SNARGs for P from Sub-exponential DDH and QR

James Hulett; Ruta Jawale; Dakshita Khurana; Akshayaram Srinivasan

Paper 2022/353 Original: eprint.iacr.org/2022/353 ↗

SNARGs for P from Sub-exponential DDH and QR

James Hulett

Ruta Jawale

Dakshita Khurana

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 $n \cdot T^{o(1)}$.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
History: 2022-03-18: last updated; 2022-03-18: published
Short URL: https://ia.cr/2022/353
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2022/353,
      author = {James Hulett and Ruta Jawale and Dakshita Khurana and Akshayaram Srinivasan},
      title = {SNARGs for P from Sub-exponential DDH and QR},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/353},
      year = {2022},
      url = {https://eprint.iacr.org/2022/353}
}