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Explore succinct non-interactive arguments of proximity (SNAPs) in this conference talk that demonstrates how a prover can convince a verifier that a statement is true through a short message while the verifier reads only a sublinear number of bits. Learn about soundness guarantees against polynomial-time adversaries that ensure statements are "close" in Hamming distance to true statements, enabling verification of extremely long statements without complete reading. Discover construction of SNAPs for P with proof length, verifier's query complexity, and verification time roughly O(n^(1/2)) from LWE for adaptive soundness, with extensions to NP using indistinguishability obfuscation and nearly optimal parameter proofs. Examine fully succinct SNAPs for NP with poly(lambda) proof length, query complexity, and verification time based on LWE and indistinguishability obfuscation in non-adaptive settings, along with implications for non-adaptively sound SNARGs for NP when restricted to P. Understand the central role of commitment of proximity, a new notion enabling sublinear-time verification of commitments, in these SNAP constructions based on joint research presented at STOC 2025.
