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• Statistical Computing 统计计算
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• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|数学建模代写math modelling代考|Differential Attacks

The differential attack is based on a symmetric property of the difference
$$D f(x, a):=f(x+a)-f(x)-f(a)+f(0),$$
for the polynomial map $f$ associated with the corresponding MPKC. For example, Dubois et al. [41] proposed the differential attack on Sflash [1] (a variant of MI) by using the following symmetric relation:
$$D \mathscr{G}(\alpha X, a)+D \mathscr{G}(X, \alpha a)=\left(\alpha^{q^{i}}+\alpha\right) D_{\mathscr{G}}(X, a)$$ where $\mathscr{G}(X):=X^{q^{i}+1}$ is the central map of MI. It is known that the differential attack is also available on $l$-IC and the internal perturbations of MI, HFE $[42,46,47]$. On the other hand, the security of HFE and its variations have been studied in [19, 32] and it was proved that HFEV- is secure against the differential attack.

## 数学代写|数学建模代写math modelling代考|Oil and Vinegar Signature Scheme

In the Oil and Vinegar signature scheme $(O V)$ proposed by Patarin [81], $n=2 m$ and the quadratic map $G$ is defined by \begin{aligned} g_{j}(x)=& \sum_{1 \leq i \leq m} x_{i} \cdot\left(\text { linear form of } x_{m+1}, \ldots, x_{n}\right) \ &\left.+\text { (quadratic form of } x_{m+1}, \ldots, x_{n}\right) \end{aligned}
for $1 \leq j \leq m$. Remark that the affine map $T$ is not necessary in OV since the polynomials in $T \circ G$ is also in the form (17). This scheme signs a message $y \in k^{m}$ as follows. First, choose $u_{1}, \ldots, u_{m} \in k$ randomly and find $z_{1}, \ldots, z_{m} \in k$ such that
$$\begin{gathered} g_{1}\left(z_{1}, \ldots, z_{m}, u_{1}, \ldots, u_{m}\right)=y_{1} \ \vdots \ g_{m}\left(z_{1}, \ldots, z_{m}, u_{1}, \ldots, u_{m}\right)=y_{m} \end{gathered}$$
The signature of $y$ is $x=S^{-1}\left(z_{1}, \ldots, z_{m}, u_{1}, \ldots, u_{m}\right)^{t} \in k^{n}$. By the definition of $G$, we see that $\left(z_{1}, \ldots, z_{m}\right)$ is given as a solution of $m$ linear equations of $m$ variables.
As already given in Sect. 3.3, an equivalent secret key of OV is recovered in polynomial time by Kipnis-Shamir’s attack [63] since the coefficient matrices of $g_{1}, \ldots, g_{m}$ are in the form $\left(\begin{array}{cc}0_{m} & * \ * & *{m}\end{array}\right)$ and $\left(\begin{array}{cc}0{m} & * \ * & *{m}\end{array}\right)^{-1}\left(\begin{array}{cc}0{m} & * \ * & {m}\end{array}\right)=\left(\begin{array}{cc}{m} * \ 0 & *_{m}\end{array}\right)$. To enhance its security, Kipnis-Patarin-Goubin [65] proposed an arrangement of OV called the Unbalanced Oil and Vinegar signature scheme $(U O V)$. On this scheme, $n>2 m(v:=n-2 m)$ and $G$ is given as (17) for $1 \leq j \leq m$. The signature generweak key of UQV.

Different to the original OV, Kipnis-Shamir’s attack is not available on UOV directly since the coefficient matrices are in the form $\left(\begin{array}{l}0_{m} {} \ *{m+v}\end{array}\right)$ but Kipnis-Shamir’s attack to be available on UOV with the complexity $O\left(q^{v} \cdot(\right.$ polyn. $)$ ).

# 数学建模代写

## 数学代写|数学建模代写math modelling代考|Differential Attacks

$$D f(x, a):=f(x+a)-f(x)-f(a)+f(0),$$

$$D \mathscr{G}(\alpha X, a)+D \mathscr{G}(X, \alpha a)=\left(\alpha^{q^{i}}+\alpha\right) D \mathscr{g}(X, a)$$ 进行了研究，并证明了 HFEV- 对差分攻击是安全的。

## 数学代写|数学建模代写math modelling代考|Oil and Vinegar Signature Scheme

$$g_{j}(x)=\sum_{1 \leq i \leq m} x_{i} \cdot\left(\text { linear form of } x_{m+1}, \ldots, x_{n}\right) \quad+\left(\text { quadratic form of } x_{m+1}, \ldots, x_{n}\right)$$

$$g_{1}\left(z_{1}, \ldots, z_{m}, u_{1}, \ldots, u_{m}\right)=y_{1} \vdots g_{m}\left(z_{1}, \ldots, z_{m}, u_{1}, \ldots, u_{m}\right)=y_{m}$$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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