SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
On Z_4-Linear Goethals Codes and KloostermanSums
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
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 algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Classical and quantum function reconstruction via character evaluation
Journal of Complexity - Special issue on coding and cryptography
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
SIAM Journal on Computing
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
Hyper-bent functions and cyclic codes
Journal of Combinatorial Theory Series A
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Unconditional lower bounds for learning intersections of halfspaces
Machine Learning
The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts
SIAM Journal on Computing
Quantum Algorithms for Hidden Nonlinear Structures
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Inverse conjecture for the gowers norm is false
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
On the power of quantum computation
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Superpolynomial Speedups Based on Almost Any Quantum Circuit
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum lower bound for recursive Fourier sampling
Quantum Information & Computation
Quantum algorithms for shifted subset problems
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Quantum binary field inversion: improved circuit depth via choice of basis representation
Quantum Information & Computation
Reduction from non-injective hidden shift problem to injective hidden shift problem
Quantum Information & Computation
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
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Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while there were some early successes in the form of hidden subgroup problems for abelian groups-which generalize Shor's factoring algorithm perhaps most faithfully-only for a handful of non-abelian groups efficient quantum algorithms were found. Recently, problems have gotten increased attention that seek to identify hidden sub-structures of other combinatorial and algebraic objects besides groups. In this paper we provide new examples for exponential separations by considering hidden shift problems that are defined for several classes of highly non-linear Boolean functions. These so-called bent functions arise in cryptography, where their property of having perfectly flat Fourier spectra on the Boolean hypercube gives them resilience against certain types of attack. We present new quantum algorithms that solve the hidden shift problems for several well-known classes of bent functions in polynomial time and with a constant number of queries, while the classical query complexity is shown to be exponential. Our approach uses a technique that exploits the duality between bent functions and their Fourier transforms.