How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Modern Cryptography, Probabilistic Proofs, and Pseudorandomness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Quantum Entanglement and the Communication Complexity of the Inner Product Function
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
How to Convert the Flavor of a Quantum Bit Commitment
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Perfectly concealing quantum bit commitment from any quantum one-way permutation
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Quantum DNF Learnability Revisited
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Universal test for quantum one-way permutations
Theoretical Computer Science - Mathematical foundations of computer science 2004
Zero-knowledge against quantum attacks
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Quantum lower bounds for the Goldreich-Levin problem
Information Processing Letters
Improved algorithms for quantum identification of Boolean oracles
Theoretical Computer Science
Statistical Zero Knowledge and quantum one-way functions
Theoretical Computer Science
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Quantum lower bounds for the Goldreich--Levin problem
Information Processing Letters
Nearly one-sided tests and the Goldreich-Levin predicate
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding
SIAM Journal on Computing
On quantum one-way permutations
Quantum Information & Computation
Quantum hardcore functions by complexity-theoretical quantum list decoding
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Improved algorithms for quantum identification of boolean oracles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Robust quantum algorithms with ε-biased oracles
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Computational indistinguishability between quantum states and its cryptographic application
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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We investigate the Goldreich-Levin Theorem in the context of quantum information. This result is a reduction from the problem of inverting a one-way function to the problem of predicting a particular bit associated with that function. We show that the quantum version of the reduction is quantitatively more efficient than the known classical version. If the one-way function acts on n-bit strings then the overhead in the reduction is by a factor of O(n/驴2) in the classical case but only by a factor of O(1/驴) in the quantum case, where 1/2 + 驴 is the probability of predicting the hard-predicate. We also show that, using the Goldreich-Levin Theorem, a quantum bit (or qubit) commitment scheme that is perfectly binding and computationally concealing can be obtained from any quantum one-way permutation.