Verifiable quantum secure modulo summation

Masahito Hayashi, Takeshi Koshiba

Research output: Contribution to journalArticlepeer-review


We propose a new cryptographic task, which we call verifiable quantum secure modulo summation. Secure modulo summation is a calculation of modulo summation Y1 + . . . + Ym when m players have their individual variables Y1, . . ., Ym with keeping the secrecy of the individual variables. However, the conventional method for secure modulo summation uses so many secret communication channels. We say that a quantum protocol for secure modulo summation is quantum verifiable secure modulo summation when it can verify the desired secrecy condition. If we combine device independent quantum key distribution, it is possible to verify such secret communication channels. However, it consumes so many steps. To resolve this problem, using quantum systems, we propose a more direct method to realize secure modulo summation with verification. To realize this protocol, we propose modulo zero-sum randomness as another new concept, and show that secure modulo summation can be realized by using modulo zero-sum randomness. Then, we construct a verifiable quantum protocol method to generate modulo zero-sum randomness. This protocol can be verified only with minimum requirements.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Oct 14


  • Collusion resistance
  • Modulo summation
  • Quantum verification
  • Secure multiparty computation
  • Selftesting

ASJC Scopus subject areas

  • General

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