  We propose a new cryptographic task, which we call verifiable quantum secure
modulo summation. Secure modulo summation is a calculation of modulo summation
$Y_1+\ldots+ Y_m$ when $m$ players have their individual variables $Y_1,\ldots,
Y_m$ 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.
