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# FUTUR. Website for the scientific production of UPC researchers

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

Author
Martínez, R.; Morillo, M.
Type of activity
Presentation of work at congresses
Name of edition
17th IMA International Conference on Cryptography and Coding
Date of publication
2019
Presentation's date
2019-12-18
Book of congress proceedings
Cryptography and Coding: 17th IMA International Conference, IMACC 2019, Oxford, UK, December 16–18, 2019, Proceedings
First page
252
Last page
277
Publisher
Springer International Publishing
DOI
10.1007/978-3-030-35199-1_13
Project funding
Advanced cryptography to face new challenges in the e-society
PRivacy preserving pOst-quantuM systEms from advanced crypTograpHic mEchanisms Using latticeS
Repository
http://hdl.handle.net/2117/175977
https://eprint.iacr.org/2019/1486
URL
https://link.springer.com/chapter/10.1007/978-3-030-35199-1_13
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...
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.
Keywords
Commitment scheme, Ring learning with errors, Zero-knowledge proofs of knowledge
Group of research
MAK - Mathematics Applied to Cryptography