关于最大距离可分矩阵的直接方幂(英文)

On direct exponentiation of maximum distance separable matrices

最大距离可分(MDS)矩阵代表一类在密码学和编码论中有实际应用的、具有一定扩散性质的函数.近来,Murtaza and Ikram提出了一个通过直接方幂生成MDS矩阵的新方法.针对其中指数e=2的一个命题的伪证明,研究了若干隐藏其后的方法论及逻辑问题,进而构造域特征p≥2两种情形下的两类反例.

Maximum Distance Separable（MDS） matrices represents a class of functions with certain diffusion properties that have practical applications in cryptography and code theory.Recently,Murtaza and Ikram proposed a novel method of generating MDS matrices via direct exponentiation.This paper investigates some problems in the methodology and logic behind a false proof of one of their propositions where exponent.Furthermore,two classes of counterexamples are constructed for two cases of field characteristics.