Sharing the Path: A Threshold Scheme from Isogenies and Error Correcting Codes

TL;DR

This paper introduces a new threshold cryptographic scheme based on isogenies and error-correcting codes, leveraging recent algorithmic advances to enhance security and functionality in isogeny-based cryptography.

Contribution

It presents a novel threshold scheme combining isogeny paths with error-correcting codes, building on recent polynomial-time algorithms for cryptographic transformations.

Findings

Constructed a threshold scheme using isogenies and error-correcting codes

Demonstrated the scheme's security based on the isogeny path problem

Extended the cryptographic toolkit with new encoding techniques

Abstract

In 2022, a prominent supersingular isogeny-based cryptographic scheme, namely SIDH, was compromised by a key recovery attack. However, this attack does not undermine the isogeny path problem, which remains central to the security of isogeny-based cryptography. Following the attacks by Castryck and Decru, as well as Maino and Martindale, Robert gave a mature and polynomial-time algorithm that transforms the SIDH key recovery attack into a valuable cryptographic tool. In this paper, we combine this tool with advanced encoding techniques to construct a novel threshold scheme.