What a lovely hat

Paper 2026/805

Compact Verifiable Shuffles for ElGamal Ciphertexts

Abstract

A verifiable shuffle proves that output ciphertexts are a rerandomized permutation of the inputs without revealing the permutation or rerandomization factors. It is a core primitive in mix-nets for electronic voting and blockchain-based anonymization, where each mix server publishes an auditable proof. Existing deployed schemes typically have proof size $O(N)$ or $O(\sqrt{N})$ in the number of ciphertexts $N$, making shuffle proofs a major bandwidth cost. We present a logarithmic-size verifiable shuffle for ElGamal ciphertexts. The logarithmic term in our proof size is one third of that in the previously known logarithmic construction for the same shuffle relation by Hoffmann et al. (CCS 2019). Our protocol is public coin, non-interactive via the Fiat--Shamir transform, and relies on an updatable structured reference string that can be generated once in a powers-of-tau ceremony and reused across applications. We implement the protocol in Rust and provide, to our knowledge, the first benchmarks for a logarithmic-size ElGamal shuffle. At \(N=2^{20}\), the proof is 2.6 KiB. In a four-server mix-net election, the four shuffle proofs occupy approximately 10.6 KiB in total, excluding ballot-validity and decryption proofs.