Forgeable quantum messages in arbitrated quantum signature schemes

TL;DR

This paper investigates the existence of forgeable quantum messages in arbitrated quantum signature schemes, providing conditions under which such messages can or cannot exist, thus enhancing the understanding of security in quantum signatures.

Contribution

It extends previous results to general unitary rotations and identifies conditions for the absence of forgeable messages in quantum signature schemes.

Findings

Derived necessary and sufficient conditions for forgeable messages.

Identified schemes with no forgeable quantum message-signature pairs.

Extended previous results to more general rotation operators.

Abstract

Recently, the concept on `forgeable quantum messages' in arbitrated quantum signature schemes was introduced by T. Kim et al. [Phys. Scr., 90, 025101 (2015)], and it has been shown that there always exists such a forgeable quantum message for every known arbitrated quantum signature scheme with four quantum encryption operators and the specific two rotation operators. We first extend the result to the case of any two unitary rotation operators, and then consider the forgeable quantum messages in the schemes with four quantum encryption operators and three or more rotation operators. We here present a necessary and sufficient condition for existence of a forgeable quantum message, and moreover, by employing the condition, show that there exists an arbitrated quantum signature scheme which contains no forgeable quantum message-signature pairs.