# 数学代写|密码学代写cryptography theory代考|Feistel Networks

This is a technique that is applied in several symmetric ciphers, so it is important to be familiar with it. Fortunately, it is rather simple to understand. A pseudo-Hadamard transform (often simply called a PHT) is a transformation of a bit string that is designed to produce diffusion in the bit string. The bit string must be of even length because it is split into two equal halves. So, for example, a 64-bit string is divided into two 32-bit halves. To compute the transform of $a$, you add $a+b\left(\bmod 2^n\right)$. To compute the transform of $b$, you add $a+2 b\left(\bmod 2^n\right)$. The $n$ is the number of bits of each half, in our example 32. Put in more formal mathematical notation \begin{aligned} & a^{\prime}=a+b\left(\bmod 2^n\right) \ & b^{\prime}=a+2 b\left(\bmod 2^n\right) \end{aligned}
The key is that this transform is reversible, as you can see here:
\begin{aligned} & a=2 a^{\prime}-b^{\prime}\left(\bmod 2^n\right) \ & b=a^{\prime}-b^{\prime}\left(\bmod 2^n\right) \end{aligned}
That is it, PHT is a rather simple transform, and because of its simplicity, it is computationally fast, making it attractive for cryptographic applications.

## 数学代写|密码学代写cryptography theory代考|The Serpent Algorithm

The cipher begins with an initial permutation (IP), much as DES does. It then has 32 rounds; each round consists of a key mixing operation (note that the key mixing is simply XORing the round key with the text), s-boxes, and a linear transformation (except for the last round). In the final round, that linear transformation is instead replaced with a key mixing step. Then there is a final permutation (FP). The IP and FP do not have any cryptographic significance; instead, they simply optimize the cipher.

The cipher uses one s-box per round. Then during $R_0$, the $S_0$ s-box is used, and then during $R_1$, the $S_1 s$-box is used. Since there are only eight s-boxes, each one is used four times, so that $R_{16}$ uses $S_0$ again.

It should be obvious that Serpent and Rijndael have some similarities. The following table shows a comparison of the two algorithms.Clearly, Serpent has more rounds than Rijndael, but the round functions of the two algorithms are different enough that simply having more rounds does not automatically mean Serpent is more secure. Serpent is slower due to more rounds, and it is particularly slower on computers that do not support multiprocessing. That was the norm for personal computers at the time of the AES competition. Now, however, multiprocessing computers are ubiquitous. This indicates that today, Serpent can be a secure and efficient algorithm.

# 密码学代考

$$a^{\prime}=a+b\left(\bmod 2^n\right) \quad b^{\prime}=a+2 b\left(\bmod 2^n\right)$$

$$a=2 a^{\prime}-b^{\prime}\left(\bmod 2^n\right) \quad b=a^{\prime}-b^{\prime}\left(\bmod 2^n\right)$$

## 数学代写|密码学代写cryptography theory代考|The Serpent Algorithm

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