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密码函数安全性指标的研究进展 被引量:3

Recent Progress in Properties of Cryptographic Functions
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摘要 密码函数包含布尔函数与向量函数(S-盒)两大类,是构成序列密码、分组密码和Hash函数这三类密码算法的重要组件,其密码学性质的好坏直接关系到密码算法的安全性.密码算法对于各种已知攻击的抵抗性可以由它所使用的密码函数的相应密码学指标来衡量,密码函数的差分均匀度反映了其抵抗差分攻击的能力,密码函数的非线性度反映了其抵抗线性攻击或快速相关攻击的能力,密码函数的代数免疫度反映了其抵抗代数攻击的能力,密码函数的相关免疫度反映了其抵抗相关攻击的能力,密码函数的代数次数反映其抵抗Berlekamp Massey攻击或高阶差分攻击的能力,其中非线性度、代数免疫度、差分均匀度是三个重要的密码学指标.本文总结了近年来在高度非线性函数、高代数免疫度函数和低差分函数研究方面的进展,重点归纳了Bent函数和向量Bent函数这两类高度非线性函数的性质与构造、具有最优代数免疫度且同时满足高非线性度等其它密码指标较优的布尔函数与向量函数构造、三类低差分函数(PN函数、APN函数和4-差分函数)的性质与构造三个方面的研究现状与进展情况,并对这三方面的下一步研究作了展望. Boolean functions and vectorial functions are two large classes of cryptographic functions, and they are the most important components of stream ciphers, block ciphers and Hash functions. Their cryptographic properties are crucial to the security of the underlying ciphers. The resistance against different attacks of cryptographic algorithms are largely measured by the cryptographic properties of their underlying cryptographic functions. The differential uniformity measures the resistance against differential attack, the nonlinearity measures the resistance against linear attack or fast correlation attack, and the algebraic immunity measures the resistance against algebraic attack, and correlation immunity measures the resistance against correlation attack, the algebraic degree measures the resistance against Berlekamp Massey attack or higher order differential attack, where noninearity, algebraic immunity and differential uniformity are three important security criteria of cryptographic functions. In this paper, we present a survey on the recent progress about cryptographic functions with low differential uniformity, those with high nonlinearity and those with high algebraic immunity respectively, with emphasis being on the constructions and the distribution of the functions with high nonlinearity such as Bent functions and vectorial Bent functions; construction of Boolean functions and vectorial functions with optimum algebraic immunity and good cryptographic properties; properties and constructions of the functions with low uniformity such as perfect nonlinear functions, almost perfect nonlinear functions, 4-uniform functions. We also propose some research problems on these criteria.
出处 《密码学报》 2014年第6期578-588,共11页 Journal of Cryptologic Research
基金 国家自然科学基金项目(61272484) 网络与交换技术国家重点实验室开放基金(SKLNST-2013-1-05)
关键词 密码函数 非线性度 代数免疫度 差分均匀度 cryptographic functions nonlinearity differential uniformity algebraic immunity
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