2018计算机 第一次作业,计算机安全学-第四次实践作业-2018/4/17

[new] 1、用Python或Sage实现RSA算法的加密、解密、签名/验证签名

使用sage实现RSA算法进行加密、解密、签名/验证签名

#GenerateKeys - e, d, N

def generateKeys(bits):

p = random_prime(2**(bits//2), lbound = 2**(bits//2-1))

q = random_prime(2**(bits//2), lbound = 2**(bits//2-1))

N = p * q

EulerN = (q-1) * (p-1)

e = randint(1, EulerN)

while(gcd(e, EulerN)! = 1):

e = randint(1, EulerN)

d = inverse_mod(e, EulerN)

return e, d, N

#Encode func

def encode(M):

m = str(M)

return sum(ord(m[i]) * pow(256, i) for i in range(len(m)))

#Decode func

def decode(n):

m = ""

while(n > 0):

m += chr(n%256)

n = n//256

return m

#Encrypt func

def encrypt(m, e, N):

return lift(mod(m, N)**e)

#Decrypt func

def decrypt(n,d,N):

return lift(mod(n, N)**d)

#RSA e.g.

e, d, N = generateKeys(1024)

M_encode = encode('Iamttyy')

N_encrypt = encrypt(M_encode, e, N)

N_decrypt = decrypt(N_encrypt, d, N)

M_decode = decode(N_decrypt)

print M_encode

print M_decode

#Signature e.g.

Signature = encrypt(M_encode, d, N)

Verify_me = decrypt(signature, e, N)

print 'Signature:'

print signature

print 'Verify_me:'

print Verify_Me

print 'is same as'

print M_encode

print 'Accept -- else: Reject'

[new]2、用Python或Sage实现DH秘钥交换协议的。

更新版本

#Set Up and Down boundary

Up = 2^32

Down = 2^16

#Random prime - q

q = random_prime(Up, lbound=Down)

#Root - g

while True:

g = randint(1, q-1)

#Add judgement of g^(q-1) mod q ==1

if(multiplicative_order(mod(g, q)) == q-1):

break

#Random Private Key1

X1 = randint(1, q-1)

#Calu

Y1 = mod(g, q)^X1

#Random Private Key2

X2 = randint(1, q-1)

#Calu

Y2 = mod(g, q)^X2

#Calu

Key1 = mod(Y2, q)^X1

Key2 = mod(Y1, q)^X2

#Verify

if Key1 == Key2:

print 'Accept!'

else :

print 'Reject!'

1、用Python或Sage实现RSA算法的加密、解密、签名/验证签名

python实现

注: 不要将文件名写成rsa.py

#-*-coding : utf-8 -*-

#anthor: tyty

import rsa

(PubK, PriK) = rsa.newkeys(1024)

print PubK

print PriK

#SaveToFile .pem

# with open('Public_Key.pem', 'w+') as f:

# f.write(PubK.save_pkcs1().decode())

# with open('Privacy_Key.pem', 'w+') as f:

# f.write(PriK.save_pkcs1().decode())

#Message

M = "tyty is a boy"

#Encryption

encry_M = rsa.encrypt(M.encode(), PubK)

print "encrypt M = " + encry_M

#Decryption

decry_M = rsa.decrypt(encry_M, PriK).decode()

print "decrypt M = " + decry_M

#Signature

M = "tyty"

signature = rsa.sign(M.encode(), PriK, 'SHA-1')

print signature

#Verify

rsa.verify(M.encode(), sign, PubK) # right

rsa.verify("tttt", signature, PubK) # wrong

2、用Python或Sage实现DH秘钥交换协议的。

Sage实现

注:开头须判断p是否为素数

#isPrime

sage: a = 787

sage: factor(a)

787

#param

sage: p = 787

sage: F = GF(p)

#root

sage: g = F(2)

#random int x

sage: x = randint(1, 786);x

621

sage: X = g^x;X

673

#random int y

sage: y = randint(1, 786);y

213

sage: Y = g^y;Y

627

#shared secret key

sage: Y^x

211

sage: X^y

211