李艳俊,王琦,项勇,等.动态密码组件对合MDS矩阵的设计与实现[J]. 微电子学与计算机,2024,41(7):37-45. doi: 10.19304/J.ISSN1000-7180.2023.0490
引用本文: 李艳俊,王琦,项勇,等.动态密码组件对合MDS矩阵的设计与实现[J]. 微电子学与计算机,2024,41(7):37-45. doi: 10.19304/J.ISSN1000-7180.2023.0490
LI Y J,WANG Q,XIANG Y,et al. Design and implementation of dynamic cipher component involutory MDS matrix[J]. Microelectronics & Computer,2024,41(7):37-45. doi: 10.19304/J.ISSN1000-7180.2023.0490
Citation: LI Y J,WANG Q,XIANG Y,et al. Design and implementation of dynamic cipher component involutory MDS matrix[J]. Microelectronics & Computer,2024,41(7):37-45. doi: 10.19304/J.ISSN1000-7180.2023.0490

动态密码组件对合MDS矩阵的设计与实现

Design and implementation of dynamic cipher component involutory MDS matrix

  • 摘要: 随着密码的应用领域不断扩大,应用程度不断加深,应用认可度不断提升,密码算法的需求量越来越大,对不同领域使用的类似算法进行有效分割成为必须。对有限域 \mathrmGF(2^m) 上4阶矩阵进行了研究,重点对 m = 8 的对合最大距离可分(Maximum Distance Separable, MDS)矩阵进行了详细分析和设计。首先,给出了有限域 \mathrmGF(2^8) 上对合矩阵 \boldsymbolG' 满足的形式和限制条件。然后,通过MDS矩阵判定条件给出了4阶对合MDS矩阵的性质以及参数取值范围。最后,计算得出对合MDS矩阵个数不小于 2^58.9 。该研究成果为基于软件实现的分组密码设计提供了大量安全高效的动态扩散组件,使其能够保证基于SP结构设计的分组密码在加解密相同的情形下不增加计算量,可作为不同领域密码算法分割的参数使用。

     

    Abstract: With the continuous expansion of the application fields of cryptography, deepening of application level, and increasing recognition of applications, the demand for ciphers is increasing. It is necessary to effectively segment similar algorithms used in different fields. The fourth-order matrices over \mathrmGF(2^m) are studied in this paper, and the involutory Maximum Distance Separable (MDS) matrices with m = 8 are carefully analyzed and designed. Firstly, the form of the involutory matrix \boldsymbolG' is proposed with restriction conditions over the finite field \mathrmGF(2^8) . Secondly, the properties and the range of parameters of fourth-order involutory MDS matrices are given based on the judgment conditions of MDS matrices. Finally, the number of involutory MDS matrices is calculated, which is not less than 2^58.9 . The research results provide a large number of safe and efficient dynamic diffusion components for the design of block ciphers suitable for software implementation, which can ensure that the block ciphers based on SP structure do not increase the computational complexity for the same structure of encryption and decryption. These involutory MDS matrices can be used as parameters to segment the cryptographic algorithm for different fields.

     

/

返回文章
返回