Verifiable Quantum Secure Modulo Summation

TL;DR

The paper tackles secure multi-party modulo summation by proposing a verifiable quantum approach that minimizes secret-channel verification. It defines secure modulo zero-sum randomness as a correlated resource where $X_i\in\mathbb{F}_2^c$ satisfy $\sum_i X_i=0$, with independence of any $m-1$ variables and secrecy per player, and shows how this resource enables verifiable modulo summation when broadcast channels are available. A GHZ-based quantum protocol with self-testing verifies the secrecy and generates the randomness, and a subsequent protocol combines this with a modulo-sum computation to achieve verifiable secure modulo summation under minimal trust assumptions. The work further develops cryptographic applications, including secret sharing and anonymous multi-party authentication, all leveraging the modulo zero-sum randomness and a public broadcast channel, and it provides comparisons to prior quantum methods, highlighting verified secrecy and reduced reliance on secret channels. Although the current construction focuses on $\mathbb{F}_2$, the authors discuss extensions to general finite fields $\mathbb{F}_q$ as a path for future work, with potential impact on practical quantum-secure multi-party computation.

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.

Figures (5)

• Figure 1: Mismatched recognition.
• Figure 2: Multi-party Anonymous Authentication
• Figure 3: Secure Multi-party Anonymous Authentication
• Figure 4: Selftesting of Bell state
• Figure 5: Verifiable Generation of Secure Modulo Zero-Sum Randomness

Theorems & Definitions (18)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Definition 1
• Definition 2
• Theorem 5
• Theorem 6
• Proposition 1
• Theorem 7