Paper 2017/1258 Original: eprint.iacr.org/2017/1258 ↗
Remarks on Quaternions/Octonion Based Diffie-Hellman Key Exchange Protocol Submitted to NIST PQC Project
Abstract
In November 2017, Juan edro Hecht and Jorge Alejandro Kamlofsky submitted a quaternions/octonions based Diffie-Hellman key agreement protocol HK17 to NIST post quantum cryptography project. Daniel J. Bernstein and Tanja Lange showed how to break the scheme in O(p) steps where p is the modulo used in the scheme. One may wonder whether the scheme could be secure if p is sufficiently large (e.g., p is 1000 bits long)? In this note, we show that the scheme could be broken by solving a homogeneous quadratic equation system of eight equations in four unknowns. Thus no matter how big the p it is, it could be trivailly broken using Kipnis and Shamir’s relinearization techniques.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2017-12-31: last updated
- 2017-12-31: published
- Short URL
- https://ia.cr/2017/1258
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2017/1258,
author = {Yongge Wang and Qutaibah m. Malluhi},
title = {Remarks on Quaternions/Octonion Based Diffie-Hellman Key Exchange Protocol Submitted to NIST PQC Project},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/1258},
year = {2017},
url = {https://eprint.iacr.org/2017/1258}
}