RLWE-Based Zero-Knowledge Proofs for Linear and Multiplicative Relations

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/175977

dc.contributor	Universitat Politècnica de Catalunya. Doctorat en Matemàtica Aplicada
dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.contributor.author	Martínez Pinilla, Ramiro
dc.contributor.author	Morillo Bosch, M. Paz
dc.date	2019
dc.identifier.citation	Martinez, R.; Morillo, M. RLWE-Based Zero-Knowledge Proofs for Linear and Multiplicative Relations. A: IMA Conference on Cryptography and Coding. "Cryptography and Coding: 17th IMA International Conference, IMACC 2019, Oxford, UK, December 16–18, 2019, Proceedings". Springer International Publishing, 2019, p. 252-277.
dc.identifier.citation	978-3-030-35198-4
dc.identifier.citation	https://eprint.iacr.org/2019/1486
dc.identifier.citation	10.1007/978-3-030-35199-1_13
dc.identifier.uri	http://hdl.handle.net/2117/175977
dc.language.iso	eng
dc.publisher	Springer International Publishing
dc.relation	https://link.springer.com/chapter/10.1007/978-3-030-35199-1_13
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Informàtica::Seguretat informàtica::Criptografia
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Cryptography
dc.subject	Data encryption (Computer science)
dc.subject	Zero-knowledge proofs of knowledge
dc.subject	Commitment scheme
dc.subject	Ring learning with errors
dc.subject	Criptografia
dc.subject	Xifratge (Informàtica)
dc.title	RLWE-Based Zero-Knowledge Proofs for Linear and Multiplicative Relations
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/conferenceObject
dc.description.abstract	We present efficient Zero-Knowledge Proofs of Knowledge (ZKPoK) for linear and multiplicative relations among secret messages hidden as Ring Learning With Errors (RLWE) samples. Messages are polynomials in $\mathbb{Z}_q[x]/\left$ and our proposed protocols for a ZKPoK are based on the celebrated paper by Stern on identification schemes using coding problems (Crypto'93). Our 5-moves protocol achieves a soundness error slightly above 1/2 and perfect Zero-Knowledge. As an application we present Zero-Knowledge Proofs of Knowledge of relations between committed messages for a commitment scheme perfectly binding with overwhelming probability over the choice of the public key, and computationally hiding under the RLWE assumption. Compared with previous Stern-based commitment scheme proofs we decrease computational complexity, improve the size of the parameters and reduce the soundness error of each round.
dc.description.abstract	Peer Reviewed

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