A Provably Secure Group Signature Scheme from Code-Based Assumptions

Abstract. We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from code-based assumptions. Specifically, the scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise prob-lem, and a variant of the Syndrome Decoding problem. Our construction produces smaller key and signature sizes than the existing post-quantum group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed the population of the Netherlands ( ≈ 224 users). The feasibility of the scheme is supported by implementa-tion results. Additionally, the techniques introduced in this work might be of independent interest: a new verifiable encryption protocol for the randomized McEliece encryption and a new approach to design formal security reductions from the Syndrome Decoding problem