基于线性划分的陷门S盒的设计与分析  

Design and Analysis of Trapdoor S-Box Based on Linear Partition

作　　者：韩羽 张文政 董新锋 HAN Yu;ZHANG Wen-zheng;DONG Xin-feng(Science and Technology on Communication Security Laboratory,Chengdu 610041,China)

机构地区：[1]保密通信重点实验室,成都610041

出　　处：《计算机科学》2020年第S02期368-372,共5页Computer Science

基　　金：国家重点研发计划(2017YFB0802000)。

摘　　要：带陷门的分组密码算法是一种可以满足特定场景下特殊需求的密码算法,陷门函数被广泛地应用于非对称加密算法中,考虑将非对称加密中陷门函数的思想引入分组密码。分组密码算法的核心是S盒,是绝大多数分组算法中唯一的非线性部件,在加密过程中起到混淆的作用,因此在构造分组算法的陷门时主要就是研究在S盒中植入陷门。针对这个问题,文中主要研究了基于陪集对有限域进行线性划分的代数性质来构造陷门S盒的方法,这种陷门S盒的陷门信息就是线性划分的方法。文中首先介绍了线性划分设计陷门算法和陷门S盒的原理,构造了一种映射在线性划分上的8×8陷门S盒,给出了具体的构造方法,并分析了这种S盒的线性性质和差分性质。为了说明这种S盒的安全性和实用性,采用Bannier等提出的陷门分组算法作为模型,简要地验证分析了陷门的有效性,证明了陷门S盒和陷门算法对线性分析和差分分析的安全性。The block cipher algorithm with trapdoor is a kind of cipher algorithm that can meet the special needs in specific scenarios.The trapdoor function is widely used in asymmetric encryption algorithms.The idea of trapdoor function in asymmetric encryption is considered to be introduced into block cipher.the S-box isthe core of block cipher,which is the only non-linear component in mostly block cipher algorithm.It plays a role of confusion in the encryption process.Therefore,when constructing the trapdoor of the block cipher,the main research is to implant trapdoor into S-box.Aiming at this problem,this paper first studies the method of constructing trapdoor S-box based on the algebraic properties of linear partition of finite fields based on cosets.The trapdoor information is the linear partition method.This article first introduces the principle of trapdoor algorithm and trapdoor S-box based on linear partition.The 8×8 trapdoor S-box mapped on the linear partition is constructed,and the specific construction method is given.The linear and differential properties of this type of S-box are analyzed.In order to illustrate the safety and practicability of this type of S-box,the trapdoor block cipher proposed by Bannier et al is used as a model to briefly verify and ana-lyze the effectiveness of the trapdoor,and prove the safety of trapdoor S-box and trapdoor algorithm to linear analysis and differential analysis.

关 键 词：陷门函数 陪集划分 陷门S盒 差分分析 线性分析 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]