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Paper 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.

Metadata
Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
authenticated key exchangekey encapsulation mechanismsupersingular elliptic curve isogenypost quantum
Contact author(s)
xuxiu @ iie ac cn
History
2020-12-13: last of 6 revisions
2018-08-20: received
See all versions
Short URL
https://ia.cr/2018/760
License
Creative Commons Attribution
CC BY
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