CAJ | 학술논문

从研究全局雪崩准则的表达方式出发，提出了全局雪崩准则的矩阵表示方法，并证明了布尔函数f（x）与f（x＋α）全局雪崩的绝对值指标和平方和指标相同。依据矩阵表示方法得到了全局雪崩准则与布尔函数Walsh谱值的关系，并给出了一个布尔函数同一个仿射函数的互相关全局雪崩准则绝对指标的上、下限。最后，分析了修改序列中的一位对布尔函数全局雪崩准则指标的影响，结合爬山算法设计了一种修改M-M型Bent函数的优化算法，得到的布尔序列在非线性度和全局雪崩准则指标上优于已有的构造。
종연구전국설붕준칙적표체방식출발，제출료전국설붕준칙적구진표시방법，병증명료포이함수f（x）여f（x＋α）전국설붕적절대치지표화평방화지표상동。의거구진표시방법득도료전국설붕준칙여포이함수Walsh보치적관계，병급출료일개포이함수동일개방사함수적호상관전국설붕준칙절대지표적상、하한。최후，분석료수개서렬중적일위대포이함수전국설붕준칙지표적영향，결합파산산법설계료일충수개M-M형Bent함수적우화산법，득도적포이서렬재비선성도화전국설붕준칙지표상우우이유적구조。
The global avalanche characteristics matrix representation method was proposed by starting from the expres-sion of global avalanche characteristics.And the same absolute value indicator of Boolean functions f(x)and f(x+α) were proved.The relationship between global avalanche characteristics (GAC)and Walsh spectrum was studied by ma-trix representation and the GAC absolute indicators limits between a Boolean function and an affine functions.At last, the influence on GAC indicator by modifying sequence of a Boolean function was analyzed.In combination with hill-climbing algorithm,a large number of Boolean functions with good absolute value indicator were achieved via M-MF Bent functions.