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#第8章 信息安全（Information Security）的python程序
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#8.3 措施和技術
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#8.3.1 密碼學
#++++++++++++++++++++#非對稱加密#<程序：把n分解成p*q>
import math
n = 221
m = int(math.ceil(math.sqrt(n)))
flag = 0
for i in range(2,m+1,1):if n % i == 0:print(i,int(n/i))flag = 1break
if flag == 0:print ("Cannot find!")#<程序：RSA加密解密實現>
# All the functions are written by Edwin Sha
def change_number (x, b): #這個函數把一個十進制數x轉換成一串二進制數if x < b: L=[x]; return(L)a=x % b; x=x//breturn([a]+change_number(x,b))   #the least one goes first!
def mod (a,x,b): #計算 a^x mod bL=change_number(x,2)#print("x in binary = ",L)r=a % b; final=1for i in L:if i ==1: final= (final*r) % br = (r*r) % breturn(final)
def GCD(x,y): #計算 x與y的最大公約數if x>y: a=x;b=yelse: a=y;b=xif a%b ==0: return(b)return(GCD(a%b,b))
def Extended_Euclid(x,y,Vx,Vy): #return [a, b] s.t. ax + by = GCD(x,y)#by Edwin Shar=x%y; z=x//yif r==0: return(y,Vy)Vx[0]=Vx[0]-z*Vy[0]Vx[1]=Vx[1]-z*Vy[1]        return(Extended_Euclid(y, r, Vy, Vx))
def Mod_inverse(e, n): # return x : e*x mod n = 1  by Edwin ShaVx=[1,0]Vy=[0,1]if e>n:G,X=Extended_Euclid(e,n,Vx,Vy)d=X[0]%n        else:G,X=Extended_Euclid(n,e,Vx,Vy)d=X[1]%nreturn(d)import random
def RSA_key_generation(p,q): #p and q are primes, compute keys e and dphi=(p-1)*(q-1)e=random.randint(3,phi)if e%2==0: e+=1while(GCD(e,phi) !=1):e=random.randint(3,phi)if e%2==0: e+=1d=Mod_inverse(e,phi)if e*d % phi !=1: print("ERROR: e and d are not generated correctly")return (e,d)def RSA_test(p,q):e,d=RSA_key_generation(p,q)n=p*qprint("e, d, n: ", e, d, n)M=int(input("Please enter M (<n): "));while M>=n: M=int(input("Please enter M (< n)"))C=mod(M,e,n)print("Before transmission, original M=",M," is encrypted to Cipher=",C)M1=mod(C,d,n)if M!=M1:print("!!! Error  !!!")print("After transmission, Cipher",C, "is decrypted back to:",M1,"\n\n")
p=19
q=97
RSA_test(p,q) 

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