Complexity-Theoretical Quantum List Decoding and Applications to Quamtum Hardcore Functions (計算理論とアルゴリズムの新展開 RIMS研究集会報告集)

Akinori Kawachi, Tomoyuki Yamakami

正人 林, 一雄 岩間, 治道 西村

亮周 河内, 茂 山下

Akinori Kawachi, Tomoyuki Yamakami

We poesent thoee new quantum hardcore functions for any quantum one-way function.We also give a quantum" solution to Damgdrd's question $(\mathrm{C}\mathrm{R}\mathrm{Y}\mathrm{F}\Gamma \mathrm{O}88)$ 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" crrorcorrecting codes (rather than ' quantum" error-correcting codes).which is deflned on the platform of computational complexity theory and cryptography (rather than infonnation theory).In panicular, we give a simple but powerful criterion that makes a polynomial-time computable code (seen as a $\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\dot{\mathrm{u}}\mathrm{o}\mathrm{n})$ a quantum hardcore for any quantum one-way function.On their own inteoest, we also give quantum list-decoding algorithms for codes whose associated quantum states (called codeword states) are ' almost" orthogonal using the technique of poetty good measurement.

Satoshi Iriyama, Makoto Ohya

Akinori Kawachi, Tomoyuki Yamakami

Abstract. We present three new quantum hardcore functions for any quantum one-way function. We also give a “quantum ” solution to Damg˚ard’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 “almost ” orthogonal using the technique of pretty good measurement. 1 Introduction: From Hardcore to List-Decoding