International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Group Action Key Encapsulation and Non-Interactive Key Exchange in the QROM

Julien Duman , Ruhr-University Bochum
Dominik Hartmann , Ruhr-University Bochum
Eike Kiltz , Ruhr-University Bochum
Sabrina Kunzweiler , Ruhr-University Bochum
Jonas Lehmann , Ruhr-University Bochum
Doreen Riepel , Ruhr-University Bochum
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Presentation: Slides
Conference: ASIACRYPT 2022
Abstract: In the context of quantum-resistant cryptography, cryptographic group actions offer an abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) setting. In this work, we revisit the security of two previously proposed natural protocols: the Group Action Hashed ElGamal key encapsulation mechanism (GA-HEG KEM) and the Group Action Hashed Diffie-Hellman non-interactive key-exchange (GA-HDH NIKE) protocol. The latter protocol has already been considered to be used in practical protocols such as Post-Quantum WireGuard (S&P '21) and OPTLS (CCS '20). We prove that active security of the two protocols in the Quantum Random Oracle Model (QROM) inherently relies on very strong variants of the Group Action Strong CDH problem, where the adversary is given arbitrary quantum access to a DDH oracle. That is, quantum accessible Strong CDH assumptions are not only sufficient but also necessary to prove active security of the GA-HEG KEM and the GA-HDH NIKE protocols. Furthermore, we propose variants of the protocols with QROM security from the classical Strong CDH assumption, i.e., CDH with classical access to the DDH oracle. Our first variant uses key confirmation and can therefore only be applied in the KEM setting. Our second but considerably less efficient variant is based on the twinning technique by Cash et al. (EUROCRYPT '08) and in particular yields the first actively secure isogeny-based NIKE with QROM security from the standard CDH assumption.
Video from ASIACRYPT 2022
  title={Group Action Key Encapsulation and Non-Interactive Key Exchange in the QROM},
  author={Julien Duman and Dominik Hartmann and Eike Kiltz and Sabrina Kunzweiler and Jonas Lehmann and Doreen Riepel},