Paper 2024/933
A Pure Indistinguishability Obfuscation Approach to Adaptively-Sound SNARGs for NP
Abstract
We construct an adaptively-sound succinct non-interactive argument (SNARG) for NP in the CRS model from sub-exponentially-secure indistinguishability obfuscation ($i\mathcal{O}$) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for NP by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with $i\mathcal{O}$. We first give a direct construction of an adaptively-sound SNARG for NP assuming (sub-exponentially-secure) $i\mathcal{O}$ and an injective one-way function. Then, we show that it suffices to have an injective one-way function that has an inefficient sampler (i.e., sampling a challenge for the one-way function requires super-polynomial time). Because we rely on the existence of injective one-way functions only in the security proof and not in the actual construction, having an inefficient sampling procedure does not impact correctness. We then show that injective one-way functions with an inefficient sampler can be built generically from any vanilla one-way function. Our approach may be independently useful in other settings to replace injective one-way functions with standard one-way functions in applications of $i\mathcal{O}$.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- succinct non-interactive argumentsSNARGadaptive soundnessindistinguishability obfuscation
- Contact author(s)
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bwaters @ cs utexas edu
dwu4 @ cs utexas edu - History
- 2024-06-12: approved
- 2024-06-11: received
- See all versions
- Short URL
- https://ia.cr/2024/933
- License
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CC BY
BibTeX
@misc{cryptoeprint:2024/933, author = {Brent Waters and David J. Wu}, title = {A Pure Indistinguishability Obfuscation Approach to Adaptively-Sound {SNARGs} for {NP}}, howpublished = {Cryptology ePrint Archive, Paper 2024/933}, year = {2024}, note = {\url{https://eprint.iacr.org/2024/933}}, url = {https://eprint.iacr.org/2024/933} }