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Title:
On the Security of Isogeny Based AKE in the Quantum Random Oracle Model
Authors: Haiyang Xue, Man Ho Au, Rupeng Yang, Bei Liang, and Haodong Jiang
Abstract:Several quantum-resistant authenticated key exchange protocols (AKEs) have been proposed from supersingular isogenies. SIAKE [Xu et al. ASIACRYPT 2019] is one of the most efficient schemes for achieving strong security. However, its security analyses are conducted in the classical random oracle model, thereby leaving security in the quantum random oracle model (QROM) as an open problem. In this paper, we prove that SIAKE is also secure in the QROM with a slight modification by adding public keys in hash functions. Our approach provides a new AKE based on communicative supersingular isogeny. Our technique could be extended to show that a modified X3LH [Xue et al. ASIACRYPT 2018], a generic AKE based on double-key PKE, is QROM secure under the one-way assumption of double-key PKE.
ePrint: https://eprint.iacr.org/2020/1282
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