一类模加差分方程系统解个数的期望与方差
发布时间：2018-11-26 18:14
【摘要】：模2~n加法是一个非常重要的密码运算部件,它已经被广泛用于各种对称密码算法的设计,如MD5、SNOW 3G、SPECK和ZUC等.差分故障攻击是针对密码算法实现的一种通用的安全性分析方法,该攻击假设攻击者能在算法运行过程中动态注入故障.在对采用模加运算的密码算法进行差分故障分析时,攻击者往往会导出一个模加差分方程系统,该方程系统中,方程的个数恰好等于法注入故障的次数,其与方程系统的解个数密切相关.由于注入故障次数和方程系统解个数是评估故障攻击复杂度的两个关键参数,因此,研究它们之间的关系非常有意义.本文讨论了上述模加差分方程系统中一类特殊方程系统(即模加差分相互独立且服从均匀分布)的解个数的统计特性.作为结果,本文给出了它们的期望和方差.本文的结果表明,对一般的模加差分方程系统,平均意义下,需要注入大约log_2(n)+5个故障可以确定方程系统的候选解.
[Abstract]:Modular 2n addition is a very important part of cryptographic computing. It has been widely used in the design of various symmetric cryptographic algorithms, such as MD5,SNOW 3G / SPECK and ZUC. Differential fault attack is a general security analysis method for cryptographic algorithms, which assumes that the attacker can dynamically inject the fault during the operation of the algorithm. In the differential fault analysis of cryptographic algorithms using modular addition, attackers often derive a modular additive differential equation system in which the number of equations is exactly equal to the number of times the method injects faults. It is closely related to the number of solutions of the equation system. Since the number of injection faults and the number of solutions to the equation system are two key parameters to evaluate the complexity of the fault attack, it is very meaningful to study the relationship between them. In this paper, we discuss the statistical properties of the number of solutions of a special equation system (i.e., the module addition difference is independent of each other and obeys the uniform distribution) in the above modular additive difference equation system. As a result, their expectations and variances are given. The results of this paper show that for a general modular additive difference equation system, the candidate solution of the equation system can be determined by injecting about five log_2 (n) faults in the average sense.
【作者单位】： 中国科学院数学与系统科学研究院数学机械化重点实验室;武汉软件工程职业学院人文学院;
【基金】：国家自然科学基金(批准号:61572491和11688101) 国家重点基础研究发展计划(批准号:2016YFB0800401)资助项目
【分类号】：O175.7
[Abstract]:Modular 2n addition is a very important part of cryptographic computing. It has been widely used in the design of various symmetric cryptographic algorithms, such as MD5,SNOW 3G / SPECK and ZUC. Differential fault attack is a general security analysis method for cryptographic algorithms, which assumes that the attacker can dynamically inject the fault during the operation of the algorithm. In the differential fault analysis of cryptographic algorithms using modular addition, attackers often derive a modular additive differential equation system in which the number of equations is exactly equal to the number of times the method injects faults. It is closely related to the number of solutions of the equation system. Since the number of injection faults and the number of solutions to the equation system are two key parameters to evaluate the complexity of the fault attack, it is very meaningful to study the relationship between them. In this paper, we discuss the statistical properties of the number of solutions of a special equation system (i.e., the module addition difference is independent of each other and obeys the uniform distribution) in the above modular additive difference equation system. As a result, their expectations and variances are given. The results of this paper show that for a general modular additive difference equation system, the candidate solution of the equation system can be determined by injecting about five log_2 (n) faults in the average sense.
【作者单位】： 中国科学院数学与系统科学研究院数学机械化重点实验室;武汉软件工程职业学院人文学院;
【基金】：国家自然科学基金(批准号:61572491和11688101) 国家重点基础研究发展计划(批准号:2016YFB0800401)资助项目
【分类号】：O175.7
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