On SNARGs for NP and Nullstellensatz Proofs - Alex Lombardi
Автор: Institute for Advanced Study
Загружено: 2026-03-09
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Computer Science/Discrete Mathematics Seminar I
11:00am|West Lecture Hall and Remote Access
Topic: On SNARGs for NP and Nullstellensatz Proofs
Speaker: Alex Lombardi
Affiliation: Princeton University
Date: March 09, 2026
We revisit the question of whether it is possible to build succinct non-interactive arguments (SNARGs) for all of NP under standard cryptographic assumptions. In particular, we give a candidate non-adaptive SNARG for NP and prove its soundness under
the learning with errors assumption (or other standard assumptions such as bilinear maps), and
a mathematical conjecture about multivariate polynomials over the reals. In more detail, our conjecture is an upper bound on the minimum total coefficient size of Nullstellensatz proofs (Potechin-Zhang, ICALP 2024) of membership in a concrete polynomial ideal.
In this talk, we will discuss the construction, security analysis, and our current understanding of the conjecture.
Based on joint work with Lali Devadas, Sam Hopkins, Yael Kalai, Pravesh Kothari, and Surya Mathialagan.
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