@inbook{ad348930caa54a9e94c7a3c28de4e4f7,

title = "Universal test for quantum one-way permutations",

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, though 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 relax their sufficient condition and give a new condition that is necessary and sufficient for quantum one-way permutations. Our condition can be regarded as a universal test for quantum one-way permutations, since our condition is described as a collection of stepwise tests similar to the next bit test for pseudorandom generators.",

author = "Akinori Kawachi and Hirotada Kobayashi and Takeshi Koshiba and Putra, {Raymond H.}",

note = "Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2004",

doi = "10.1007/978-3-540-28629-5_66",

language = "English",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "839--850",

editor = "Jir{\'i} Fiala and Jan Kratochv{\'i}l and Koubek, {V{\'a} clav}",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}