On the hardness of the computational ring-LWR problem and its applications

Document Type

Conference Proceeding

Publication Date

1-1-2018

Abstract

In this paper, we propose a new assumption, the Computational Learning With Rounding over rings, which is inspired by the computational Diffie-Hellman problem. Assuming the hardness of R-LWE, we prove this problem is hard when the secret is small, uniform and invertible. From a theoretical point of view, we give examples of a key exchange scheme and a public key encryption scheme, and prove the worst-case hardness for both schemes with the help of a random oracle. Our result improves both speed, as a result of not requiring Gaussian secret or noise, and size, as a result of rounding. In practice, our result suggests that decisional R-LWR based schemes, such as Saber, Round2 and Lizard, which are among the most efficient solutions to the NIST post-quantum cryptography competition, stem from a provable secure design. There are no hardness results on the decisional R-LWR with polynomial modulus prior to this work, to the best of our knowledge.

Identifier

85057621363 (Scopus)

ISBN

[9783030033255]

Publication Title

Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

External Full Text Location

https://doi.org/10.1007/978-3-030-03326-2_15

e-ISSN

16113349

ISSN

03029743

First Page

435

Last Page

464

Volume

11272 LNCS

Grant

U1536205

Fund Ref

National Natural Science Foundation of China

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