python版教科書級RSA產生key

有些版次的車輪沒造好，就自己造，以下為教科書版能處理1024-bit RSA的python程式

print('利用sympy、numpy來實作RSA演算，含字串的加解密')

import sympy
import numpy as np

?sympy

先產生質數

def generate_prime(): 
  prime = sympy.randprime(2**511, 2**512)
  return prime

p=generate_prime()
q=generate_prime()
print('p=',p,'\nq=',q)
print(type(p))

n=p*q
print('模數n=',n)

公鑰e與私鑰d

phi_n=(p-1)*(q-1)
print('phi_n=',phi_n)

lambda_n=phi_n/sympy.gcd(p-1, q-1)
lambda_n

e=sympy.randprime(phi_n//2, phi_n)
print('公鑰e=',e)

?sympy.gcdex

d, _, gcd = sympy.gcdex(e, phi_n)
if gcd!=1:
  print('gcd(e, phi_n)!=1錯')
d=(d+phi_n)%phi_n
print("私鑰d=",d)

e*d%phi_n==1