Provably secure group signature schemes from code-based assumptions

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,...

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Main Authors: Ezerman, Martianus Frederic, Lee, Hyung Tae, Ling, San, Nguyen, Khoa, Wang, Huaxiong
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
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Online Access:https://hdl.handle.net/10356/143454
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1434542023-02-28T19:55:29Z Provably secure group signature schemes from code-based assumptions Ezerman, Martianus Frederic Lee, Hyung Tae Ling, San Nguyen, Khoa Wang, Huaxiong School of Physical and Mathematical Sciences Science::Mathematics::Applied mathematics::Information theory Science::Mathematics::Discrete mathematics::Cryptography Code-based Group Signature Zero-knowledge Protocol 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. Accepted version 2020-09-02T06:29:41Z 2020-09-02T06:29:41Z 2020 Journal Article 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 0018-9448 https://hdl.handle.net/10356/143454 10.1109/TIT.2020.2976073 9 66 5754 5773 en IEEE Transactions on Information Theory © 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: https://doi.org/10.1109/TIT.2020.2976073 application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics::Applied mathematics::Information theory
Science::Mathematics::Discrete mathematics::Cryptography
Code-based Group Signature
Zero-knowledge Protocol
spellingShingle Science::Mathematics::Applied mathematics::Information theory
Science::Mathematics::Discrete mathematics::Cryptography
Code-based Group Signature
Zero-knowledge Protocol
Ezerman, Martianus Frederic
Lee, Hyung Tae
Ling, San
Nguyen, Khoa
Wang, Huaxiong
Provably secure group signature schemes from code-based assumptions
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Ezerman, Martianus Frederic
Lee, Hyung Tae
Ling, San
Nguyen, Khoa
Wang, Huaxiong
format Article
author Ezerman, Martianus Frederic
Lee, Hyung Tae
Ling, San
Nguyen, Khoa
Wang, Huaxiong
author_sort Ezerman, Martianus Frederic
title Provably secure group signature schemes from code-based assumptions
title_short Provably secure group signature schemes from code-based assumptions
title_full Provably secure group signature schemes from code-based assumptions
title_fullStr Provably secure group signature schemes from code-based assumptions
title_full_unstemmed Provably secure group signature schemes from code-based assumptions
title_sort provably secure group signature schemes from code-based assumptions
publishDate 2020
url https://hdl.handle.net/10356/143454
_version_ 1759853679921332224