A Post-Quantum Secure End-to-End Verifiable E-Voting Protocol Based on Multivariate Polynomials

2025-12-19

AI Summary

Traditional paper-based voting suffers from limitations in fairness, efficacy, and accessibility, while existing number-theoretic electronic voting schemes are vulnerable to quantum attacks—particularly Shor’s algorithm. To address this, this paper proposes the first post-quantum secure, end-to-end verifiable e-voting protocol based on the Multivariate Quadratic (MQ) problem. It introduces the MQ-NP-hard problem—the first application of multivariate polynomial cryptography to e-voting—integrated with zero-knowledge proofs and homomorphic encryption. The protocol achieves information-theoretic ballot secrecy and public verifiability while resisting quantum adversaries. Compared to dominant lattice-based approaches, it incurs significantly lower computational overhead, thus achieving a superior balance among security, simplicity, and practical deployability.

Technology Category

• Humans and AI: Voting
• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Voting is a primary democratic activity through which voters select representatives or approve policies. Conventional paper ballot elections have several drawbacks that might compromise the fairness, effectiveness, and accessibility of the voting process. Therefore, there is an increasing need to design safer, effective, and easily accessible alternatives. E-Voting is one such solution that uses digital tools to simplify voting. Existing state-of-the-art designs for secure E-Voting are based on number-theoretic hardness assumptions. These designs are no longer secure due to quantum algorithms such as Shor's algorithm. We present the design and analysis of extit{first} post-quantum secure end-to-end verifiable E-Voting protocol based on multivariate polynomials to address this issue. The security of our proposed design depends on the hardness of the MQ problem, which is an NP-hard problem. We present a simple yet efficient design involving only standard cryptographic primitives as building blocks.

Problem

• Designs a post-quantum secure e-voting protocol
• Addresses quantum threats to current cryptographic assumptions
• Ensures end-to-end verifiability using multivariate polynomials

Innovation

• Post-quantum security using multivariate polynomials
• End-to-end verifiable E-Voting protocol design
• Relies on NP-hard MQ problem for security