Cryptology ePrint Archive: Report 2018/760

Strongly Secure Authenticated Key Exchange from Supersingular Isogeny

Xiu Xu and Haiyang Xue and Kunpeng Wang and Bei Liang and Song Tian and Wei Yu

Abstract: In this paper, we study the authenticated key exchange (AKE) based on supersingular isogeny problems which are believed to be difficult for quantum computers. We first propose a 3-pass AKE based on 1-Oracle SIDH assumption whose soundness is guaranteed by a strictly limited gap problem. The 1-Oracle SIDH and the limited gap assumptions are of independent interest. To enhance the soundness, we also propose a 2-pass AKE based on standard SIDH assumption, which involves more bandwidth. Both the 3-pass and 2-pass AKE protocols allow arbitrary registrant of public keys, and achieve CK$^+$ security (a security model which covers wPFS security, KCI attack, and MEX attack). Our results move us one step forward to the target set by Galbraith of looking for new techniques to design and prove security of AKE in the SIDH setting with the widest possible adversarial goals.

Category / Keywords: authenticated key exchange, key encapsulation mechanism, supersingular elliptic curve isogeny, post quantum

Date: received 18 Aug 2018, last revised 12 Oct 2018

Contact author: xuxiu at iie ac cn

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Version: 20181012:183317 (All versions of this report)

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