Universal test for quantum one-way permutations

Akinori Kawachi, Hirotada Kobayashi, Takeshi Koshiba*, Raymond H. Putra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


The next bit test was introduced by Blum and Micali and proved by Yao to be a universal test for cryptographic pseudorandom generators. On the other hand, no universal test for the cryptographic one-wayness of functions (or permutations) is known, although the existence of cryptographic pseudorandom generators is equivalent to that of cryptographic one-way functions. In the quantum computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of (cryptographic) quantum one-way permutations and conjectured that the condition would be necessary. In this paper, we affirmatively settle their conjecture and complete a necessary and sufficient condition for quantum one-way permutations. The necessary and sufficient condition can be regarded as a universal test for quantum one-way permutations, since the condition is described as a collection of stepwise tests similar to the next bit test for pseudorandom generators.

Original languageEnglish
Pages (from-to)370-385
Number of pages16
JournalTheoretical Computer Science
Issue number2-3
Publication statusPublished - 2005 Nov 22
Externally publishedYes


  • Computational cryptography
  • One-way function
  • One-way permutation
  • Quantum computation
  • Universal test

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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