Compact Isogeny PQC can replace HD wallets, key-tweaking, silent payments

A recent publication by Korean researchers has introduced a novel approach to constructing threshold signatures using PRISM, as detailed in their paper available here. This innovative method leverages the properties of isogenies, specifically their ability to be composed and to undergo a process known as a "pushforward." Essentially, a multisig isogeny key involves a sequence of isogenies. For the generation of a PRISM signature, one needs to push a prime-degree isogeny from an initial elliptic curve through this sequence. The preservation of the prime degree throughout this process ensures the validity of the resulting PRISM signature.

The technical complexity of the discussed paper primarily revolves around adapting these concepts into a viable threshold scheme. This adaptation seems to depend on the presence of a trusted dealer to manage the intricacies involved. However, it is also possible to achieve an n-of-n threshold without such a dealer by employing a Distributed Key Generation (DKG) ceremony. In this setup, each participant contributes by generating a random isogeny starting from the codomain designated by the previous participant's isogeny. The sequence culminates with the final participant, whose codomain serves as the public key for the group.

It is important to note that while this research presents a significant advancement in the field of cryptographic signatures, the security aspects of the proposed method remain uncertain due to its recent publication. As with any new cryptographic technique, thorough vetting and analysis are crucial to ensure its security and practicality before widespread adoption.