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# 数学代写|密码学代写Cryptography代考|CSE546 Attacks on SPNs: Linear cryptanalysis

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## 数学代写|密码学代写CRYPTOGRAPHY代考|Attacks on SPNs: Linear cryptanalysis

A related attack is linear cryptanalysis

• Objective: Find targeted key bits.
• Known plaintext attack: attacker has a set of plaintext-ciphertext pairs encrypted with the same key $k$.
• Using probabilistic analysis we find biased linear approximations for the S-boxes. We construct a linear approximation, with a large bias, of the SPN (excepting the final round) in terms of plaintext bits and state bits.
• For each candidate key we partially decrypt each ciphertext and see if the linear approximation holds for state, incrementing a counter for the key if it does.
• The candidate key with largest bias (from |input pairs $\mid / 2$ ) should contain the targeted key bits.
If you are interested in reading more about linear cryptanalysis then there is a description in the recommended textbook.
Cost of differential cryptanalysis
If $p$ is the propagation ratio of the differential trail then the attack is often successful if the number of tuples $\left(x, x^{}, y, y^{}\right)$ is approximately $c / p$ where $c$ is some small constant.
Cost of linear cryptanalysis
If $p$ is the “bias” of the linear approximation then the attack is often successful if the number of plaintext-ciphertext pairs is approximately $c / p^{2}$ where $c$ is some small constant.
Can we protect against these attacks?
• It is possible to design S-boxes to reduce the effectiveness of these attacks.
• DES was protected against differential cryptanalysis but not linear cryptanalysis.
• AES was protected against both attacks.
• The attacks are still theoretically possible but require infeasible quantities of input data.
In the next lecture we will introduce DES which was designed to withstand differential cryptanalysis and is also one of the most important examples of block ciphers.

## 数学代写|密码学代写CRYPTOGRAPHY代考|The Data Encryption Standard (DES)

Early timeline

• Early 1970’s: IBM starts to develop a system for encrypting ATM data.
• 1973: National Bureau of Standards (NBS) puts out a call for submissions for cryptosystems. 1974: NBS repeats call for submissions. IBM submits the Feistel cipher Lucifer.
• 1974/75: The National Security Agency (NSA) provides technical advice to IBM and changes are made to the algorithm.
• 1975: NBS publishes the algorithm for comment.
• 1977: The Data Encryption Standard (DES) adopted for “unclassified” applications.
Feistel ciphers
Definition 11 (Feistel cipher).
A Feistel cipher is an iterated cipher in which the state on round $i$ is divided into two halves of equal length: $L^{i}$ and $R^{i}$.
The round function $g$ has the form $g\left(L^{i-1}, R^{i-1}, k^{i}\right)=\left(L^{i}, R^{i}\right)$ and is computed:
\begin{aligned} L^{i} &=R^{i-1} \ R^{i} &=L^{i-1} \oplus f\left(R^{i-1}, k^{i}\right) \end{aligned}
for some function $f$.

## 数学代写|密码学代写CRYPTOGRAPHY代考|Attacks on SPNs: Linear cryptanalysis

If $p$ 是线侏近似的“偏差”，那奻果明文-密文对的数量约为 $c / p^{2}$ 在哪里 $c$ 是一些小的常数。

DES 可以防止差分密码分析，但不能防止线性密码分析。

AES 被保护免受这两种攻击。

## 数学代写|密码学代写CRYPTOGRAPHY代考|The Data Encryption Standard (DES)

1970 年代初期：IBM 开始开发用于加密 ATM 数据的系统。

1973 年: 国家标准同 (NBS) 呼吁提交密码系统。1974 年: 国家统计局再次征集投稿。IBM 提交 Feistel 密码 Lucifer。

1974/75：美国国家安全局 (NSA) 向 IBM 提供技术建议，并对算法进行了更改。

1975 年: NBS 发布了该算法以供评论。

1977 年: “末分类”应用程序采用数据加密标准 (DES)。
Feistel 密码

Feistel 密码是一种迭代密码，其中循环状态 $i$ 分成等长的两半: $L^{i}$ 和 $R^{i}$.

$$L^{i}=R^{i-1} R^{i} \quad=L^{i-1} \oplus f\left(R^{i-1}, k^{i}\right)$$

## MATLAB代写

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