### On the Hardness of the Computational Ring-LWR Problem and its Applications

Long Chen, Zhenfeng Zhang, and Zhenfei Zhang

##### 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 ring-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 ring-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 ring-LWR with polynomial modulus prior to this work, to the best of our knowledge.

Note: Revise some typos.

Available format(s)
Category
Foundations
Publication info
A minor revision of an IACR publication in ASIACRYPT 2018
Keywords
Lattice TechniquesPublic Key Cryptography
Contact author(s)
chenlong0405 @ qq com
History
2019-09-24: last of 2 revisions
See all versions
Short URL
https://ia.cr/2018/536

CC BY

BibTeX

@misc{cryptoeprint:2018/536,
author = {Long Chen and Zhenfeng Zhang and Zhenfei Zhang},
title = {On the Hardness of the Computational Ring-LWR Problem and its Applications},
howpublished = {Cryptology ePrint Archive, Paper 2018/536},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/536}},
url = {https://eprint.iacr.org/2018/536}
}

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