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def f(r, x, n):
"""
计算 x 的 r 次方模 n
"""
a = x
b = r
c = 1
while b != 0:
while b % 2 == 0:
b = b // 2
a = (a * a) % n
if b % 2 != 0:
b = b - 1
c = (c * a) % n
return c
def Enclid(n, d):
"""
计算模逆运算
"""
a = n
b = d
t = 0
v = 1
w = 0
while True:
r = a % b
if r != 0:
q = (a - r) // b
a = b
b = r
w = v
v = t - q * v
t = w
else:
break
if b == 1:
if v >= 0:
return v
else:
return n + v
else:
return 0
def gcd(a, b):
"""
计算最大公约数
"""
r = a % b
while True:
r = a % b
if r != 0:
a = b
b = r
else:
break
if b == 1:
return 1
else:
return b
def rsa():
"""
RSA 加密算法
"""
p = int(input("输入两个素数:(p、q)\n"))
q = int(input())
n = p * q
fn = (p - 1) * (q - 1)
e = int(input("输入e:\n"))
while True:
if gcd(fn, e) == 1:
break
else:
e = int(input("必须满足gcd(fn,e)=1\n"))
d = Enclid(fn, e)
if d == 0:
print("出错了!\n")
else:
print("公钥(%d,%d)\n" % (e, fn))
print("私钥:(%d,%d)\n" % (d, fn))
m = int(input("Enc: 输入明文:\n"))
while m >= p * q:
print("错误！明文需要小于p*q=%d!\n" % (p * q))
m = int(input())
print("密文:%d\n" % f(e, m, n))
print("解密:m=%d\n" % f(d, f(e, m, n), n))
print("RSA加密算法\n")
print("姓名: W1ndys\n")
print("学号: 10000001\n")
rsa()
input("按Ctrl+C退出")
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