南京大学：《计算机问题求解》课程教学资源（PPT课件讲稿）密码算法

计算机问题求解一论题4-6 密码算法 2021年4月12日

计算机问题求解 – 论题4-6 - 密码算法 2021年4月12日

问题1： Cryptosystem是什么意思？它要解决 的基本问题是什么？

最古典：Caesar's Cipher Plain a b d e h k 1 m Cipher D E F G H K L M N P Plain n 0 P T t 心 U 0 E y Cipher Q R S T U W X Z A B a b c d e g h k m 0 1 2 3 4 5 6 7 8 9 10 11 12 m 0 p q r t u U U E y 2 13 14 15 16 17 18 19 20 21 22 23 24 25 Cipher =(Plain+3)mod 26 你试试：VKH GLH LV FDVW The die is cast

最古典: Caesar’s Cipher Cipher = (Plain + 3)mod 26 你试试: WKH GLH LV FDVW The die is cast

问题2： 你能不能用数学概念来描述加密和解密？

Transformations An enciphering transformation (also called an enciphering function)is a bijective function Ee MC, where the key e EK uniquely determines Ee acting upon plaintert message units m E M to get ciphertert message units Ee(m)=c∈C. A deciphering transformation (or deciphering function)is a bijective function Da:e→M, which is uniquely determined by a given key d E K,acting upon ciphertext message units c Ee to get plaintert message units Da(c)=m. The application of Ee to m,namely the operation Ee(m),is called enciphering, encoding,or encrypting m E M,whereas the application of Da to c is called deciphering,decoding,or decrypting ceC

Transformations

Cryptosystem A cryptosystem is composed of a set Ee eEK) consisting of enciphering transformations and the corresponding set (Eel:ee)={Da:deX) of deciphering transformations.In other words,for each eK,there exists a unique deK such that Da=E,so that Da(Ee(m))=m for all mM. The keys (e,d)are called a key pair where possibly e=d.A cryptosystem is also called a cipher

Cryptosystem

问题3： 所谓“key”究竟是什么？

古典密码：德国陆军强于恺撒 The German ADFGVX Field Cipher A G X Plaintext:field cipher A B 3 D ↓ F H DF AX FG AV GF FA AX VX FX FG AG G ↓ key X R F L 5 3 2 4 D A X F G A G F 你试试： F A XFVAXAFFGXFFGXFXFXXGDXDAFGVA A G FFVGAVAXFAAFGXGXFDGFXA

古典密码：德国陆军强于恺撒 Plaintext: field cipher key 你试试：

你试试： XFVAXAFFGXFFGXFXFXXGDXDAFGVA 5 3 2 4 1 A D F G X D F A X X A B 3 M R I A G F X F D A 6 F 中 8 2 F X F G V F C 7 E U H G F G D A G Z 9 D X K V V X X X X 1 W 5 P A F F X 4 G DF AX XA GE XE FX FGVG FG DAVXXX XAFF FINDTHEWEAPONS

你试试： 5 3 2 4 1 D F A X X A G F X F F X F G V G F G D A V X X X X A F F FINDTHEWEAPONS DF AX XA GF XF FX FG VG FG DA VX XX XA FF

问题4： 现在你能说清楚“钥”和 函数”之间的关系了吗