Computational indistinguishability between quantum states and its cryptographic application

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

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

34 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)268-284
Number of pages17
Publication statusPublished - 2005
Externally publishedYes
Event24th Annual International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology - EUROCRYPT 2005 - Aarhus, Denmark
Duration: 2005 May 222005 May 26

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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