elliptic differential operator

elliptic differential operator的基本解释

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椭圆型微分算子

与elliptic differential operator相关的网络例句 [注：此内容来源于网络，仅供参考]

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ)，这两类序列具有&优&的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

Op1 + op2 The addition operator will add two numbers. op1 - op2 The subtraction operator will subtract two numbers. op1 * op2 The multiplication operator will multiply two numbers. op1 / op2 The division operator will divide two numbers. op1 % op2 The modulus operator will return the remainder of the division of two integer operands. op1 xx op2 The exponentiation operator will raise op1 to the power of op2.++op1 The pre-increpment operator will increase the value of op1 first, then assign it. op1++ The post-increment operator will increase the value of op1 after it is assigned.--op1 The pre-decrement operator will decrease the value of op1 before it is assigned. op1-- The post-decrement operator will decrease the value of op1 after it is assigned.

op1 + op2 对两个数值做加法操作 op1 - op2 对两个数值做减法操作 op1 * op2 对两个数值做乘法操作 op1 / op2 对两个数值做除法操作 op1 % op2 求两个整型数值的余数 op1 xx op2 求幂操作：求 op1 的 op2 次幂++op1 前加操作： op1 的值先增加，然后将值赋给自身 op1++后加操作： op1 的值先赋给自身，再增加值--op1 前减操作： op1 的值先减少，然后将值赋给自身 op1—后减操作： op1 的值先赋给自身，再减少值

与elliptic differential operator相关的网络解释 [注：此内容来源于网络，仅供参考]

elliptic differential operator：椭圆型微分算子

elliptic cylinder function 椭圆柱函数 | elliptic differential operator 椭圆型微分算子 | elliptic equation 椭圆型微分方程

strongly elliptic differential operator：强椭圆[型]微分算子

强椭圆[型]方程组|system of strongly elliptic equations | 强椭圆[型]微分算子|strongly elliptic differential operator | 强椭圆性|strong ellipticity

strongly elliptic differential operator：强椭圆微分算子

strongly elcctronegative metal 强负电性金属 | strongly elliptic differential operator 强椭圆微分算子 | strongly elliptic operator 强椭圆算子

self-adjoint elliptic differential operator：自伴椭圆型微分算子

self-adjoint differential operator 自伴微分算子 | self-adjoint elliptic differential operator 自伴椭圆型微分算子 | self-adjoint elliptic operator 自伴椭圆型算子