RSA加密算法 python实现

基于python实现rsa加密算法，并生成可执行程序 exe

import PySimpleGUI as sg

# 拓展欧几里得算法求最大公约数
def ex_gcd(a,b,arr):
    if b == 0:
        arr[0] = 1
        arr[1] = 0
        return a
    r = ex_gcd(b,a%b,arr)
    tmp = arr[0]
    arr[0] = arr[1]
    arr[1] = tmp - int(a/b)*arr[1]
    return r

# 将最大公因数回代 辗转相除法回代求得模逆
def get_d(a,b):
    arr = [0,0]
    r = ex_gcd(a,b,arr)
    if r == 1:
        return int((arr[0]%b+b)%b)
    else:
        return -1

# 求解a^b % r 用平方乘（快速幂算法）
def fast_power(a,b):
    if b == 0:
        return 1
    else:
        ans = 1
        while b > 0:
            if b % 2 == 1:
                ans = ans * a
            a = a * a
            b = b // 2
        return ans

# 加密
def encrypt(m,e,n):
    c = fast_power(m,e) % n
    return c

# 解密
def decrypt(c,d,n):
    m = fast_power(c,d) % n
    return m


layout = [
    [sg.T('请输入两个大的素数',size=(15)),sg.In(key='-sushu-',focus=True)],
    [sg.T('请输入您的公钥',size=(15)),sg.In(key='-pk-')],
    [sg.B('产生密钥'),sg.In(key='-sk-',size=(54),disabled=True)],
    [sg.T('请输入明文(整数)',size=(15)),sg.In(key='-P-')],
    [sg.T('加密后的密文',size=(15)),sg.In(key='-C-',disabled=True)],
    [sg.T('解密输出后的明文',size=(15)),sg.In(key='-RES-',disabled=True)],
    [sg.B('加密'),sg.B('解密'),sg.B('重置')]
]

window = sg.Window('RSA算法演示程序',layout)

while 1:
    event, values = window.read()
    # print(values)
    if event == None:
        break

    if event == '产生密钥':
        if values['-sushu-'] == '' or values['-pk-'] == '':
            sg.Popup('提示', '请输入素数和私钥！', title='提示')
        else:
            p, q = map(int, values['-sushu-'].split())
            e = int(values['-pk-'])
            n = p * q
            r = (p - 1) * (q - 1)
            d = get_d(e, r)
            window['-sk-'].update(value='公钥为{e,n}={'+str(e)+','+str(n)+'}  私钥为{d,n}={'+str(d)+','+str(n)+'}')


    if event == '加密':
        if values['-P-'] == '' or values['-sushu-'] == '' or values['-pk-'] == '':
            sg.Popup('提示', '请自己实现加密函数！', title='提示')
        else:
            m = int(values['-P-'])
            p, q = map(int, values['-sushu-'].split())
            e = int(values['-pk-'])
            n = p * q
            c = encrypt(m, e, n)
            window['-C-'].update(value=c)

    if event == '解密':
        if values['-C-'] == '':
            sg.Popup('提示', '请自己实现解密函数！', title='提示')
        else:
            c = int(values['-C-'])
            p, q = map(int, values['-sushu-'].split())
            e = int(values['-pk-'])
            n = p * q
            r = (p - 1) * (q - 1)
            d = get_d(e, r)
            m = decrypt(c, d, n)
            window['-RES-'].update(value=m)

    if event == '重置':
        for item in values:
            window[item].update(value='')
        window['-sushu-'].SetFocus()

window.close()

平方乘函数（快速幂）代码也可以写成（采用位运算，这样更容易理解）

# 输入(a为底数 n为指数 b为模数) 输出就是表达式的值
def fast_power(a,n,b):
    ans = 1
    base = a
    while n != 0:
        if n & 1 != 0:
            ans *= base
        base *= base
        n >>= 1
    return ans % b