rsa lesson added

training/h4tum/Intro_to_RSA/demo/rsa_crt_demo.py

@@ -0,0 +1,50 @@
+from Crypto.Util.number import getPrime, bytes_to_long, long_to_bytes
+from math import gcd
+from sympy.ntheory.modular import crt
+import time
+
+# key generation
+p = getPrime(512)		# 512-bit prime number
+q = getPrime(512)		# 512-bit prime number
+n = p * q
+phi = (p - 1) * (q - 1)
+e = 65537       # = 2^16 +1 = 10000000000000001
+assert gcd(e, phi) == 1
+
+d = pow(e, -1, phi)
+
+# encryption
+def encrypt(message):
+    m = bytes_to_long(message.encode())
+    c = pow(m, e, n)
+    return c
+
+# CRT
+dp    = d % (p - 1)        # d_p = d mod (p-1)
+dq    = d % (q - 1)        # d_q = d mod (q-1)
+q_inv = pow(q, -1, p)      # q^{-1} mod p
+
+def decrypt(cipher_int):
+    m1 = pow(cipher_int, dp, p)   # c^dp mod p
+    m2 = pow(cipher_int, dq, q)   # c^dq mod q
+    
+    m, mod = crt([p, q], [m1, m2])  # m ≡ m1 (mod p), m ≡ m2 (mod q)
+    
+    # Garner's Algorithm
+    # h = (m1 - m2) * q_inv % p
+    # m = (m2 + h * q) % n
+
+    message = long_to_bytes(m).decode()
+    return message
+
+m = "Hello World"
+c = encrypt(m)
+
+start = time.perf_counter()
+m_recover = decrypt(c)
+end = time.perf_counter()
+
+print("Ciphertext: ", c)
+
+print("Message: ", m_recover)
+print(f"decrypt time: {(end-start)*1e3:.3f} ms")