Quantum verifiable protocol for secure modulo zero-sum randomness

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 Y-1 +( )... + Y-m when m players have their individual variables Y-1 ,..., Y-m with keeping the secrecy of the individual variables. Secure modulo zero-sum randomness is a set of m variables X-1, ..., X-m held by m players that satisfy the zero sum condition X-1 + ... + X-m = 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.