Paper 2026/1457

Identity-Based Encryption from Isogenies

Abstract

We provide the first construction of identity-based encryption from isogeny-based assumptions. Security of our construction relies on a novel assumption called the "CDH with Mismatched Torsion” (CD-HwMT) assumption, which we introduce. At a high level, the assumption posits the hardness of solving a CDH-like problem even when the adversary is given some additional “safe” leakage. We justify our assumption by showing that, in the Algebraic Isogeny Model, our assumption reduces to well-known assumptions from the literature. As a bonus feature, our identity-based encryption enjoys anonymity, which means that the ciphertexts hide not only the message but also the target identity. We additionally obtain the first isogeny based constructions of laconic oblivious transfer, as well as public-key encryption that simultaneously satisfies security against high-rate key leakage and key-dependent message/circular security from the CDHwMT assumption. All our constructions can be conjectured to be post-quantum secure. At the heart of our results lie several new techniques, which we believe will help in building even more advanced cryptography in isogeny-land.