SNARGs for P from Sub-exponential DDH and QR

James Hulett; Ruta Jawale; Dakshita Khurana; Akshayaram Srinivasan

Paper 2022/353

SNARGs for P from Sub-exponential DDH and QR

James Hulett, Ruta Jawale, 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 $n \cdot T^{o (1)}$ .

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: A major revision of an IACR publication in EUROCRYPT 2022
Keywords: SNARGs Fiat-Shamir non-interactive
Contact author(s): jhulett2 @ illinois edu
jawale2 @ illinois edu
dakshita @ illinois edu
akshayaram srinivasan @ tifr res in
History: 2022-03-18: received
Short URL: https://ia.cr/2022/353
License: CC BY

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}
}