### 数学代写|密码学作业代写Cryptography代考|CS388H

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|密码学作业代写Cryptography代考|Multiple Keys

In practice a system that uses symmetric cryptosystems is unlikely to confine itself to a single key. Usually, there is a huge number of keys, even when there is not a huge number of users. Studying systems with more than one key is therefore important.

It is possible to design variants of the security games where the experiment has multiple independent keys, and the adversary may choose which key the experiment should use when answering a query.

As usual, these multi-key notions contain the single-key notions as special cases. Conversely, we can prove that any adversary against the multi-key notions can be turned into an adversary against a single-key notion, and the advantage of the multi-key adversary is at most that of the single-key adversary times the number of keys.

Exercise 7.12. Define a multi-key variant of ror-cca, state a precise variant of the above informal claim and use a hybrid argument to prove the statement.
Another multi-key variant is to allow key reveal, where the adversary may learn a subset of the keys, chosen adaptively. The immediate problem is that the adversary cannot first ask for any challenge ciphertexts under some key, and then later ask for the key, since this will immediately reveal the challenge bit. The underlying problem is that revealing ciphertexts commits the experiment to a certain key, which is difficult to reveal. Most of the natural generalisations of the theorems we have proven for the single-key case are hard to prove for the multi-key case with key compromise. Stateful encryption is one approach to achieve multi-key security with key compromise which we shall investigate later.

## 数学代写|密码学作业代写Cryptography代考|Stream Ciphers

We shall only consider what is often called synchronious or additive stream ciphers, where a key stream generator expands a key and an initialisation vector into a string of symbols which is then added to the message (which is interpreted as a string of symbols). Traditionally, stream ciphers were bit oriented, but we can take the alphabet to be any group.

Definition 7.9. Let $f: \mathfrak{R} \times \mathfrak{V} \rightarrow G^N$ be a key stream generator. A $\left(\tau, l_c\right)$ adversary against $f$ is an interactive algorithm $\mathcal{A}$ that interacts with the experiment in Figure $7.12$ making at most $l_c$ queries to the experiment, and where the runtime of the adversary and the experiment is at most $\tau$.
$$\operatorname{Ad}_f^{\mathrm{kgg}}(\mathcal{A})=2|\operatorname{Pr}[E]-1 / 2|,$$
where $E$ is the event that $b^{\prime}$ output by $\mathcal{A}$ equals the experiment’s $b$.
We will only compute as many key stream elements as is needed. The key stream must be computed by some algorithm whose cost is essentially linear in the number of key stream elements computed.

Remark. Sometimes we want a pseudo-random generator $f: \mathfrak{K} \rightarrow G^N$. Since there is no initialisation vector, each key expands into a single key stream. The security game is the single-query variant of the key stream security game.
Remark. There is a stronger notion of security for key stream generators, where the adversary is allowed to specify the initialisation vector to be used (a pseudo-random function). This is usually too strong a requirement, since it is not needed and may make key stream generator design harder. An interme-diate variant is to specify some fixed sequence of initialisation vectors, which is often easy to design for and has advantages in many applications.

# 密码学代写

## 数学代写|密码学作业代写Cryptography代考|Stream Ciphers

$$\operatorname{Ad}_f^{\mathrm{kgg}}(\mathcal{A})=2|\operatorname{Pr}[E]-1 / 2|,$$

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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。