Recently, the concept on ‘forgeable quantum messages’ in arbitrated quantum signature schemes was introduced by 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.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2016R1A2B4014928). T. Kim was supported by the Ministry of Science, ICT & Future Planning (NRF- 2013R1A1A2063279), and H.S. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1A2A1A15054564).
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- Arbitrated quantum signature schemes
- Forgeable quantum messages
- Quantum signature