Paper 2006/148

Computational Indistinguishability between Quantum States and Its Cryptographic Application

Akinori Kawachi, Takeshi Koshiba, Harumichi Nishimura, and Tomoyuki Yamakami


We introduce a computational problem of distinguishing between two specific quantum states as a new cryptographic problem to design a quantum cryptographic scheme that is ``secure'' against any polynomial-time quantum adversary. Our problem QSCDff is to distinguish between two types of random coset states with a hidden permutation over the symmetric group of finite degree. This naturally generalizes the commonly-used distinction problem between two probability distributions in computational cryptography. As our major contribution, we show three cryptographic properties: (i) QSCDff has the trapdoor property; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is computationally at least as hard in the worst case as the graph automorphism problem. These cryptographic properties enable us to construct a quantum public-key cryptosystem, which is likely to withstand any chosen plaintext attack of a polynomial-time quantum adversary. We further discuss a generalization of QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme relying on the cryptographic properties of QSCDcyc.

Note: References are added.

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Published elsewhere. Unknown where it was published
quantum cryptographycomputational indistinguishabilitytrapdoor propertyworst-caseaverage-case equivalencegraph automorphism problemquantum public-key cryptosystem
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kawachi @ is titech ac jp
2006-05-17: revised
2006-04-22: received
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      author = {Akinori Kawachi and Takeshi Koshiba and Harumichi Nishimura and Tomoyuki Yamakami},
      title = {Computational Indistinguishability between Quantum States and Its Cryptographic Application},
      howpublished = {Cryptology ePrint Archive, Paper 2006/148},
      year = {2006},
      note = {\url{}},
      url = {}
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