Nonlinear Components of a Block Cipher over Eisenstein Integers  

作　　者：Mohammad Mazyad Hazzazi Muhammad Sajjad Zaid Bassfar Tariq Shah Ashwag Albakri 

机构地区：[1]Department of Mathematics,College of Science,King Khalid University,Abha,61413,Saudi Arabia [2]Department of Mathematics,Quaid-I-Azam University,Islamabad,45320,Pakistan [3]Department of Information Technology,University of Tabuk,Tabuk,71491,Saudi Arabia [4]Department of Computer Science,College of Computer Science&Information Technology,Jazan University,Jazan,45142,Saudi Arabia

出　　处：《Computers, Materials & Continua》2023年第12期3659-3675,共17页计算机、材料和连续体（英文）

基　　金：extend their appreciation to the Deanship of Scientific Research at King Khalid University,for funding this work through the General Research Groups Program under Grant No.R.G.P.2/109/43.

摘　　要：In block ciphers,the nonlinear components,also known as substitution boxes(S-boxes),are used with the purpose to induce confusion in cryptosystems.For the last decade,most of the work on designing S-boxes over the points of elliptic curves,chaotic maps,and Gaussian integers has been published.The main purpose of these studies is to hide data and improve the security levels of crypto algorithms.In this work,we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers(EI).The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters.However,in the same way,by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve(EC),chaotic maps,and Gaussian integers.The newly designed pair of S-boxes are assessed by various tests like nonlinearity,bit independence criterion,strict avalanche criterion,linear approximation probability,and differential approximation probability.

关 键 词：Eisenstein integers residue class of Eisenstein integers block cipher S-boxes analysis of S-boxes 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]