Characterizing the Existence of Quantum One-Way Permutations
Akinori Kawachi, Hirotada Kobayashi, Takeshi Koshiba, Rudy Raymond Harry Putra · arXiv (Cornell University) · 2004
We first give a full characterization of average-case quantum one-way permutations. Our characterization is an extension of the characterization of worst-case quantum one-way permutations (or, a partial characterization of average-case quantum one-way permutations) by Kashefi, Nishimura and Vedral. As in the previous results, our characterization is also written in terms of reflection operator and pseudo identity. To prove the full characterization of average-case quantum one-way permutations, we incorporate their basic ideas with the universal hashing technique and modify the reduction between inverting average-case quantum one-way permutation and another problem appeared in the characterization of worst-case quantum one-way permutations. In a sense, our characterization says that the hardness of inverting quantum one-way permutations comes from the hardness to efficiently implement some reflection operators.