本人研究生密码学的大作业
import itertools
import copy
# 从私钥构造公钥
def create_pubkey(data):
# 构造m 此时m应大于超递增序列的所有和
# m = sum(data) + 2
# m = 250
m = int(input("请输入m: "))
# 构造n 这里的n应当与m互素，这里先取值为31
# n = 31
# n = 113
n = int(input("请输入n: "))
# 将序列中的每一个值都乘以n
for i in range(len(data)):
data[i] = data[i] * n
# 序列中的每一个值都对m求余
for j in range(len(data)):
data[j] = data[j] % m
print("构造的公钥是{} ".format(data))
return data,m,n
# 将二进制数据进行加密
def encryp(clear_txt,pubkey):
# 定义 密文列表
cipher_list = []
for i in range(len(clear_txt)):
if clear_txt[i] == 1:
cipher_list.append(clear_txt[i] * pubkey[i])
# 密文的值
cipher = sum(cipher_list)
print("加密后的密文为{}".format(cipher))
return cipher
# 将加密后的数据进行解密
def decryption(cipher,input_list,m,inv_n):
# 私钥序列和
sumx = 0
# for i in cipher:
sumx = (inv_n * cipher) % m
# for k in range(len(input_list)):
result_list = []
clear_list = []
for s in range(0,7):
for p in itertools.combinations(input_list,s):
if sum(list(p)) == sumx:
result_list = list(p)
# print(result_list)
for l in input_list:
if l in result_list:
clear_list.append(1)
else:
clear_list.append(0)
result_str = ''
for t in clear_list:
result_str = result_str + str(t)
print("解密后的明文为{}".format(result_str))
return True
# 下面两个函数是用来求乘法逆元的
def EX_GCD(a,b,arr): #扩展欧几里得
if b == 0:
arr[0] = 1
arr[1] = 0
return a
g = EX_GCD(b, a % b, arr)
t = arr[0]
arr[0] = arr[1]
arr[1] = t - int(a / b) * arr[1]
return g
def ModReverse(a,n): #ax=1(mod n) 求a模n的乘法逆x
arr = [0,1,]
gcd = EX_GCD(a,n,arr)
if gcd == 1:
return (arr[0] % n + n) % n
else:
return -1
if __name__ == "__main__":
# 将函数生成的超递增序列进行赋值
input_list = eval（'['+input("请输入一个6位数的超递增序列：")+']')
clear_txt = list(input("请输入要加密的二进制数据(6位)："))
for t in range(len(clear_txt)):
clear_txt[t] = int(clear_txt[t])
my_key = copy.deepcopy(input_list)
pubkey,m,n = create_pubkey(input_list)
cipher = encryp(clear_txt,pubkey)
# print(n,'模',m,'的乘法逆：',ModReverse(n,m))
# n的逆元
inv_n = ModReverse(n,m)
decryption(cipher,my_key,m,inv_n)
