Quantum Hardcore Functions by Complexity-Theoretical Quantum List Decoding

  • Akinori Kawachi
  • Tomoyuki Yamakami
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4052)


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.


Quantum Algorithm Pseudorandom Generator Quantum Fourier Transformation List Decode Hadamard Code 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Akinori Kawachi
    • 1
  • Tomoyuki Yamakami
    • 2
  1. 1.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.ERATO-SORST Quantum Computation and Information ProjectJapan Science and Technology AgencyTokyoJapan

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