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Meeting Abstract

On Interactive Oracle Proofs for Boolean R1CS Statements

Publicated to:Lecture Notes In Computer Science. 13411 LNCS 230-247 - 2022-01-01 13411 LNCS(), DOI: 10.1007/978-3-031-18283-9_11

Authors: Cascudo I; Giunta E

Affiliations

IMDEA Software Institute - Author
IMDEA Software Institute , Scuola Superiore di Catania , Universidad Politécnica de Madrid - Author

Abstract

The framework of interactive oracle proofs (IOP) has been used with great success to construct a number of efficient transparent zk-SNARKs in recent years. However, these constructions are based on Reed-Solomon codes and can only be applied directly to statements given in the form of arithmetic circuits or R1CS over large enough fields F. This motivates the question: what is the best way to apply these IOPs to statements that are naturally written as R1CS over small fields, and more concretely, the binary field F2 ? While one can just see the system as one over an extension field F2e containing F2, this seems wasteful, as it uses e bits to encode just one “information” bit. In fact, in FC21 the work BooLigero devised a way to apply the well-known Ligero while being able to encode e bits into one element of F2e. In this paper, we introduce a new protocol for F2 -R1CS which among other things relies on a more efficient embedding which (for practical parameters) allows to encode ≥ e/ 4 bits into an element of F2e. Our protocol makes then black box use of lincheck and rowcheck protocols for the larger field. Using the lincheck and rowcheck introduced in Aurora and Ligero respectively we obtain 1.31 - 1.65 × smaller proofs for Aurora and 3.71 × for Ligero. We also estimate the reduction of prover time by a factor of 24.7 × for Aurora and between 6.9 - 32.5 × for Ligero without interactive repetitions. Our methodology uses the notion of reverse multiplication friendly embeddings introduced in the area of secure multiparty computation, combined with a new IOPP to test linear statements modulo a subspace V≤F2e which may be of independent interest.

Keywords

Administração pública e de empresas, ciências contábeis e turismoAdministração, ciências contábeis e turismoArquitetura e urbanismoArquitetura, urbanismo e designArtesAstronomia / físicaBiodiversidadeBiotecnologíaCiência da computaçãoCiências agrárias iCiências ambientaisCiências biológicas iCiências biológicas iiCiências biológicas iiiCiências sociais aplicadas iComputer science (all)Computer science (miscellaneous)Computer science, artificial intelligenceComputer science, theory & methodsComunicação e informaçãoComunicació i informacióDireitoEducaçãoEducação físicaEngenharias iEngenharias iiEngenharias iiiEngenharias ivEnsinoFarmaciaGeneral computer scienceGeneral o multidisciplinarGeociênciasGeografíaInterdisciplinarLinguística e literaturaMatemática / probabilidade e estatísticaMateriaisMedicina iMedicina iiMedicina iiiMedicina veterinariaOdontologíaPlanejamento urbano e regional / demografiaPsicologíaQuímicaSaúde coletivaTheoretical computer science

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-06-11:

  • Open Alex: 5
  • Scopus: 3
  • OpenCitations: 5

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-11:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Italy.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (GIUNTA, EMANUELE).