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Title: Provably secure group signature schemes from code-based assumptions
Authors: Ezerman, Martianus Frederic
Lee, Hyung Tae
Ling, San
Nguyen, Khoa
Wang, Huaxiong
Keywords: Science::Mathematics::Applied mathematics::Information theory
Science::Mathematics::Discrete mathematics::Cryptography
Issue Date: 2020
Source: Ezerman, M. F., Lee, H. T., Ling, S., Nguyen, K., & Wang, H. (2020). Provably secure group signature schemes from code-based assumptions. IEEE Transactions on Information Theory, 66(9), 5754-5773. doi:10.1109/TIT.2020.2976073
Journal: IEEE Transactions on Information Theory
Abstract: We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the \textsf{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. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, \ie, \textsf{CCA}-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.
ISSN: 0018-9448
DOI: 10.1109/TIT.2020.2976073
Rights: © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
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