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Paper: On the Hardness of the Computational Ring-LWR Problem and Its Applications

Authors:
Long Chen
Zhenfeng Zhang
Zhenfei Zhang
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DOI: 10.1007/978-3-030-03326-2_15
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Conference: ASIACRYPT 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.
BibTeX
@inproceedings{asiacrypt-2018-29150,
  title={On the Hardness of the Computational Ring-LWR Problem and Its Applications},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11272},
  pages={435-464},
  doi={10.1007/978-3-030-03326-2_15},
  author={Long Chen and Zhenfeng Zhang and Zhenfei Zhang},
  year=2018
}