A new McEliece-type cryptosystem using Gabidulin-Kronecker product codes

• Published in: Theoretical computer science Vol. 994; p. 114480
• Main Authors: Sun, Zhe, Zhuang, Jincheng, Zhou, Zimeng, Fu, Fang-Wei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-05-2024
• Subjects: Code-based cryptography; Gabidulin-Kronecker product codes; IND-CCA2; McEliece-type cryptosystem; Rank metric; Code-based cryptography; IND-CCA2; McEliece-type cryptosystem; Rank metric; Gabidulin-Kronecker product codes
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2024.114480

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.