Lattice-Based Updatable KEM for Group Messaging

Abstract

Updatable Public-Key Encryption (UPKE) augments the security of PKE with Forward Secrecy properties. While requiring more coordination between parties, UPKE enables much more efficient constructions than full-fledged Forward-Secret PKE. Alwen, Fuchsbauer and Mularczyk (AFM, Eurocrypt’24) presented the strongest security notion to date. It is the first to meet the needs of UPKE’s most important applications: Secure Group Messaging and Continuous Group Key Agreement. The authors provide a very efficient construction of an Updatable Key Encapsulation Mechanism (UKEM), implying UPKE, that satisfies their notion with classic security based on the Computational Diffie-Hellman (CDH) assumption in the Random Oracle Model (ROM). No existing post-quantum UPKE/UKEM construction is known to meet the AFM definition. We present and implement practical secret-key recovery attacks in the AFM adversarial model for all proposed parameter sets of two PQ schemes including the most efficient one to date, due to Abou Haidar, Passelègue and Stehlé (APS, Asiacrypt’23). If the UKEM schemes were used in a real-world group messaging application, the attacks would correspond to realistic execution scenarios, even when targeting a 100% success probability. Next, we present the first post-quantum UKEM construction meeting (a slight relaxation of) the AFM security notion. When based on the Module-LWE assumption, our construction is more efficient than prior PQ constructions, while achieving stronger security. More concretely, public key sizes are about 1/2 that of APS and ciphertext sizes are about 14% smaller. As the AFM security proof relies on random self-reducibility of CDH, which has no analogue for lattices, we develop a new proof technique for strong UKEM, identifying the core properties required from the underlying (lattice-based) encryption scheme.