We solve an open question in code-based cryptography by introducing the first provably secure group signature scheme from codebased 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 problem, 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 implementation 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.
CITATION STYLE
Ezerman, M. F., Lee, H. T., Ling, S., Nguyen, K., & Wang, H. (2015). A provably secure group signature scheme from code-based assumptions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9452, pp. 260–285). Springer Verlag. https://doi.org/10.1007/978-3-662-48797-6_12
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