1、1234-1 mod 4321
(1234, 4321)=>
4321 = 1234*3 + 619
1234 = 619*1 + 615
619 = 615*1 + 4
615 = 4*153 + 3
4 = 3*1 + 1 =>
1 = 4 – 3*1
= 4 – 615 + 4*153 = 4*154 – 615
= (619 – 615)*154 -615 = 619*154 – 615*155
= 619*154 – (1234 – 619)*155 = 619*309 – 1234*155
= (4321 – 1234*3)*309 – 1234*155 = 4321*309 – 1234*(927+155) = 4321*309 – 1234*1082 =>
1234*(-1082) = 1 mod 4321 =>
1234*3239 = 1 mod 4321
所以 1234-1 mod 4321 == 3239
2、下式是仿射密码的加密变换
c= (3m+5) mod 26,试求:
(1) 该密码的密钥空间是多少
26*φ(26)=26*12=312
(2) 求出消息“hello”对应的密文
h: 7, e: 4, l: 11, o: 14
3*7+5 mod 26 = 0 => a
3*4+5 mod 26 = 17 => r
3*11+5 mod 26 = 12 => m
3*14+5 mod 26 = 21 => v
密文:armmv
(3) 写出它的解密变换
(26, 3) => 26 = 3*8+2
3 = 2*1 + 1 =>
1 = 3 - 2*1
= 3 – (26-3*8) = 3*9 -26
3*9 = 1 mod 26
D=9(y-5) mod 26
(4) 试对密文进行解密
9*-5 mod 26 = 7 => h
9*12 mod 26 = 4 => e
9*7 mod 26 = 11 => l
9*16 mod 26 = 14 => o
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