  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 Damgard's question (CRYPTO'88) 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.
