RSA算法python实现

RSA算法

这个代码主要分六块

1

这个是扩展欧几里得的代码 输入a,b 得到一组x,y使得ax+by=gcd(a,b)

def ex_gcd(a, b):
	"""
	扩展欧几里得
	"""
	if b == 0:
		return 1, 0
	else:
		k = a // b
		remainder = a % b
		x1, y1 = ex_gcd(b, remainder)
		x, y = y1, x1 - k * y1
	return x, y

2

快速幂算法 加快乘方速度

def fast_expmod(b, e, m):
	"""
	快速幂
	"""
	result = 1
	while e != 0:
		if (e&1) == 1:
			# ei = 1, then mul
			result = (result * b) % m
		e >>= 1
		# b, b^2, b^4, b^8, ... , b^(2^n)
		b = (b*b) % m
	return result

3

这个是获得公钥和密钥的代码,输入p,q,e 返回两个两个列表 形式为[[n,e],[n,d]]

def make_key(p,q,e):
	"""
	生成公钥和密钥
	"""
	n=p*q
	fin=(p-1)*(q-1)
	d=ex_gcd(e,fin)[0]
	while d<0:
		d=(d+fin)%fin
	return [[n,e],[n,d]]

4

加密算法 输入字符串 返回一个密文密钥的列表

def encryption(key,data):
	"""
	加密
	"""
	n,e=key
	data=list(data)
	out=[]
	for i in data:
		out.append(fast_expmod(ord(i),e,n))
	return out

5

解密算法 输入一个密文密钥列表(4的输出) 输出对应的明文

def Decrypt(key,data):
	"""
	解密
	"""
	n,d=key
	data=data
	out=''
	for i in data:
		out+=(chr(fast_expmod(i,d,n)))
	return out

6

测试代码 其中p,q,e可以任意修改

p=33478071698956898786044169848212690817704794983713768568912431388982883793878002287614711652531743087737814467999489
q=36746043666799590428244633799627952632279158164343087642676032283815739666511279233373417143396810270092798736308917
e=65537

public_key,private_key=make_key(p,q,e)

Plaintext='Hello World!'
print('明文:',Plaintext)
ciphertext=encryption(public_key,Plaintext)
print('密文:',ciphertext)
Plaintext2=Decrypt(private_key,ciphertext)
print('解密明文:',Plaintext2)

exit(0)

完整代码

# coding=utf-8
"""
name:RSA算法
auther:王智峰
version:1.1
"""
def ex_gcd(a, b):
	"""
	扩展欧几里得
	"""
	if b == 0:
		return 1, 0
	else:
		k = a // b
		remainder = a % b
		x1, y1 = ex_gcd(b, remainder)
		x, y = y1, x1 - k * y1
	return x, y
def fast_expmod(b, e, m):
	"""
	快速幂
	"""
	result = 1
	while e != 0:
		if (e&1) == 1:
			# ei = 1, then mul
			result = (result * b) % m
		e >>= 1
		# b, b^2, b^4, b^8, ... , b^(2^n)
		b = (b*b) % m
	return result
def make_key(p,q,e):
	"""
	生成公钥和密钥
	"""
	n=p*q
	fin=(p-1)*(q-1)
	d=ex_gcd(e,fin)[0]
	while d<0:
		d=(d+fin)%fin
	return [[n,e],[n,d]]
def encryption(key,data):
	"""
	加密
	"""
	n,e=key
	data=list(data)
	out=[]
	for i in data:
		out.append(fast_expmod(ord(i),e,n))
	return out
def decrypt(key,data):
	"""
	解密
	"""
	n,d=key
	data=data
	out=''
	for i in data:
		out+=(chr(fast_expmod(i,d,n)))
	return out

p=33478071698956898786044169848212690817704794983713768568912431388982883793878002287614711652531743087737814467999489
q=36746043666799590428244633799627952632279158164343087642676032283815739666511279233373417143396810270092798736308917
e=65537

public_key,private_key=make_key(p,q,e)

Plaintext='Hello World!'
print('明文:',Plaintext)
ciphertext=encryption(public_key,Plaintext)
print('密文:',ciphertext)
Plaintext2=decrypt(private_key,ciphertext)
print('解密明文:',Plaintext2)

exit(0)