A hard-core predicate for all one-way functions
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CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding
SIAM Journal on Computing
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We present three new quantum hardcore functions for any quantum one-way function. We also give a “quantum” solution to Damgård's question (CRYPTO'88) on his pseudorandom generator by proving the quantum hardcore property of his generator, which has been unknown to have the classical hardcore property. Our technical tool is 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 cryptography (rather than information theory). In particular, we give a simple but powerful criterion that makes a polynomial-time computable code (seen as a function) a quantum hardcore for any quantum one-way function. On their own interest, we also give quantum list-decoding algorithms for codes whose associated quantum states (called codeword states) are “nearly” orthogonal using the technique of pretty good measurement