Polynomial commitments schemes are a powerful tool that enables one party to commit to a polynomial p of degree d, and prove that the committed function evaluates to a certain value z at a specified point u, i.e. p(u) = z, without revealing any additional information about the polynomial. Recently, polynomial commitments have been extensively used as a cryptographic building block to transform polynomial interactive oracle proofs (PIOPs) into efficient succinct arguments.
In this talk, we present new constructions of lattice-based polynomial commitments that achieve succinct proof size and verification time in the degree d of the polynomial. Extractability of the schemes holds in the random oracle model under the standard Module-SIS assumption. Concretely, the most optimized version achieves proof in the order of 600KB for d = 2^20, which becomes competitive with the hash-based FRI commitment.
Ngoc Khanh Nguyen is a lecturer at King's College London. His current topics of interests are (but not limited to) efficient lattice-based constructions and efficient post-quantum zero-knowledge proofs.
Previously, Khanh was a postdoctoral researcher at EPFL, hosted by Prof. Alessandro Chiesa. He obtained his PhD degree at ETH Zurich and IBM Research Europe - Zurich, supervised by Dr Vadim Lyubashevsky and Prof. Dennis Hofheinz. Before that, he did his undergraduate and master studies at the University of Bristol, UK.