FAST COMPUTATION OF DIRECT EXPONENTIATION TO SPEED UP IMPLEMENTATION OF DYNAMIC BLOCK CIPHERS

Luong Tran Thi
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Abstract

MDS (maximum distance separable) matrices are ones that come from MDS codes that have been studied for a long time in error correcting code theory and have many applications in block ciphers. To improve the security of block ciphers, dynamic block ciphers can be created. Using MDS matrix transformations is a method used to make block ciphers dynamic. Direct exponentiation is a transformation that can be used to generate dynamic MDS matrices to create a dynamic diffusion layer of the block ciphers. However, for cryptographic algorithms that use an MDS matrix as a component of them, the implementation of matrix multiplication is quite expensive, especially when the matrix has a large size. In this paper, the mathematical basis for quick calculation of direct exponentiation of an MDS matrix will be presented. On that basis, it is to suggest how to apply that fast calculation to dynamic algorithms using the direct exponentiation. This result is very meaningful in software implementation for MDS matrices, especially when implementing dynamic block ciphers to increase execution speed.
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直接幂的快速计算,加快动态分组密码的实现
最大距离可分离矩阵来源于纠错码理论中研究已久的最大距离可分离码,在分组密码中有着广泛的应用。为了提高分组密码的安全性,可以创建动态分组密码。使用MDS矩阵变换是一种使分组密码动态的方法。直接幂是一种转换,可用于生成动态MDS矩阵,以创建分组密码的动态扩散层。然而,对于使用MDS矩阵作为其组件的加密算法,矩阵乘法的实现非常昂贵,特别是当矩阵具有很大的尺寸时。本文给出了快速计算MDS矩阵直接幂的数学基础。在此基础上,提出了如何将这种快速计算应用于直接求幂的动态算法。该结果对MDS矩阵的软件实现,特别是实现动态分组密码以提高执行速度具有重要意义。
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