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数理解析研究所講究録

Quantum Bit-Commitment for Small Storage Based on Quantum One-Way Permutations (New Aspects of Theoretical Computer Science)

Toshiyuki Isshiki, Keisuke Tanaka

Published May 1, 2003• 0 citations
OpenAlex

Abstract

We propose quantum bit-commitment schemes based on quantum one-way permutations.Our schemes reduces exponentially the number of bits which Bob needs to store until the opening phase compared with the classical counterpart.

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Although Mayers, Lo and Chau successfully showed that unconditionally secure quantum bit commitment (QBC) is impossible, we present a secure QBC protocol which is quite different from the model used in their proofs. If Alice wants to commit a bit b, she first encodes b into a series of classical bit strings of the same length. The requirement is that the modulo 2 sum of all bits in every bit string equals to b. Then Alice uses quantum one-way function to produce quantum states which are corresponding to the encoded classical bit strings and will be sent to Bob as evidence. The quantum one-way function used here is just that was successfully applied in Gottesman and Chuang's quantum digital signatures. When it comes to the unveilingtime, Alice only sends the bit strings to Bob. Finally, Bob generates quantum states form the bit strings by the same quantum one-way function and uses controlled-swap circuit to check whether the quantum states are identical with the evidence.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 11, 2002•2 citations
Although Mayers, Lo and Chau successfully showed that unconditionally secure quantum bit commitment (QBC) is impossible, we present a secure QBC protocol which is quite different from the model used in their proofs. If Alice wants to commit a bit b, she first encodes b into a series of classical bit strings of the same length. The requirement is that the modulo 2 sum of all bits in every bit string equals to b. Then Alice uses quantum one-way function to produce quantum states which are corresponding to the encoded classical bit strings and will be sent to Bob as evidence. The quantum one-way function used here is just that was successfully applied in Gottesman and Chuang's quantum digital signatures. When it comes to the unveilingtime, Alice only sends the bit strings to Bob. Finally, Bob generates quantum states form the bit strings by the same quantum one-way function and uses controlled-swap circuit to check whether the quantum states are identical with the evidence.