zkDaily - 2026-04-30

零知识证明 zkDaily

ZKP Frontier Tracker 🎯

Thu

04.30

2026

Pairing-Based Verifiable Shuffles with Logarithmic-Size Proofs

Paper

https://eprint.iacr.org/2026/805

Xingye Lu Verifiable Shuffle Mix-net

Lu et al. propose a pairing-based verifiable shuffle for ElGamal ciphertexts with O(log N) proof size, significantly reducing bandwidth compared to prior O(N) schemes, and provide the first benchmarks for logarithmic-size shuffle proofs.

Notes

Proof size is O(log N) group elements, far better than traditional O(N) schemes.
Public-coin protocol with Fiat-Shamir transform, non-interactive.
Supports updatable SRS from powers-of-tau ceremony.
Proof is only ~1.6 MB for 1M ciphertexts, vs. hundreds of KB to MB for others.
First benchmark for logarithmic-size verifiable shuffle.
Applicable to e-voting and blockchain anonymization.

Collected by @icerdesign

零知识证明 zkDaily

Q&A Deep Dive 💬

Thu

04.30

2026

What is a verifiable shuffle?

A verifiable shuffle proves that a set of ciphertexts is a rerandomized permutation of another set, without revealing the permutation or randomness.

What is the main optimization in this paper?

The paper achieves logarithmic-size proofs, reducing proof size from linear or quadratic to logarithmic, significantly lowering bandwidth costs.

How does the scheme reduce prover and verifier costs?

It optimizes algebraic structure and proof representation, reducing exponentiations and the number of group elements, improving efficiency.

Prompted by @icerdesign