Remarks on Quaternions/Octonion Based Diffie-Hellman Key Exchange Protocol Submitted to NIST PQC Project

Yongge Wang; Qutaibah m.  Malluhi

Paper 2017/1258

Remarks on Quaternions/Octonion Based Diffie-Hellman Key Exchange Protocol Submitted to NIST PQC Project

Yongge Wang and Qutaibah m. Malluhi

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. MINOR revision.
Keywords: Diffie-Hellman key agreement
Contact author(s): yonwang @ uncc edu
History: 2017-12-31: received
Short URL: https://ia.cr/2017/1258
License: CC BY

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}
}