Paper 2024/521 Original: eprint.iacr.org/2024/521 ↗

LIT-SiGamal: An efficient isogeny-based PKE based on a LIT diagram

Abstract

We propose LIT-SiGamal, a novel isogeny-based public key encryption (PKE) scheme that combines the structure of SiGamal with the recently introduced LIT diagram framework. While SiGamal relies on a commutative CSIDH-based diagram involving an auxiliary point, LIT-SiGamal replaces this with a LIT diagram -- a commutative diagram consisting of large-degree horizontal isogenies and relatively low-degree vertical isogenies. LIT-SiGamal is an efficient and secure isogeny-based PKE scheme. Our analysis suggests that it is more efficient than QFESTA, proposed by Nakagawa and Onuki. Although LIT-SiGamal appears to be less efficient than POKÉ, proposed by Basso and Maino, it offers stronger security guarantees. Moreover, we provide a Rust implementation of LIT-SiGamal, which represents the first low-level language implementation of an isogeny-based PKE scheme developed after the break of SIDH.