a finitenumber of values of d with constant probability and that has a running time that is onlypolylogarithmic in d.