Arithmetisation of computation via polynomial semantics for first-order logic

Murdoch J. Gabbay

Paper 2024/954

Arithmetisation of computation via polynomial semantics for first-order logic

Murdoch J. Gabbay

, Heriot-Watt University

Abstract

We propose a compositional shallow translation from a first-order logic with equality, into polynomials; that is, we arithmetise the semantics of first-order logic. Using this, we can translate specifications of mathematically structured programming into polynomials, in a form amenable to succinct cryptographic verification. We give worked example applications, and we propose a proof-of-concept succinct verification scheme based on inner product arguments. First-order logic is widely used, because it is simple, highly expressive, and has excellent mathematical properties. Thus a compositional shallow embedding into polynomials suggests a simple, high-level, yet potentially very practical new method for expressing verifiable computation.

Note: Typos corrected. Exposition clarified. Style file brought up-to-date.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: First-order logic cryptology verifiable computation verifiable logic zero-knowledge proofs polynomial semantics
Contact author(s): m gabbay @ hw ac uk
History: 2024-06-27: last of 2 revisions; 2024-06-13: received; See all versions
Short URL: https://ia.cr/2024/954
License: CC BY

BibTeX

@misc{cryptoeprint:2024/954,
      author = {Murdoch J. Gabbay},
      title = {Arithmetisation of computation via polynomial semantics for first-order logic},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/954},
      year = {2024},
      url = {https://eprint.iacr.org/2024/954}
}