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我们提供的网络安全network security及其相关学科的代写，服务范围广, 其中包括但不限于:
非线性方法 nonlinear method functional analysis
变分法 Calculus of Variations
数学代写|网络安全作业代写network security代考|A Fixed-Length MAC
Pseudorandom functions are a natural tool for constructing secure message authentication codes. Intuitively, if the tag $t$ is obtained by applying a pseudorandom function to the message $m$, then forging a tag on a previously unauthenticated message requires the adversary to correctly guess the value of the pseudorandom function at a “new” input point. The probability of guessing the value of a random function on a new point is $2^{-n}$ (if the output length of the function is $n$ ). The probability of guessing such a value for a pseudorandom function can be only negligibly greater.
数学代写|网络安全作业代写network security代考|Domain Extension for MACs
Construction $4.5$ is important in that it shows a general paradigm for constructing secure message authentication codes from pseudorandom functions. Unfortunately, the construction is only capable of handling fixed-length messages that are furthermore rather short. ${ }^{2}$ These limitations are unacceptable in most real-world applications. We show here how a MAC handling arbitrarylength messages can be constructed from any fixed-length MAC for messages of length $n$. The construction we show is not very efficient and is unlikely to be used in practice; far more efficient constructions of secure MACs are known, as we will see later. We include the present construction for its simplicity and generality, and for pedagogical purposes.
Let $\Pi^{\prime}=\left(\right.$ Mac $^{\prime}$, Vrfy $\left.^{\prime}\right)$ be a secure fixed-length MAC for messages of length $n$. Before presenting the construction of a MAC for arbitrary-length messages based on $\Pi^{\prime}$, we rule out some simple ideas and describe some canonical attacks that must be prevented.
- A natural first idea is to parse the message $m$ as a sequence of $n$-bit blocks $m_{1}, \ldots, m_{d}$ and authenticate each block separately, i.e., compute $t_{i}:=\operatorname{Mac}{k}^{\prime}\left(m{i}\right)$ and output $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ as the tag. This prevents an adversary from sending any previously unauthenticated block without being detected. However, it does not prevent a block re-ordering attack in which the attacker shuffles the order of blocks in an authenticated message. Specifically, if $\left\langle t_{1}, t_{2}\right\rangle$ is a valid tag on the message $m_{1}, m_{2}$ (with $\left.m_{1} \neq m_{2}\right)$, then an attacker can construct a valid tag $\left\langle t_{2}, t_{1}\right\rangle$ on the (new) message $m_{2}, m_{1}$, something that is not allowed by Definition 4.2.
- We can prevent the previous attack by authenticating a block index along with each block. That is, we now compute $t_{i}=\operatorname{Mac}{k}^{\prime}\left(i | m{i}\right)$ for all $i$, and output $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ as the tag. (Note that now $\left|m_{i}\right|<n$.) This does not prevent a truncation attack whereby an attacker simply drops blocks from the end of the message (and drops the corresponding blocks of the tag as well).
- A truncation attack can be thwarted by additionally authenticating the message length along with each block. (Authenticating the message length as a separate block does not work. Do you see why?) That is, compute $t_{i}=\operatorname{Mac}{k}^{\prime}\left(\ell|i| m{i}\right)$ for all $i$, where $\ell$ denotes the length of the message in bits. (Once again, the block length $\left|m_{i}\right|$ will need to decrease.) This scheme is vulnerable to a “mix-and-match” attack where the adversary combines blocks from different messages. For example, if the adversary obtains tags $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ and $\left\langle t_{1}^{\prime}, \ldots, t_{d}^{\prime}\right\rangle$ on messages $m=m_{1}, \ldots, m_{d}$ and $m^{\prime}=m_{1}^{\prime}, \ldots, m_{d}^{\prime}$, respectively, it can output the valid tag $\left\langle t_{1}, t_{2}^{\prime}, t_{3}, t_{4}^{\prime}, \ldots\right\rangle$ on the message $m_{1}, m_{2}^{\prime}, m_{3}, m_{4}^{\prime}, \ldots .$
网络安全作业代写
数学代写|网络安全作业代写NETWORK SECURITY代考|A FIXED-LENGTH MAC
伪随机函数是构建安全消息验证码的自然工具。直观地说，如果标签吨通过对消息应用伪随机函数获得米，然后在先前未经身份验证的消息上伪造标签需要对手正确猜测“新”输入点处的伪随机函数的值。在新点上猜测随机函数值的概率为2−n 一世F吨H和这在吨p在吨l和nG吨H这F吨H和F在nC吨一世这n一世s$n$. 为伪随机函数猜测这样一个值的概率只能忽略不计。
数学代写|网络安全作业代写NETWORK SECURITY代考|DOMAIN EXTENSION FOR MACS
建造4.5很重要，因为它显示了从伪随机函数构造安全消息认证代码的一般范例。不幸的是，该结构只能处理固定长度的消息，而且相当短。2这些限制在大多数实际应用中是不可接受的。我们在这里展示了如何从任何固定长度的 MAC 构造处理任意长度消息的 MAC，用于长度的消息n. 我们展示的构造不是很有效，不太可能在实践中使用；正如我们稍后将看到的，更有效的安全 MAC 结构是已知的。我们包括目前的结构是因为它的简单性和普遍性，以及出于教学目的。
让圆周率′=(苹果电脑′,′)是长度消息的安全固定长度 MACn. 在介绍基于任意长度消息的 MAC 的构造之前圆周率′，我们排除了一些简单的想法并描述了一些必须防止的规范攻击。
- 一个自然的第一个想法是解析消息米作为一个序列n位块米1,…,米d并分别验证每个块，即计算 $n$-bit blocks $m_{1}, \ldots, m_{d}$ and authenticate each block separately, i.e., compute $t_{i}:=\operatorname{Mac}{k}^{\prime}\left(m{i}\right)$ and output $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ as the tag. This prevents an adversary from sending any previously unauthenticated block without being detected. However, it does not prevent a block re-ordering attack in which the attacker shuffles the order of blocks in an authenticated message. Specifically, if $\left\langle t_{1}, t_{2}\right\rangle$ is a valid tag on the message $m_{1}, m_{2}$ (with $\left.m_{1} \neq m_{2}\right)$, then an attacker can construct a valid tag $\left\langle t_{2}, t_{1}\right\rangle$ on the (new) message $m_{2}, m_{1}$, something that is not allowed by Definition 4.2.
- We can prevent the previous attack by authenticating a block index along with each block. That is, we now compute $t_{i}=\operatorname{Mac}{k}^{\prime}\left(i | m{i}\right)$ for all $i$, and output $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ as the tag. (Note that now $\left|m_{i}\right|<n$.) This does not prevent a truncation attack whereby an attacker simply drops blocks from the end of the message (and drops the corresponding blocks of the tag as well).
- A truncation attack can be thwarted by additionally authenticating the message length along with each block. (Authenticating the message length as a separate block does not work. Do you see why?) That is, compute $t_{i}=\operatorname{Mac}{k}^{\prime}\left(\ell|i| m{i}\right)$ for all $i$, where $\ell$ denotes the length of the message in bits. (Once again, the block length $\left|m_{i}\right|$ will need to decrease.) This scheme is vulnerable to a “mix-and-match” attack where the adversary combines blocks from different messages. For example, if the adversary obtains tags $\left\langle t_{1}, \ldots, t_{d}\right\rangle$ and $\left\langle t_{1}^{\prime}, \ldots, t_{d}^{\prime}\right\rangle$ on messages $m=m_{1}, \ldots, m_{d}$ and $m^{\prime}=m_{1}^{\prime}, \ldots, m_{d}^{\prime}$, respectively, it can output the valid tag $\left\langle t_{1}, t_{2}^{\prime}, t_{3}, t_{4}^{\prime}, \ldots\right\rangle$ on the message $m_{1}, m_{2}^{\prime}, m_{3}, m_{4}^{\prime}, \ldots .$
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