## CryptoDB

### Paper: Limits on the Efficiency of (Ring) LWE Based Non-interactive Key Exchange

Authors: Siyao Guo Pritish Kamath Alon Rosen Katerina Sotiraki DOI: 10.1007/978-3-030-45374-9_13 Search ePrint Search Google Slides $mathsf {LWE}$ based key-exchange protocols lie at the heart of post-quantum public-key cryptography. However, all existing protocols either lack the non-interactive nature of Diffie-Hellman key-exchange or polynomial $mathsf {LWE}$ -modulus, resulting in unwanted efficiency overhead. We study the possibility of designing non-interactive $mathsf {LWE}$ -based protocols with polynomial $mathsf {LWE}$ -modulus. To this end, We identify and formalize simple non-interactive and polynomial $mathsf {LWE}$ -modulus variants of existing protocols, where Alice and Bob simultaneously exchange one or more (ring) $mathsf {LWE}$ samples with polynomial $mathsf {LWE}$ -modulus and then run individual key reconciliation functions to obtain the shared key. We point out central barriers and show that such non-interactive key-exchange protocols are impossible if: (1) the reconciliation functions first compute the inner product of the received $mathsf {LWE}$ sample with their private $mathsf {LWE}$ secret. This impossibility is information theoretic. (2) One of the reconciliation functions does not depend on the error of the transmitted $mathsf {LWE}$ sample. This impossibility assumes hardness of $mathsf {LWE}$ . We give further evidence that progress in either direction, of giving an $mathsf {LWE}$ -based $mathrm {NIKE}$ protocol or proving impossibility of one will lead to progress on some other well-studied questions in cryptography. Overall, our results show possibilities and challenges in designing simple (ring) $mathsf {LWE}$ -based non-interactive key exchange protocols.
##### BibTeX
@article{pkc-2020-30293,
title={Limits on the Efficiency of (Ring) LWE Based Non-interactive Key Exchange},
booktitle={Public-Key Cryptography – PKC 2020},
series={Public-Key Cryptography – PKC 2020},
publisher={Springer},
volume={12110},
pages={374-395},
doi={10.1007/978-3-030-45374-9_13},
author={Siyao Guo and Pritish Kamath and Alon Rosen and Katerina Sotiraki},
year=2020
}