51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
from Crypto.Util.number import getPrime, bytes_to_long, long_to_bytes
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from math import gcd
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from sympy.ntheory.modular import crt
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import time
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# key generation
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p = getPrime(512) # 512-bit prime number
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q = getPrime(512) # 512-bit prime number
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n = p * q
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phi = (p - 1) * (q - 1)
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e = 65537 # = 2^16 +1 = 10000000000000001
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assert gcd(e, phi) == 1
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d = pow(e, -1, phi)
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# encryption
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def encrypt(message):
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m = bytes_to_long(message.encode())
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c = pow(m, e, n)
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return c
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# CRT
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dp = d % (p - 1) # d_p = d mod (p-1)
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dq = d % (q - 1) # d_q = d mod (q-1)
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q_inv = pow(q, -1, p) # q^{-1} mod p
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def decrypt(cipher_int):
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m1 = pow(cipher_int, dp, p) # c^dp mod p
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m2 = pow(cipher_int, dq, q) # c^dq mod q
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m, mod = crt([p, q], [m1, m2]) # m ≡ m1 (mod p), m ≡ m2 (mod q)
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# Garner's Algorithm
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# h = (m1 - m2) * q_inv % p
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# m = (m2 + h * q) % n
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message = long_to_bytes(m).decode()
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return message
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m = "Hello World"
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c = encrypt(m)
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start = time.perf_counter()
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m_recover = decrypt(c)
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end = time.perf_counter()
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print("Ciphertext: ", c)
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print("Message: ", m_recover)
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print(f"decrypt time: {(end-start)*1e3:.3f} ms")
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