Threshold Post-Quantum E-Voting from Lattice Commitments

What it is

T-EVOLVE is a threshold extension of EVOLVE, a lattice-commitment homomorphic e-voting protocol. EVOLVE needs every authority to complete the tally. T-EVOLVE needs only t of n. It is a single-author preprint (Jalal Alizadeh, ePrint 2026/2500) with no peer-review venue listed.

How it works

• Each vote is Shamir-shared over the commitment message space.
• The voter proves that the committed shares form a Reed-Solomon codeword whose value at zero is a valid vote. The page says the parity checks cost no communication.
• Tallying interpolates public column sums, so norms do not grow.
• Authority complaints, including those about ciphertexts that do not decrypt, are publicly verifiable. This needs an encryption scheme with publicly verifiable opening. The paper defines that interface and shows it can be instantiated under LWE.

Caveats

• The 109 KB figure is not the full ballot. The page says it is for a yes/no ballot with four authorities, "without encryption overhead and signatures". Real ballots will be larger, and the page gives no figure for the added cost.
• Aggregation cost is a single data point. An authority aggregates 10^4 ballots in about three minutes on one core. The page does not say how this scales with n, t or ballot type.
• The security proofs are in the classical random oracle model only. The page does not claim a quantum random oracle (QROM) proof, which matters for a scheme sold as post-quantum.
• The verifiability reduction is not tight for the efficient instantiation. Concrete parameters would need to be sized with that loss in mind. The page gives no parameters.
• Privacy holds only against t-1 colluding authorities. Verifiability holds even if all authorities collude.
• The page offers no code, repository or parameter set. It mentions a C implementation but does not link it.