Abstract
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 language | English |
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Pages (from-to) | 370-385 |
Number of pages | 16 |
Journal | Theoretical Computer Science |
Volume | 345 |
Issue number | 2-3 |
DOIs | |
Publication status | Published - 2005 Nov 22 |
Externally published | Yes |
Keywords
- Computational cryptography
- One-way function
- One-way permutation
- Quantum computation
- Universal test
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)