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2020 | OriginalPaper | Buchkapitel

Practical Exact Proofs from Lattices: New Techniques to Exploit Fully-Splitting Rings

verfasst von : Muhammed F. Esgin, Ngoc Khanh Nguyen, Gregor Seiler

Erschienen in: Advances in Cryptology – ASIACRYPT 2020

Verlag: Springer International Publishing

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Abstract

We propose a very fast lattice-based zero-knowledge proof system for exactly proving knowledge of a ternary solution \(\vec {s} \in \{-1,0,1\}^n\) to a linear equation \(A\vec {s}=\vec {u}\) over \(\mathbb {Z}_q\), which improves upon the protocol by Bootle, Lyubashevsky and Seiler (CRYPTO 2019) by producing proofs that are shorter by a factor of 8.

At the core lies a technique that utilizes the module-homomorphic BDLOP commitment scheme (SCN 2018) over the fully splitting cyclotomic ring \(\mathbb {Z}_q[X]/(X^d + 1)\) to prove scalar products with the NTT vector of a secret polynomial.

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Vorheriges Kapitel Efficient Homomorphic Comparison Methods with Optimal Complexity

Nächstes Kapitel Towards Classical Hardness of Module-LWE: The Linear Rank Case

We use the term “proof” instead of the slightly more precise “argument”, and mean computationally sound zero-knowledge proof when we just write zero-knowledge proof.

Recall that a coefficient of \(\varvec{c}\) is zero with probability 1/2 and a coefficient of \(\vec {\varvec{r}}\) is zero with probability 6/16. The probabilities of \(\pm 1\) are always equal to each other.

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Titel: Practical Exact Proofs from Lattices: New Techniques to Exploit Fully-Splitting Rings
verfasst von: Muhammed F. Esgin
Ngoc Khanh Nguyen
Gregor Seiler
Verlag: Springer International Publishing
Buch: Advances in Cryptology – ASIACRYPT 2020
Print ISBN: 978-3-030-64833-6

Electronic ISBN: 978-3-030-64834-3

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-64834-3_9

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