期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 66, 期 9, 页码 5754-5773出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2020.2976073
关键词
Protocols; Encryption; Public key; Decoding; Lattices; Code-based group signature; zero-knowledge protocol; McEliece encryption; syndrome decoding
资金
- Singapore Ministry of Education [MOE2013-T2-1-041, MOE2016-T2-2-014(S)]
- National Research Foundation (NRF) through the Ministry of Science and ICT (MSIT), Korea Government [NRF-2018R1C1B6008476]
- Gopalakrishnan-NTU Presidential Postdoctoral Fellowship 2018
- National Research Foundation, Singapore Prime Minister's Office, under its Strategic Capability Research Centres Funding Initiative
- [TL-9014101684-01]
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 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, i.e., 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.
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