TY - JOUR

T1 - Universal test for quantum one-way permutations

AU - Kawachi, Akinori

AU - Kobayashi, Hirotada

AU - Koshiba, Takeshi

AU - Putra, Raymond H.

PY - 2005/11/22

Y1 - 2005/11/22

N2 - 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.

AB - 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.

KW - Computational cryptography

KW - One-way function

KW - One-way permutation

KW - Quantum computation

KW - Universal test

UR - http://www.scopus.com/inward/record.url?scp=27644535838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644535838&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2005.07.036

DO - 10.1016/j.tcs.2005.07.036

M3 - Article

AN - SCOPUS:27644535838

VL - 345

SP - 370

EP - 385

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 2-3

ER -