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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|Stream Ciphers
A pseudorandom generator $G$ as in Definition $3.14$ is rather inflexible since its output length is fixed. This makes $G$ a poor fit for adapting Construction $3.17$ to handle arbitrary-length messages. Specifically, say $G$ has expansion factor $\ell$. We cannot easily use $G$ to encrypt messages of length $\ell^{\prime}>\ell$ using a single $n$-bit key. And, although we can encrypt messages of length $\ell^{\prime}<\ell$ by truncating the output of $G$, doing so is wasteful since it involves generating $\ell$ pseudorandom bits and then discarding $\ell-\ell^{\prime}$ of them.
Stream ciphers, used in practice to instantiate pseudorandom generators, provide greater flexibility. The output bits of a stream cipher are produced gradually and on demand, so that an application can request exactly as many pseudorandom bits as it needs. This extends their usefulness (since there is no upper bound on the number of bits that can be generated) and improves efficiency (since no extraneous pseudorandom bits are generated).
Formally, a stream cipher is a pair of deterministic algorithms (Init, Next) where:
- Init takes as input a seed $s$ and an optional initialization vector $I V$, and outputs some initial state st.
- Next takes as input a current state st and outputs a bit ${ }^{3} y$ along with updated state st’.
数学代写|网络安全作业代写network security代考|Stream-Cipher Modes of Operation
We discuss two modes of operation for encrypting arbitrary-length messages using a stream cipher (Init, Next): synchronized mode and unsynchronized mode.
Synchronized mode. Stream ciphers are often used to encrypt an online communication session between two parties. In that case, a fresh key $k$ is generated by the parties (e.g., using methods described in Chapter 11) and then that key is used to encrypt the messages sent during the session. Assuming that the communication between the parties is such that all messages arrive in order and no messages are lost (as is the case, e.g., when communicating over TCP), the two parties are synchronized and the following method can be used to encrypt a series of messages from a sender $S$ to a receiver $R$ :
- Both parties call Init $(k)$ to obtain the same initial state $\mathbf{s t}_{0}$.
- Let $\mathrm{st}{S}$ be the current state of $S$. If $S$ wants to encrypt a message $m$, it computes $\left(y\right.$, st $\left.{S}^{\prime}\right):=\operatorname{GetBits}\left(\mathrm{st}{S}, 1^{|m|}\right)$, sends $c:=m \oplus y$ to the receiver, and updates its local state to $\mathrm{st}{S}^{\prime}$.
- Let $\mathrm{st}{R}$ be the current state of $R$. When $R$ receives a ciphertext $c$ from the sender, it computes $\left(y\right.$, st $\left.{R}^{\prime}\right):=\operatorname{GetBits}\left(\mathrm{st}{R}, 1^{|c|}\right)$, outputs the message $m:=c \oplus y$, and updates its own local state to $\mathrm{st}{R}^{\prime}$.
数学代写|网络安全作业代写NETWORK SECURITY代考|Block Ciphers and Block-Cipher Modes of Operation
A block cipher is simply another name for a (strong) pseudorandom permutation. That is, a block cipher $F:{0,1}^{n} \times{0,1}^{\ell} \rightarrow{0,1}^{\ell}$ is a keyed function such that, for all $k$, the function $F_{k}$ defined by $F_{k}(x) \stackrel{\text { def }}{=} F(k, x)$ is a bijection (i.e., a permutation). Recall that $n$ is the key length of $F$, and $\ell$
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is its block length. The main distinction between block ciphers and pseudorandom permutations is that the former typically only support a specific set of key/block lengths, and in particular do not support arbitrary-length keys. For simplicity, we will assume in this section that $\ell=n$.
As shown earlier (cf. Construction 3.30), a block cipher can be used to construct a stream cipher that accepts an $I V$; this means we can use any block cipher $F$ to implement the stream-cipher modes of operation discussed in Section 3.6.2. Several other block-cipher modes of operation are also possible; here, we present four of the most common ones and discuss their security. In our discussion, we assume for simplicity that all messages $m$ being encrypted have length a multiple of $n$ (the block length of $F$ ), and write $m=m_{1}, m_{2}, \ldots, m_{\ell}$ where each $m_{i} \in{0,1}^{n}$ represents a block of the plaintext. (Messages whose length is not a multiple of $n$ can be unambiguously padded to have length a multiple of $n$ by appending a 1 followed by sufficiently many 0 s, and so this assumption is without much loss of generality.)
网络安全作业代写
数学代写|网络安全作业代写NETWORK SECURITY代考|STREAM CIPHERS
一个伪随机生成器G如定义3.14相当不灵活，因为它的输出长度是固定的。这使得G不适合适应建筑3.17处理任意长度的消息。具体来说，说G有膨胀系数ℓ. 我们不能轻易使用G加密长度的消息ℓ′>ℓ使用单个n位密钥。而且，虽然我们可以加密长度的消息ℓ′<ℓ通过截断的输出G, 这样做是浪费的，因为它涉及生成ℓ伪随机位，然后丢弃ℓ−ℓ′其中。
在实践中用于实例化伪随机生成器的流密码提供了更大的灵活性。流密码的输出位是逐渐按需生成的，因此应用程序可以根据需要请求尽可能多的伪随机位。这扩展了它们的用处s一世nC和吨H和r和一世sn这在pp和rb这在nd这n吨H和n在米b和r这Fb一世吨s吨H一种吨C一种nb和G和n和r一种吨和d并提高效率s一世nC和n这和X吨r一种n和这在sps和在d这r一种nd这米b一世吨s一种r和G和n和r一种吨和d.
形式上，流密码是一对确定性算法一世n一世吨,ñ和X吨在哪里：
- Init 将种子作为输入s和一个可选的初始化向量一世在, 并输出一些初始状态 st。
- 接下来将当前状态 st 作为输入并输出一个位3是以及更新的状态 st’。
数学代写|网络安全作业代写NETWORK SECURITY代考|STREAM-CIPHER MODES OF OPERATION
我们讨论了使用流密码加密任意长度消息的两种操作模式一世n一世吨,ñ和X吨：同步模式和非同步模式。
同步模式。流密码通常用于加密两方之间的在线通信会话。在这种情况下，一个新的密钥ķ由当事人产生和.G.,在s一世nG米和吨H这dsd和sCr一世b和d一世nCH一种p吨和r11然后该密钥用于加密会话期间发送的消息。假设双方之间的通信是这样的，所有消息都按顺序到达并且没有消息丢失一种s一世s吨H和C一种s和,和.G.,在H和nC这米米在n一世C一种吨一世nG这在和r吨C磷，双方是同步的，可以使用以下方法对来自发送者的一系列消息进行加密小号到接收器R :
- Both parties call Init $(k)$ to obtain the same initial state $\mathbf{s t}_{0}$.
- Let $\mathrm{st}{S}$ be the current state of $S$. If $S$ wants to encrypt a message $m$, it computes $\left(y\right.$, st $\left.{S}^{\prime}\right):=\operatorname{GetBits}\left(\mathrm{st}{S}, 1^{|m|}\right)$, sends $c:=m \oplus y$ to the receiver, and updates its local state to $\mathrm{st}{S}^{\prime}$.
- Let $\mathrm{st}{R}$ be the current state of $R$. When $R$ receives a ciphertext $c$ from the sender, it computes $\left(y\right.$, st $\left.{R}^{\prime}\right):=\operatorname{GetBits}\left(\mathrm{st}{R}, 1^{|c|}\right)$, outputs the message $m:=c \oplus y$, and updates its own local state to $\mathrm{st}{R}^{\prime}$.
数学代写|网络安全作业代写NETWORK SECURITY代考|BLOCK CIPHERS AND BLOCK-CIPHER MODES OF OPERATION
分组密码只是一个s吨r这nG伪随机排列。也就是说，分组密码F:0,1n×0,1ℓ→0,1ℓ是一个键控函数，因此，对于所有ķ， 功能Fķ被定义为Fķ(X)= 定义 F(ķ,X)是双射一世.和.,一种p和r米在吨一种吨一世这n. 回想起那个n是密钥长度F， 和ℓ
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是它的块长度。分组密码和伪随机排列之间的主要区别在于前者通常只支持一组特定的密钥/分组长度，特别是不支持任意长度的密钥。为简单起见，我们将在本节中假设ℓ=n.
如前所述CF.C这ns吨r在C吨一世这n3.30，分组密码可以用来构造一个流密码，它接受一个一世在; 这意味着我们可以使用任何分组密码F实现第 3.6.2 节中讨论的流密码操作模式。其他几种分组密码操作模式也是可能的；在这里，我们介绍了四个最常见的并讨论了它们的安全性。在我们的讨论中，为了简单起见，我们假设所有消息米被加密的长度是的倍数n $n$ (the block length of $F$ ), and write $m=m_{1}, m_{2}, \ldots, m_{\ell}$ where each $m_{i} \in{0,1}^{n}$ represents a block of the plaintext. (Messages whose length is not a multiple of $n$ can be unambiguously padded to have length a multiple of $n$ by appending a 1 followed by sufficiently many 0 s, and so this assumption is without much loss of generality.)
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