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.

Note: Minor typos corrected as pointed out by readers.

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: 2024-06-17: revised; 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},
      note = {\url{https://eprint.iacr.org/2024/954}},
      url = {https://eprint.iacr.org/2024/954}
}