Computational indistinguishability between quantum states and its cryptographic application

  • Authors:

  • Akinori Kawachi;Takeshi Koshiba;Harumichi Nishimura;Tomoyuki Yamakami

  • Affiliations:

  • Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan;Secure Computing Laboratory, Fujitsu Laboratories Ltd., Kawasaki, Japan;ERATO Quantum Computation and Information Project, Japan Science and Technology Agency, Kyoto, Japan;Computer Science Program, Trent University, Peterborough, Ontario, Canada

  • Venue:
  • EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
  • Year:
  • 2005

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Abstract

We introduce a problem of distinguishing between two quantum states as a new underlying problem to build a computational cryptographic scheme that is ”secure” against quantum adversary. Our problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. More precisely, our problem QSCDff is the computational distinguishability problem between two types of random coset states with a hidden permutation over the symmetric group. We show that (i) QSCDff has the trapdoor property; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is at least as hard in the worst case as the graph automorphism problem. Moreover, we show that QSCDff cannot be efficiently solved by any quantum algorithm that naturally extends Shor's factorization algorithm. These cryptographic properties of QSCDff enable us to construct a public-key cryptosystem, which is likely to withstand any attack of a polynomial-time quantum adversary.