满足严格雪崩准则的高非线性弹性函数构造
发布时间：2018-07-28 12:24
【摘要】：自Shannon1949年提出完善保密的概念并证明了一次性密码本(One-time Pad:OTP)的安全性后,如何解决完善保密的可操作性则成了国内外学者所关注的问题,而流密码则是结合完善保密的安全性和可操作性所提出的实际可行的密码体制。由于流密码具有实现简单、易于硬件设计实施、加解密速度快等一系列优点,使得其在一些特殊的应用场景中有着独特的优势,特别是在一些专用或机密机构的通信系统中。实际应用中,流密码的实现通常是由较短的种子秘钥经过特定的算法得到随机性质良好的伪随机密钥流,所以伪随机序列生成算法则是流密码的核心部件。而布尔函数作为经典的密钥序列非线性组合生成器的一部分,它的逻辑结构直接决定了生成算法的安全性。为了保障在某些特定的应用场景中加密的安全性,布尔函数的一些指标需要精心地设计以抵抗相应场景下的某些攻击。本文介绍了针对流密码的一些主流攻击和如何衡量一个布尔函数抵抗这些攻击的能力,如最佳抵抗仿射逼近攻击(BAA)或线性攻击的非线性度、抵抗分别征服攻击以及相关攻击的弹性、抵抗差分攻击的严格雪崩准则(SAC)以及扩散准则(PC)和抵抗代数攻击的代数免疫度等。所以为了抵抗某些特定的攻击,构造出满足某些密码学特性的布尔函数则是密码学中的重要课题。而具有高非线性度,满足弹性和严格雪崩准则(SAC)的布尔函数则是其中一类,在流密码、分组密码设计中,特别是对称密钥算法的设计中,这些指标都是必不可少的。为此,本文引入了一些经典的设计方法来构造满足以上多个指标的布尔函数,如广义Maiorana-McFarland构造、Dillon构造和Dobbertin构造方法,并对这些构造方法所得到的函数的各个指标进行了分析。本文还给出了一种构造高非线性弹性函数的有效方法,并在该方法的基础上进行扩展,使其满足了严格雪崩准则。该构造方法可以构造出n(偶数)变元满足SAC并且非线性度1 22 2n?n??的布尔函数,这在之前是未曾得到过的。随后对其进行了一些改进,使得改进后的非线性度在某些情况下得到了一定的提高。
[Abstract]:Since Shannon1949 put forward the concept of perfect security and proved the security of one-off cryptographic book (One-time Pad:OTP), how to solve the problem of how to improve the operation of security has become a concern of scholars at home and abroad. Stream cipher is a practical and feasible cryptosystem which combines the security and maneuverability of security. Because stream cipher has a series of advantages, such as simple implementation, easy hardware design and fast encryption and decryption, it has unique advantages in some special application scenarios, especially in some communication systems of special or confidential organizations. In practical applications, the implementation of stream cipher is usually from a short seed secret key through a specific algorithm to obtain a pseudorandom key stream of good random properties, so pseudorandom sequence generation algorithm is the core component of stream cipher. The Boolean function is a part of the classical key sequence nonlinear composition generator, its logical structure directly determines the security of the generation algorithm. In order to ensure the security of encryption in some specific application scenarios, some metrics of Boolean functions need to be carefully designed to resist some attacks in the corresponding scenarios. This paper introduces some mainstream attacks against stream ciphers and how to measure the ability of a Boolean function to resist these attacks, such as the best resistance to the nonlinear degree of affine approximation attack (BAA) or linear attack. To resist the elasticity of subjugation attack and related attack, the strict avalanche criterion (SAC) against differential attack, the diffusion criterion (PC) and the algebraic immunity of resisting algebraic attack, etc. Therefore, in order to resist some specific attacks, it is an important subject in cryptography to construct Boolean functions that satisfy some cryptographic characteristics. Boolean functions with high nonlinearity and satisfying elastic and strict avalanche criteria (SAC) are one of them. These parameters are essential in stream cipher and block cipher design, especially in the design of symmetric key algorithms. In this paper, some classical design methods are introduced to construct Boolean functions which satisfy the above indexes, such as generalized Maiorana-McFarland construction and Dobbertin construction, and the indexes of the functions obtained by these methods are analyzed. In this paper, an effective method for constructing high nonlinear elastic functions is presented, which is extended to satisfy the strict avalanche criterion. The method can construct n (even number) variables satisfying SAC and the degree of nonlinearity is 1 22 2 n? A Boolean function, which has not been obtained before. Then some improvements are made to improve the degree of nonlinearity in some cases.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.2
本文编号：2150130
[Abstract]:Since Shannon1949 put forward the concept of perfect security and proved the security of one-off cryptographic book (One-time Pad:OTP), how to solve the problem of how to improve the operation of security has become a concern of scholars at home and abroad. Stream cipher is a practical and feasible cryptosystem which combines the security and maneuverability of security. Because stream cipher has a series of advantages, such as simple implementation, easy hardware design and fast encryption and decryption, it has unique advantages in some special application scenarios, especially in some communication systems of special or confidential organizations. In practical applications, the implementation of stream cipher is usually from a short seed secret key through a specific algorithm to obtain a pseudorandom key stream of good random properties, so pseudorandom sequence generation algorithm is the core component of stream cipher. The Boolean function is a part of the classical key sequence nonlinear composition generator, its logical structure directly determines the security of the generation algorithm. In order to ensure the security of encryption in some specific application scenarios, some metrics of Boolean functions need to be carefully designed to resist some attacks in the corresponding scenarios. This paper introduces some mainstream attacks against stream ciphers and how to measure the ability of a Boolean function to resist these attacks, such as the best resistance to the nonlinear degree of affine approximation attack (BAA) or linear attack. To resist the elasticity of subjugation attack and related attack, the strict avalanche criterion (SAC) against differential attack, the diffusion criterion (PC) and the algebraic immunity of resisting algebraic attack, etc. Therefore, in order to resist some specific attacks, it is an important subject in cryptography to construct Boolean functions that satisfy some cryptographic characteristics. Boolean functions with high nonlinearity and satisfying elastic and strict avalanche criteria (SAC) are one of them. These parameters are essential in stream cipher and block cipher design, especially in the design of symmetric key algorithms. In this paper, some classical design methods are introduced to construct Boolean functions which satisfy the above indexes, such as generalized Maiorana-McFarland construction and Dobbertin construction, and the indexes of the functions obtained by these methods are analyzed. In this paper, an effective method for constructing high nonlinear elastic functions is presented, which is extended to satisfy the strict avalanche criterion. The method can construct n (even number) variables satisfying SAC and the degree of nonlinearity is 1 22 2 n? A Boolean function, which has not been obtained before. Then some improvements are made to improve the degree of nonlinearity in some cases.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.2
【共引文献】
相关期刊论文 前5条
1 张振民;史瑞;刘金涛;;密码学安全性指标的分析与应用[J];测试技术学报;2014年06期
2 屈龙江;付绍静;李超;;密码函数安全性指标的研究进展[J];密码学报;2014年06期
3 杨小龙;胡红钢;;Bent函数构造方法研究[J];密码学报;2015年05期
4 高莹;梅佳;;两类基于完全非线性函数的线性码[J];系统科学与数学;2014年02期
5 郑秀林;张聪;郭星;史瑞;;Keccak算法非线性变换x的分析[J];北京电子科技学院学报;2013年04期
相关硕士学位论文 前6条
1 高凌;弹性布尔函数的构造[D];国防科学技术大学;2011年
2 郭星;典型密码模块的研究与应用[D];西安电子科技大学;2014年
3 李恒;猜测决定攻击在流密码分析中的应用[D];国防科学技术大学;2012年
4 叶露晨;低相关序列集的分析与构造[D];国防科学技术大学;2012年
5 张聪;基于SHA-3的分组密码算法设计[D];西安电子科技大学;2014年
6 王彦平;偶特征域上的两类低差分置换多项式[D];湖北大学;2014年
，本文编号：2150130
本文链接：https://www.wllwen.com/kejilunwen/wltx/2150130.html
