Cryptology ePrint Archive: Report 2022/353

SNARGs for P from Sub-exponential DDH and QR

James Hulett and Ruta Jawale and Dakshita Khurana and Akshayaram Srinivasan

Abstract: We obtain publicly verifiable Succinct Non-Interactive Arguments (SNARGs) for arbitrary deterministic computations and bounded space non-deterministic computation from standard group-based assumptions, without relying on pairings. In particular, assuming the sub-exponential hardness of both the Decisional Diffie-Hellman (DDH) and Quadratic Residuosity (QR) assumptions, we obtain the following results, where $n$ denotes the length of the instance: 1. A SNARG for any language that can be decided in non-deterministic time $T$ and space $S$ with communication complexity and verifier runtime $(n + S) \cdot T^{o(1)}$. 2. A SNARG for any language that can be decided in deterministic time $T$ with communication complexity and verifier runtime $n \cdot T^{o(1)}$.

Category / Keywords: cryptographic protocols / SNARGs, Fiat-Shamir, non-interactive

Original Publication (with major differences): IACR-EUROCRYPT-2022

Date: received 14 Mar 2022

Contact author: jhulett2 at illinois edu, jawale2 at illinois edu, dakshita at illinois edu, akshayaram srinivasan at tifr res in

Available format(s): PDF | BibTeX Citation

Version: 20220318:094358 (All versions of this report)

Short URL: ia.cr/2022/353


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