Cryptology ePrint Archive: Report 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.

Category / Keywords: Diffie-Hellman key agreement

Date: received 26 Dec 2017, last revised 26 Dec 2017

Contact author: yonwang at uncc edu

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Version: 20171231:020422 (All versions of this report)

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