python学习实例（7）

Love The Way You Lie 2022-05-08 14:04 175阅读 0赞

#=========================================================
    #第8章 信息安全（Information Security）的python程序
    #=========================================================
    
    #====================
    #8.3 措施和技术
    #====================
    
    #++++++++++++++++++++
    #8.3.1 密码学
    #++++++++++++++++++++
    
    #非对称加密
    
    #<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 = 1
            break
    if flag == 0:
        print ("Cannot find!")
    
    
    
    #<程序：RSA加密解密实现>
    # All the functions are written by Edwin Sha
    def change_number (x, b): #这个函数把一个十进制数x转换成一串二进制数
        if x < b: L=[x]; return(L)
        a=x % b; x=x//b
        return([a]+change_number(x,b))   #the least one goes first!
    def mod (a,x,b): #计算 a^x mod b
        L=change_number(x,2)
        #print("x in binary = ",L)
        r=a % b; final=1
        for i in L:
            if i ==1: final= (final*r) % b
            r = (r*r) % b
        return(final)
    def GCD(x,y): #计算 x与y的最大公约数
        if x>y: a=x;b=y
        else: a=y;b=x
        if 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 Sha
            r=x%y; z=x//y
            if 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 Sha
        Vx=[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]%n
        return(d)
    
    
    import random
    def RSA_key_generation(p,q): #p and q are primes, compute keys e and d
        phi=(p-1)*(q-1)
        e=random.randint(3,phi)
        if e%2==0: e+=1
        while(GCD(e,phi) !=1):
            e=random.randint(3,phi)
            if e%2==0: e+=1
        d=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*q
        print("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)