Recent Advances in Zero-Knowledge Proofs and SNARKs: Faster Provers, Shorter Proofs, and Post-Quantum Security

Abstract: Zero-knowledge proofs let a prover convince a verifier that a statement is true without revealing anything else. SNARKs (succinct non-interactive arguments of knowledge) add succinctness: proofs are short and fast to verify, even for very large computations. A major obstacle to deploying them has long been prover cost. In this talk, I will give a gentle introduction to SNARK design and survey recent advances in prover speed and proof size. These advances build on the use of the sum-check protocol, optimizations tailored to binary fields, and new polynomial commitment schemes based on both hash functions and lattices, which are plausibly secure against quantum computers. I will also discuss applications these advances make possible, from privacy-preserving digital credentials to aggregating many post-quantum signatures into a single short proof.

Joint work: Mohammadtaghi Badakhshan, Alberto Centelles, Quang Dao, Justin Thaler.

Suggested readings

• Aerie: Efficient Aggregation of Falcon Signatures (ia.cr/2026/2501)
• Akita: A High-Performance Lattice-Based Polynomial Commitment Scheme (ia.cr/2026/1983)