A new McEliece-type cryptosystem using Gabidulin-Kronecker product codes
This paper presents a new McEliece-type cryptosystem using Gabidulin-Kronecker product codes in the rank metric. The contributions of this paper are as follows. Firstly, we propose a new Gabidulin-Kronecker product code which is a kind of block circulant code, and give an efficient decoding algorith...
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| Published in: | Theoretical computer science Vol. 994; p. 114480 |
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| Format: | Journal Article |
| Language: | English |
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01.05.2024
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | This paper presents a new McEliece-type cryptosystem using Gabidulin-Kronecker product codes in the rank metric. The contributions of this paper are as follows. Firstly, we propose a new Gabidulin-Kronecker product code which is a kind of block circulant code, and give an efficient decoding algorithm. Secondly, we design a one-way secure public key encryption scheme based on the Gabidulin-Kronecker product codes. Thirdly, we obtain an IND-CCA2 secure public key encryption scheme by converting our one-way secure public key encryption scheme under the hardness assumption of the RSD Dual Problem. In terms of efficiency, our scheme has a smaller public key size by taking advantage of the block circulant structure. For 128-bit security, the public key size of our proposal is 13% of Lau-Tan's cryptosystem (in the rank metric), and 19% of BIKE (in the Hamming metric). In terms of security, our scheme can resist Overbeck attack, Coggia-Couvreur attack and Sendrier attack. |
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| AbstractList | This paper presents a new McEliece-type cryptosystem using Gabidulin-Kronecker product codes in the rank metric. The contributions of this paper are as follows. Firstly, we propose a new Gabidulin-Kronecker product code which is a kind of block circulant code, and give an efficient decoding algorithm. Secondly, we design a one-way secure public key encryption scheme based on the Gabidulin-Kronecker product codes. Thirdly, we obtain an IND-CCA2 secure public key encryption scheme by converting our one-way secure public key encryption scheme under the hardness assumption of the RSD Dual Problem. In terms of efficiency, our scheme has a smaller public key size by taking advantage of the block circulant structure. For 128-bit security, the public key size of our proposal is 13% of Lau-Tan's cryptosystem (in the rank metric), and 19% of BIKE (in the Hamming metric). In terms of security, our scheme can resist Overbeck attack, Coggia-Couvreur attack and Sendrier attack. |
| ArticleNumber | 114480 |
| Author | Zhuang, Jincheng Sun, Zhe Zhou, Zimeng Fu, Fang-Wei |
| Author_xml | – sequence: 1 givenname: Zhe orcidid: 0000-0002-3932-7903 surname: Sun fullname: Sun, Zhe email: zhe_sun@mail.nankai.edu.cn organization: Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China – sequence: 2 givenname: Jincheng surname: Zhuang fullname: Zhuang, Jincheng email: jchzhuang@gmail.com organization: Quan Cheng Laboratory, Jinan, 250103, China – sequence: 3 givenname: Zimeng surname: Zhou fullname: Zhou, Zimeng email: zhouzimeng@sdu.edu.cn organization: Quan Cheng Laboratory, Jinan, 250103, China – sequence: 4 givenname: Fang-Wei orcidid: 0000-0002-9696-8977 surname: Fu fullname: Fu, Fang-Wei email: fwfu@nankai.edu.cn organization: Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China |
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| Cites_doi | 10.1007/s10623-012-9659-5 10.1007/s10623-019-00659-0 10.1007/s10623-017-0343-7 10.1016/S0166-218X(02)00446-8 10.3934/amc.2017042 10.1007/BF01390769 10.1109/TIT.2003.820038 10.1007/s00145-014-9187-8 10.1007/s10623-020-00781-4 10.1007/s10623-017-0402-0 10.1007/s11786-009-0015-8 10.1007/s10623-014-9967-z 10.1007/s10623-017-0434-5 10.1109/TIT.2016.2616127 10.1007/s002000050104 10.1023/A:1020369320078 10.1109/TIT.2015.2511786 10.1137/100782929 10.1109/TIT.1978.1055873 10.1007/s00145-007-9003-9 10.1007/s10623-021-00972-7 |
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| Keywords | Code-based cryptography IND-CCA2 McEliece-type cryptosystem Rank metric Gabidulin-Kronecker product codes |
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| SubjectTerms | Code-based cryptography Gabidulin-Kronecker product codes IND-CCA2 McEliece-type cryptosystem Rank metric |
| Title | A new McEliece-type cryptosystem using Gabidulin-Kronecker product codes |
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