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

Vikas Srivastava, Debasish Roy, Sihem Mesnager, Nibedita Kundu, Sumit Kumar Debnath, Sourav Mukhopadhyay

TL;DR

The paper tackles the vulnerability of number-theoretic e-voting protocols to quantum attacks by proposing PQ-EVot, a post-quantum, end-to-end verifiable e-voting protocol based on the hardness of solving multivariate quadratic equations (MQ). It uses standard cryptographic primitives (encryption, signatures, commitments) and multivariate cryptography to enable a transparent, publicly verifiable tally while preserving voter privacy. The authors detail a five-entity system architecture, formalize a threat model, and provide a full protocol flow across preparation, registration, voting, verification, and tally phases, with rigorous security arguments against insider and collusion threats. Performance analysis demonstrates feasible runtimes and storage overhead, leveraging memory-efficient field operations, making the approach practical for real-world deployment.

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 \textit{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.

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

TL;DR

The paper tackles the vulnerability of number-theoretic e-voting protocols to quantum attacks by proposing PQ-EVot, a post-quantum, end-to-end verifiable e-voting protocol based on the hardness of solving multivariate quadratic equations (MQ). It uses standard cryptographic primitives (encryption, signatures, commitments) and multivariate cryptography to enable a transparent, publicly verifiable tally while preserving voter privacy. The authors detail a five-entity system architecture, formalize a threat model, and provide a full protocol flow across preparation, registration, voting, verification, and tally phases, with rigorous security arguments against insider and collusion threats. Performance analysis demonstrates feasible runtimes and storage overhead, leveraging memory-efficient field operations, making the approach practical for real-world deployment.

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 \textit{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.

Paper Structure

This paper contains 13 sections, 6 theorems, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Paper Organization
  4. Preliminaries
  5. End-to-End (E2E) Verifiable E-Voting
  6. System Building Blocks
  7. Proposed E2E Post-Quantum E-Voting Protocol PQ-EVot
  8. System Architecture
  9. Threat/Attack Model
  10. Design of PQ-EVot
  11. Security Analysis
  12. Performance Analysis
  13. Conclusion

Key Result

Theorem 1

E2E-PQ-EVot is secure from the attacks by a malicious Poll-Officer.

Figures (3)

  • Figure 1: Multivariate Encryption
  • Figure 2: Multivariate Signature
  • Figure 3: System architecture and communication flow of E2E-PQ-EVot.

Theorems & Definitions (11)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • Theorem 4
  • proof
  • Theorem 5
  • ...and 1 more