Quantum verifiable protocol for secure modulo zero-sum randomness

Masahito Hayashi*, Takeshi Koshiba

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We propose a new cryptographic resource, secure modulo zero-sum randomness, as a resource to implement a task of secure modulo summation, and its quantum protocol. Secure modulo summation is the calculation of modulo summation Y1+ ⋯ + Ym when m players have their individual variables Y1, … , Ym with keeping the secrecy of the individual variables. Secure modulo zero-sum randomness is a set of m variables X1, … , Xm held by m players that satisfy the zero sum condition X1+ ⋯ + Xm= 0 with a certain security condition. This paper explains the relation between these two concepts and proposes a quantum verifiable protocol for secure modulo summation. The advantage for quantum protocol is the verifiability based on self-testing, which does not need to trust measurement devices and can be realized by using a statistical concept, significance level, while any classical method needs to trust several components of the protocol. Then, we propose various cryptographic applications for secure modulo zero-sum randomness. We also compare our quantum verifiable protocol with the conventional method for secure modulo summation.

Original languageEnglish
Article number291
JournalQuantum Information Processing
Issue number8
Publication statusPublished - 2022 Aug


  • Collusion resistance
  • Modulo summation
  • Quantum verification
  • Secure multiparty computation
  • Self-testing

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering


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