How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Matrix analysis
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
SIAM Journal on Computing
List decoding: algorithms and applications
ACM SIGACT News
Learning Polynomials with Queries: The Highly Noisy Case
SIAM Journal on Discrete Mathematics
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
A Foundation of Programming a Multi-tape Quantum Turing Machine
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
A Quantum Goldreich-Levin Theorem with Cryptographic Applications
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On the Randomness of Legendre and Jacobi Sequences
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Proving Hard-Core Predicates Using List Decoding
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
Quantum Algorithms for Some Hidden Shift Problems
SIAM Journal on Computing
Robust Polynomials and Quantum Algorithms
Theory of Computing Systems
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
On quantum detection and the square-root measurement
IEEE Transactions on Information Theory
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Hardcore functions have been used as a technical tool to construct secure cryptographic systems; however, little is known on their quantum counterpart, called quantum hardcore functions. With a new insight into fundamental properties of quantum hardcores, we present three new quantum hardcore functions for any (strong) quantum one-way function. We also give a “quantum” solution to Damgård's question [Advances in Cryptology, Lecture Notes in Comput. Sci. 403, Springer, Berlin, 1990, pp. 163-172] on a classical hardcore property of his pseudorandom generator by proving its quantum hardcore property. Our major technical tool is the new notion of quantum list-decoding of “classical” error-correcting codes (rather than “quantum” error-correcting codes), which is defined on the platform of computational complexity theory and computational cryptography (rather than information theory). In particular, we give a simple but powerful criterion that makes a polynomial-time computable classical block code (seen as a function) a quantum hardcore for all quantum one-way functions. On their own interest, we construct efficient quantum list-decoding algorithms for classical block codes whose associated quantum states (called codeword states) form a nearly phase-orthogonal basis.