We present two provably secure password-authenticated key exchange (PAKE) protocols
based on a commutative group action. To date the most important instantiation of isogeny …

Abstract We define the Generic Group Action Model (GGAM), an adaptation of the Generic
Group Model to the setting of group actions (such as CSIDH). Compared to a previously …

In the context of quantum-resistant cryptography, cryptographic group actions offer an
abstraction of isogeny-based cryptography in the Commutative Supersingular Isogeny Diffie …

An original key encapsulation scheme is proposed as a modification of the CSIDH algorithm
built on the isogenies of non-cyclic Edwards curves. The corresponding CSIKE algorithm …

For the PQC CSIDH and CSIKE algorithms, the advantages of two classes of quadratic and
twisted supersingular Edwards curves over complete Edwards curves are justified. These …

A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a
corresponding set of independently chosen receiver public keys. The resulting''multi …

We define and analyze the Commutative Isogeny Hidden Number Problem which is the
natural analogue of the Hidden Number Problem in the CSIDH and CSURF setting. In short …

Abstract Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common
session key among multiple parties. Usually, PKI-based AKE schemes are designed to …

The SIDH and CSIDH are now the two most well-known post-quantum key exchange
protocols from the supersingular isogeny-based cryptography, which have attracted much …

Abstract Robustly reusable Fuzzy Extractor (rrFE) allows multiple extractions from the same
fuzzy source in a reproducible way. The reusability of rrFE asks the pseudo-randomness of …