### 数学代写|密码学作业代写Cryptography代考|CIS556

statistics-lab™ 为您的留学生涯保驾护航 在代写密码学Cryptography方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写密码学Cryptography代写方面经验极为丰富，各种代写密码学Cryptography相关的作业也就用不着说。

• 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|Random-Looking Ciphertexts

Some cryptosystems actually provide a stronger notion of real-or-random than the one defined above. The idea is that encryptions of chosen messages are not only hard to distinguish from encryptions of random messages but also hard to distinguish from randomness that is completely independent not only of the chosen message and the associated data, but of the secret key itself.
This property is quite convenient when symmetric cryptography is used as part of a larger system, but it does also have direct applications. One application is to hide a ciphertext in random noise. Another is to show that ciphertexts are pseudo-random, which means that results requiring randomness (such as the left-over hash lemma) can be used.

Definition 7.5. Let $\Sigma=(\mathfrak{K}, \mathfrak{P}, \mathfrak{F}, \mathfrak{C}, \mathcal{E}, \mathcal{D})$ be a symmetric cryptosystem. A noise family $R$ is a family of sampling algorithms indexed by the non-negative integers. An $\left(\tau, l_c, l_e, l_d\right)$-adversary against $R$-random for a symmetric cryptosystem $\Sigma$ is an interactive algorithm $\mathcal{A}$ that interacts with the experiment in Figure $7.8$ making at most $l_e$ challenge queries, $l_e$ chosen plaintext queries and $l_d$ chosen ciphertext queries, and where the runtime of the adversary and the experiment is at most $\tau$.
$$\operatorname{Adv}_{\Sigma}^{\mathrm{R}-\mathrm{rnd}}(\mathcal{A})=2|\operatorname{Pr}[E]-1 / 2|,$$
where $E$ is the event that $b^{\prime}$ output by $\mathcal{A}$ equals the experiment’s $b$.
Exercise 7.7. Let $\Sigma$ be a cryptosystem with ciphertext set $\mathfrak{C}$ and let $R$ be a noise family on $\mathfrak{C}$. Prove that if $\mathcal{A}$ is any $\left(\tau, l_c, l_e, l_d\right)$-adversary against real-orrandom security, then there exists a $\left(\tau^{\prime}, l_c, l_e, l_d\right)$-adversary against $R$-random security for the cryptosystem where $\tau^{\prime}$ is essentially the same as $\tau$ and their advantage are roughly the same (up to a small multiple).

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

For many applications, integrity is more important than confidentiality. Informally, we have integrity if the adversary is unable to create valid ciphertexts that decrypt to new messages. We shall discuss variants of these notions.
We shall define two integrity notions. The first, plaintext integrity, says that the adversary cannot come up with a ciphertext that decrypts to a new message, that is, one not previously submitted as a chosen plaintext query. This intuitively seems to match the sort of integrity we want in applications.
The second integrity notion, ciphertext integrity, says that the adversary cannot come up with a new valid ciphertext, that is, one not previously returned by a chosen plaintext query. This intuitively seems too strong for applications, but this notion is easier to work with and is what we will use for proofs. It also turns out that for many applications the stronger security notion is safer and easier to work with.

Definition 7.6. An $\left(\tau, l_e, l_d\right)$-adversary against integrity for a symmetric cryptosystem $\Sigma$ is an interactive algorithm $\mathcal{A}$ that interacts with the experiment in Figure $7.9$ making at most $l_e$ chosen plaintext queries and $l_d$ test queries, and where the runtime of the adversary and the experiment is at most $\tau$.

$$\operatorname{Adv}{\Sigma}^{\mathrm{int}-\mathrm{ptxt}}(\mathcal{A})=\operatorname{Pr}[E] \quad \text { and } \quad \mathbf{A d v}{\Sigma}^{\text {int-ctxt }}(\mathcal{A})=\operatorname{Pr}[F],$$
where $E$ is the event that for some test query $(a d, c)$, the decryption $m \neq \perp$ and $(a d, m) \notin M$, and $F$ is the event that for some test query $(a d, c) \notin C$, the decryption is not $\perp$. The ciphertexts in events $E$ and $F$ are called forgeries.
Informally, we say that a scheme has plaintext integrity if we have some reasonable argument for why any feasible integrity adversary has no significant plaintext integrity advantage. Ciphertext integrity carries the corresponding informal meaning. If we do know about feasible adversaries with significant advantage, we say that the scheme has no plaintext/ciphertext integrity.
Consider the events $E$ and $F$ in the above definition. Since the event $E$ cannot happen unless $F$ happens, it is clear that for any adversary against integrity, its plaintext advantage is not smaller than its ciphertext advantage. We shall now prove that the converse is not true, which shows that unlike our confidentiality notions, these two integrity notions are not equivalent.

# 密码学代写

## 数学代写|密码学作业代写Cryptography代考|Random-Looking Ciphertexts

$$\operatorname{Adv}_{\Sigma}^{\mathrm{R}-\mathrm{rnd}}(\mathcal{A})=2|\operatorname{Pr}[E]-1 / 2|$$

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

$$\operatorname{Adv} \Sigma^{\text {int-ptxt }}(\mathcal{A})=\operatorname{Pr}[E] \quad \text { and } \quad \operatorname{Adv} \Sigma^{\text {int-ctxt }}(\mathcal{A})=\operatorname{Pr}[F],$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。