流密码中S盒的设计和分析

In a modern design of a stream cipher, one might in many situations want to consider functions mapping to a block of output bits. Such functions are referred to as S-boxes. By using S-boxes as the nonlinear combining functions, it is possible to increase the speed of the cipher systems since one may get more than one bit at each clock pulse. Yet design of cryptographically robust Boolean functions is itself a challenging task. In order to resist the known effective attacks, there are at least four main criteria that S-boxes should fulfill. These are: high nonlinearity, resiliency of reasonably high order, high algebraic degree and optimal algebraic immunity. Recently, the applicants found that it is possible to construct resilient S-boxes with higher nonlinearity than any previously known construction methods. And several resilient S-boxes with currently best known nonlinearity have been discovered. The main content of the project includes three aspects as below: 1) Designs and analysis of resilient S-boxes with higher nonlinearity; 2) Designs and analysis of S-boxes with optimal algebraic immunity; 3) Hardware implementations of some design projects of S-boxes. In this project, GMM construction technique and orthogonal spectra technique are used to design S-boxes in steam ciphers. The key on this scheme is how to realize the optimization among nonlinearity, resiliency, algebraic deree and algebraic immunity. We will also study how to apply the algebraic coding theory to the design of algebraic immune functions. This work is of profound theoretical and practical significance on designing stream ciphers which is robust to several attacks such as linear attack, correlation analysis and algebraic attack.

在现代流密码系统的设计中，非线性部件采用Ｓ盒可以大幅度提高加解密速度。为了抵抗已知的有效攻击方式，要求这种用于流密码系统的S盒具有高非线性度、合适的弹性阶、高代数次数以及最优的代数免疫等性质。如何设计能满足多种密码学性质的S盒是一个具有挑战性的课题。本项目拟研究以下内容：①高非线性度弹性S盒的设计和分析；②具有最优代数免疫的S盒的设计和分析；③给出部分设计方案的硬件实现。本项目将利用正交谱技术、GMM构造技术等研究方法来设计可用于流密码系统的S盒。实现设计方案的关键在于如何实现非线性度、弹性代数次数和代数免疫等密码指标的折中。我们还将研究代数编码理论在代数免疫函数设计中的应用等问题。本项目的研究对设计同时抵抗多种攻击的基于S盒的流密码系统具有重要的理论意义与实践价值。

为了保证流密码系统的安全性，进一步提高加解密速度，我们在本项目中研究了满足多种密码学性质的S盒的设计，得到以下研究成果：1) 提出一种新的密码函数构造技术——GMM构造技术，首次设计出非线性度严格几乎最优的弹性S盒; 2) 设计出同时满足多种密码学性质的密码函数，实现非线性度、弹性、代数次数、严格雪崩、GAC、代数免疫、抵抗快速代数攻击等多种密码学性质的优化折中; 3) 给出两种用于Feistel型分组密码的低差分均匀度、高非线性平衡S盒的设计方案，可有效抵抗针对分组密码的两种主流攻击：差分攻击和线性攻击; 4) 系统地给出利用S盒设计用于CDMA系统中大正交序列集的方法。本项目的研究对设计同时抵抗多种攻击的基于S盒的流密码系统具有重要的理论意义与实践价值。