【摘要】：模2~n加法是一個(gè)非常重要的密碼運(yùn)算部件,它已經(jīng)被廣泛用于各種對(duì)稱密碼算法的設(shè)計(jì),如MD5、SNOW 3G、SPECK和ZUC等.差分故障攻擊是針對(duì)密碼算法實(shí)現(xiàn)的一種通用的安全性分析方法,該攻擊假設(shè)攻擊者能在算法運(yùn)行過程中動(dòng)態(tài)注入故障.在對(duì)采用模加運(yùn)算的密碼算法進(jìn)行差分故障分析時(shí),攻擊者往往會(huì)導(dǎo)出一個(gè)模加差分方程系統(tǒng),該方程系統(tǒng)中,方程的個(gè)數(shù)恰好等于法注入故障的次數(shù),其與方程系統(tǒng)的解個(gè)數(shù)密切相關(guān).由于注入故障次數(shù)和方程系統(tǒng)解個(gè)數(shù)是評(píng)估故障攻擊復(fù)雜度的兩個(gè)關(guān)鍵參數(shù),因此,研究它們之間的關(guān)系非常有意義.本文討論了上述模加差分方程系統(tǒng)中一類特殊方程系統(tǒng)(即模加差分相互獨(dú)立且服從均勻分布)的解個(gè)數(shù)的統(tǒng)計(jì)特性.作為結(jié)果,本文給出了它們的期望和方差.本文的結(jié)果表明,對(duì)一般的模加差分方程系統(tǒng),平均意義下,需要注入大約log_2(n)+5個(gè)故障可以確定方程系統(tǒng)的候選解.
[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.
【作者單位】： 中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院數(shù)學(xué)機(jī)械化重點(diǎn)實(shí)驗(yàn)室;武漢軟件工程職業(yè)學(xué)院人文學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):61572491和11688101) 國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展計(jì)劃(批準(zhǔn)號(hào):2016YFB0800401)資助項(xiàng)目
【分類號(hào)】：O175.7

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