# 范式视角下的密码学学科史

Phase I: Cryptography

The classic era

\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

Phase I: Cryptography

The classic era

Phase I: Cryptography

\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

The classic era

Phase I: Cryptography

\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

The classic era

\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

Phase I: Cryptography

The classic era

\texttt{The quick brown fox jumps over the lazy dog}

Phase I: Cryptography

\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}
\texttt{Teqikbonfxjmsoe h aydg}
\texttt{h uc rw o up vrtelz o }

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}

The classic era

Phase I: Cryptography

\texttt{Ufrjlcpogykntpf!i!bzehi!vd!sx!p!vq!wsufma!p}

The classic era

Phase I: Cryptography

• 依赖人的智力和灵感进行密码的设计和加密解密计算
• 涉及比较少的数学知识
• 计算量总体处于较低水平
• 研究局限于密码安全性                                                      (例如维吉尼亚密码和单次钥匙簿的失败)

The classic era

Phase I: Cryptanalysis

The classic era

Phase I: Cryptanalysis

Al Kindi

The classic era

Phase I: Cryptanalysis

\texttt{Uif!rvjdl!cspxo!gpy!kvnqt!pwfs!uif!mbaz!eph}

The classic era

Phase I: Cryptanalysis

\texttt{Uif!rvjdl!cspxo!gpy!kvnqt!pwfs!uif!mbaz!eph}

p出现4次

f出现3次

i,s,u,v出现2次

The classic era

Phase I: Cryptanalysis

\texttt{Uif!rvjdl!cspxo!gpy!kvnqt!pwfs!uif!mbaz!eph}

p出现4次

f出现3次

i,s,u,v出现2次

The classic era

Phase I: Cryptanalysis

The classic era

Phase I: Cryptanalysis

Charles Babbage, 1792-1871

19世纪巴贝奇和卡西斯基各自独立破解维吉尼亚密码，多套字母密码法也被很大程度上破解。

The classic era

Phase I: Cryptanalysis

• 依赖人的智力和灵感发现密码中存在的数学规律和统计学规律
• 基于简单的数学和统计学工具（Al Kindi的频率分析法及其变体）
• 手工破解（计算量总体处于较低水平）

19世纪巴贝奇和卡西斯基各自独立破解维吉尼亚密码，多套字母密码法也被很大程度上破解。

Charles Babbage, 1792-1871

The classic era

Phase I: Cryptanalysis

• 依赖人的智力和灵感发现密码中存在的数学规律和统计学规律
• 基于简单的数学和统计学工具（Al Kindi的频率分析法及其变体）
• 手工破解（计算量总体处于较低水平）

19世纪巴贝奇和卡西斯基各自独立破解维吉尼亚密码，多套字母密码法也被很大程度上破解。

“Black Chamber”

The classic era

Phase II: Cryptography

The machine era

Phase II: Cryptography

The machine era

Phase II: Cryptography

The machine era

Phase II: Cryptography

The machine era

Phase II: Cryptography

The machine era

\underbrace{26^3}_{3个初始状态任意的转子} \times \underbrace{3!}_{转子先后顺序不同} \times \underbrace{\frac{{26}\choose{12}}{6!}\prod_{k=0}^5{{12-2k}\choose{2}}}_{接线板中6条电路} \approx 10^{16}

Phase II: Cryptography

The machine era

DES

Phase II: Cryptography

The machine era

DES

2^{56} \approx 7 \times 10^{16} \text{ per } 64 \text{ bit}

Phase II: Cryptography

The machine era

• 依赖排列组合原理等数学方法设计密码使得难以暴力破解
• 机械辅助加密，总体计算量处于较高水平
• 研究局限于密码安全性

Phase II: Cryptanalysis

The machine era

Marian Rejewski, 1905-1980

Phase II: Cryptanalysis

The machine era

Marian Rejewski, 1905-1980

Alan Turing, 1912-1954

Phase II: Cryptanalysis

The machine era

Marian Rejewski, 1905-1980

Alan Turing, 1912-1954

• 依赖密码的缺陷所导致的特殊性质，使用数学方法分析得出降低计算量的方法。
• 使用机械辅助破解（计算量总体处于较高水平）

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

Phase III: Cryptography

The asymmetric era

• 除此之外，还有基于离散对数问题、椭圆曲线问题等数学问题复杂性的非对称加密方式。

Phase III: Cryptography

The asymmetric era

• 除此之外，还有基于离散对数问题、椭圆曲线问题等数学问题复杂性的非对称加密方式。

• 依赖数学问题的复杂性进行非对称加密
• 总体计算量处于非常高水平                                          (多项式时间加密，指数时间解密)

​而密码分析学则因数学问题复杂性，无法破解密码

Phase IV: Cryptanalysis

The quantum era

## 量子计算！

Phase IV: Cryptanalysis

The quantum era

## 量子计算！

O\left(e^{1.9(\log N)^{1/3}(\log\log N)^{2/3}} \right)

Phase IV: Cryptanalysis

The quantum era

## 量子计算！

O\left(e^{1.9(\log N)^{1/3}(\log\log N)^{2/3}} \right)
O\left((\log N)^2 (\log\log N) (\log\log\log N) \right)

# 范式视角下的密码学学科史

## 谢谢观看

\texttt{Uibmlt!gps!xbudijmh}

By Zui Chen

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