Verifiable Quantum Secure Modulo Summation

TL;DR

This paper introduces a new quantum cryptographic protocol for verifiable secure modulo summation, enabling multiple parties to compute sums privately with minimal verification steps using novel quantum randomness concepts.

Contribution

It proposes a direct quantum method for verifiable secure modulo summation utilizing modulo zero-sum randomness, reducing verification complexity.

Findings

Protocol can verify secrecy with minimal requirements

Introduces modulo zero-sum randomness as a new concept

Achieves secure summation without extensive secret channels

Abstract

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.