rsa lesson added

training/h4tum/Intro_to_RSA/demo/PEM/dec_private.py

@@ -0,0 +1,36 @@
+from cryptography.hazmat.primitives import serialization
+
+pem_data = b"""
+-----BEGIN PRIVATE KEY-----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+-----END PRIVATE KEY-----
+"""
+
+private_key = serialization.load_pem_private_key(
+    pem_data,
+    password=None
+)
+
+numbers = private_key.private_numbers()
+
+print(f"Modulus (n): {numbers.public_numbers.n}")
+print(f"Public Exponent (e): {numbers.public_numbers.e}")
+print(f"Private Exponent (d): {numbers.d}")
+print(f"Prime 1 (p): {numbers.p}")
+print(f"Prime 2 (q): {numbers.q}")
+print(f"d mod (p-1): {numbers.dmp1}")
+print(f"d mod (q-1): {numbers.dmq1}")
+print(f"q^-1 mod p: {numbers.iqmp}")

training/h4tum/Intro_to_RSA/demo/PEM/dec_pub.py

@@ -0,0 +1,16 @@
+from cryptography.hazmat.primitives import serialization
+
+pem_data = b"""
+-----BEGIN PUBLIC KEY-----
+MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCuIDV1FN9eF91qfDkU8iQ8P1qq
+0oZ5pNkiriR6HDXPTV1m0mQf1EKY47eco5geVIJezpH0Hfud07Jicla9mWI6ajQL
+buYoyYgUN3FU3ihBszx3gh1i3nX0rVGwu+//pDQLBj0Ds5KB5l3veVJ6Kcc1Tn40
+nUer2m+mFzb6Y9Q3bwIDAQAB
+-----END PUBLIC KEY-----
+"""
+
+key = serialization.load_pem_public_key(pem_data)
+
+numbers = key.public_numbers()
+print(f"Modulus (n): {numbers.n}")
+print(f"Exponent (e): {numbers.e}")

training/h4tum/Intro_to_RSA/demo/PEM/easy_gen.py

@@ -0,0 +1,15 @@
+from cryptography.hazmat.primitives.asymmetric import rsa
+from cryptography.hazmat.primitives import serialization
+
+key = rsa.generate_private_key(public_exponent=65537, key_size=1024)
+
+print(key.private_bytes(
+    serialization.Encoding.PEM,
+    serialization.PrivateFormat.PKCS8,
+    serialization.NoEncryption()
+).decode())
+
+print(key.public_key().public_bytes(
+    serialization.Encoding.PEM,
+    serialization.PublicFormat.SubjectPublicKeyInfo
+).decode())

training/h4tum/Intro_to_RSA/demo/PEM/gen.py

@@ -0,0 +1,37 @@
+from cryptography.hazmat.primitives.asymmetric import rsa
+from cryptography.hazmat.primitives import serialization
+from Crypto.Util.number import getPrime
+
+e = 65537
+p = getPrime(512)
+q = getPrime(512)
+n = p * q
+phi = (p - 1) * (q - 1)
+d = pow(e, -1, phi)
+
+dp = d % (p - 1)
+dq = d % (q - 1)
+q_inv = pow(q, -1, p)
+
+private_numbers = rsa.RSAPrivateNumbers(
+    p=p,
+    q=q,
+    d=d,
+    dmp1=dp,
+    dmq1=dq,
+    iqmp=q_inv,
+    public_numbers=rsa.RSAPublicNumbers(e=e, n=n)
+)
+
+key = private_numbers.private_key()
+
+print(key.private_bytes(
+    encoding=serialization.Encoding.PEM,
+    format=serialization.PrivateFormat.PKCS8,
+    encryption_algorithm=serialization.NoEncryption()
+).decode())
+
+print(key.public_key().public_bytes(
+    serialization.Encoding.PEM,
+    serialization.PublicFormat.SubjectPublicKeyInfo
+).decode())

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")

training/h4tum/Intro_to_RSA/demo/rsa_demo.py

@@ -0,0 +1,37 @@
+from Crypto.Util.number import getPrime, bytes_to_long, long_to_bytes
+from math import gcd
+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
+
+# decryption
+def decrypt(cipher_int):
+    m = pow(cipher_int, d, 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")