International Association
for Cryptologic Research

We analyze the composition of symmetric encryption and digital signatures in secure group messaging protocols where group members share a symmetric encryption key. In particular, we analyze the chat encryption algorithms underlying MLS, Session, Signal, and Matrix using the formalism of symmetric signcryption introduced by Jaeger, Kumar, and Stepanovs (Eurocrypt 2024). We identify theoretical attacks against each of the constructions we analyze that result from the insufficient binding between the symmetric encryption scheme and the digital signature scheme. In the case of MLS and Session, these translate into practically exploitable replay attacks by a group-insider. For Signal this leads to a forgery attack by a group-outsider with access to a user's signing key, an attack previously discovered by Balbás, Collins, and Gajland (Asiacrypt 2023). In Matrix there are mitigations in the broader ecosystem that prevent exploitation. We provide formal security theorems that each of the four constructions are secure up to these attacks.

We introduce a new cryptographic primitive called symmetric signcryption, which differs from traditional signcryption because the sender and recipient share a secret key. We prove that a natural composition of symmetric encryption and signatures achieves strong notions of security against attackers that can learn and control many keys. We then identify that the core encryption algorithm of the Keybase encrypted messaging protocol can be modeled as a symmetric signcryption scheme. We prove the security of this algorithm, though our proof requires assuming non-standard, brittle security properties of the underlying primitives.

We give the first examples of public-key encryption schemes which can be proven to achieve multi-challenge, multi-user CCA security via reductions that are tight in time, advantage, and memory. Our constructions are obtained by applying the KEM-DEM paradigm to variants of Hashed ElGamal and the Fujisaki-Okamoto transformation that are augmented by adding uniformly random strings to their ciphertexts. The reductions carefully combine recent proof techniques introduced by Bhattacharyya'20 and Ghoshal-Ghosal-Jaeger-Tessaro'22. Our proofs for the augmented ECIES version of Hashed-ElGamal make use of a new computational Diffie-Hellman assumption wherein the adversary is given access to a pairing to a random group, which we believe may be of independent interest.