文档介绍：西安电子科技大学博士学位论文密码函数及其构造姓名:张卫国申请学位级别:博士专业:密码学指导教师:肖国镇 20061201 摘要密码函数在流密码、,取得以下主要结果: 1) 利用Maiorana-MeFarland构造法构造出一类Plateaued函数,这种密码函数可以满足多个密码学准则:平衡性、高非线性度、适当阶数的相关免疫性、严格雪崩准则、不存在非零线性结构、好的GAC性质等. 2) 引入多输出Plateaued函数的概念,讨论了其密码学性质和构造方法. 给出构造【力,k】≥2k时,可以找到一个基数是2”‘+I加一k)/k ,,<2k时,【玎,k,_-.Fa/2]] . 3) 给出可分布尔函数和可分Plateaued函数的一些性质;提出两个度量密码函数不可分性的指标:. 4) :给出判定Bent函数正规性的一个算法. 5) 利用毗连非线性函数的方法构造出一大类弹性函数,可以限定条件使构造的函数达到Siegenthalor界,同时也考虑了这类函数的非线性度等密码学性质;通过毗连24个满足某些条件的Plateaued函数构造出具有高非线性度的弹性函数. 6) 给出计算乘积多项式周期的方法和公式,并将其用于计算卷积序列的周期. 关键词:密码学Plateaued函数构造毗连不相交码不可分度正规性 Abstract Cryptographic Boolean functions play animportant roleinbothstreamciphers and block thisdissertation,some importantproblems on eryptographic Boolean functions results are asfollows: 1)A class ofplateaued functions has been getby way ofusing theMaiorana- McFariand variety of desirable criteria for functions with cryptographic application could besatisfied:balancedness,hJ曲nonlinearity, correlationimmunity ofreasonably high order,strict avalanche criterion,non— existence of non-zero linear structures andgood globalavalanche characteristics etc. 21 The plateaued functions iSin廿oduced andsome methods to construct thiskindofcryptographie functions effectivemethod forfmding a sctof【玎,k】disjoint linearcodes n≥2k,we could find asetof【^,胡disjoint linearcodes withcardinality2“+L∽一k)/kJ; When n<2k,there does notexist aset adisjoint Iinearcodes withcardinality at least ’hemethod onc∞strI】cting asetof【g/,t,≥[d/2]】disjoint linear codes isalso show how,thanks to0111"method,a(9,2,1)multi- output plateaued functions withhighlynonlinearity could beconstructed. 31We derive several resultstowards abetterunderstanding thecharacterization of separable Boolean fun