Add solution

TP-Link/crack_512_rsa_solution.md

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+# Crack a 512-bit RSA public key and learn the private key
+
+## Attack Step 1: Print the number n and e from the public key file
+
+I have prepared a [script](./read_n_e_from_rsa_key.py) for this purpose. Run this script with your 512-bit RSA public key file. 
+
+![](./print_n_e.png)
+
+My number n in RSA is:
+`10194421925714091479168644488467502646386138254367497052153922599663232361010270415141154162088882150710608345234221701696770734074532297681915467648125021`
+
+## Attack Step 2: Factor the big number n and get p and q
+
+Read [this blog](http://gilchrist.great-site.net/jeff/factoring/nfs_beginners_guide.html?i=1)
+
+This step might take several days. 
+
+I have my p and q here: 
+`98475604330270434872663742776655274553799038562230192750546533524033149071703`
+`103522308850461414952118967146955078800028111873755980559168280414306621177707`
+
+## Attack Step 3: Reconstruct the private key with p and q
+
+I have prepared another [script](./generate_private_key_from_p_q.py) for this purpose. Run this script with your p and q. 
+
+![](./generate_private_key.png)
+
+## Attack Step 4: Let openssl parse this private key and produce a new private key in openssl format
+You have to execute this command with openssl on Ubuntu 20.04, not on macOS. 
+`openssl rsa -in private_key_tplink.pem -out private_key_tplink_new.pem`
+
+![](./show_pem.png)
+
+Then you can switch back to the [main tutorial](./README.md)

TP-Link/generate_private_key_from_p_q.py

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+import argparse
+from cryptography.hazmat.primitives.asymmetric import rsa
+from cryptography.hazmat.primitives import serialization
+from cryptography.hazmat.backends import default_backend
+from sympy import mod_inverse
+
+def generate_private_key_pem(p, q, public_exponent=65537):
+    """Generate a private key in PEM format from given primes p and q."""
+    # Calculate modulus n
+    n = p * q
+    # Calculate Euler's totient function φ(n)
+    phi_n = (p - 1) * (q - 1)
+
+    # Calculate private exponent d
+    d = mod_inverse(public_exponent, phi_n)
+
+    # Convert primes into RSA parameters
+    dmp1 = d % (p - 1)
+    dmq1 = d % (q - 1)
+    iqmp = mod_inverse(q, p)
+
+    # Construct the private key
+    private_key = rsa.RSAPrivateNumbers(
+        p=p,
+        q=q,
+        d=d,
+        dmp1=dmp1,
+        dmq1=dmq1,
+        iqmp=iqmp,
+        public_numbers=rsa.RSAPublicNumbers(public_exponent, n)
+    ).private_key(default_backend())
+
+    # Serialize the private key to PEM format
+    pem = private_key.private_bytes(
+        encoding=serialization.Encoding.PEM,
+        format=serialization.PrivateFormat.PKCS8,
+        encryption_algorithm=serialization.NoEncryption()
+    )
+    return pem
+
+def main():
+    parser = argparse.ArgumentParser(description="Generate an RSA private key PEM file using given primes p and q.")
+    parser.add_argument("p", type=int, help="First large prime number (p)")
+    parser.add_argument("q", type=int, help="Second large prime number (q)")
+    parser.add_argument("--output", type=str, default="private_key.pem", help="Output file name for the private key (default: private_key.pem)")
+
+    args = parser.parse_args()
+
+    # Generate PEM
+    pem = generate_private_key_pem(args.p, args.q)
+
+    # Save to file
+    with open(args.output, "wb") as pem_file:
+        pem_file.write(pem)
+
+    print(f"Private key saved to '{args.output}'")
+
+if __name__ == "__main__":
+    main()

TP-Link/my_tplink_pub.pub

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+ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAAAQQDCpUvga/nk2lu+KxLsaEqrRXBZzflAJ2YYNwvSNzC8Ro+yxTJxpZ+V8qBYzZ54Kntc+Ojx0nZdR530CIdRhshd

TP-Link/private_key_tplink.pem

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+-----BEGIN PRIVATE KEY-----
+MIIBVQIBADANBgkqhkiG9w0BAQEFAASCAT8wggE7AgEAAkEAwqVL4Gv55NpbvisS
+7GhKq0VwWc35QCdmGDcL0jcwvEaPssUycaWflfKgWM2eeCp7XPjo8dJ2XUed9AiH
+UYbIXQIDAQABAkBJLx89TTvTCSrPcKCX1IqmpOAeU+xwa5/eYOwH6Qpg7zr0XXJD
+ab1a8gQFMpeg+E7urddKPcH207/qPiIabn6dAiEA2bc3hL64S/pX3gkFW769eIRA
+nJaqY4Tqdk2oQvcD8VcCIQDk34znNwaLJtYqLjgE2dHpdJyvIrjS9Lq2UyCBRRe/
+awIgMfhNc9hacIXbGQk1A6O51Sl1svsZzJG7Rr/4OLZ9Xy0CIQCHlKJcqe0Xa5c8
+/4ox3XMLMAhNe20vksg0j8PWsD5kJwIhALtIHKwQ/aTpHYHnXEOjma+kkVyje3h2
+s+MHzPSM+Vnx
+-----END PRIVATE KEY-----

TP-Link/private_key_tplink_new.pem

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+-----BEGIN PRIVATE KEY-----
+MIIBVQIBADANBgkqhkiG9w0BAQEFAASCAT8wggE7AgEAAkEAwqVL4Gv55NpbvisS
+7GhKq0VwWc35QCdmGDcL0jcwvEaPssUycaWflfKgWM2eeCp7XPjo8dJ2XUed9AiH
+UYbIXQIDAQABAkBJLx89TTvTCSrPcKCX1IqmpOAeU+xwa5/eYOwH6Qpg7zr0XXJD
+ab1a8gQFMpeg+E7urddKPcH207/qPiIabn6dAiEA2bc3hL64S/pX3gkFW769eIRA
+nJaqY4Tqdk2oQvcD8VcCIQDk34znNwaLJtYqLjgE2dHpdJyvIrjS9Lq2UyCBRRe/
+awIgMfhNc9hacIXbGQk1A6O51Sl1svsZzJG7Rr/4OLZ9Xy0CIQCHlKJcqe0Xa5c8
+/4ox3XMLMAhNe20vksg0j8PWsD5kJwIhALtIHKwQ/aTpHYHnXEOjma+kkVyje3h2
+s+MHzPSM+Vnx
+-----END PRIVATE KEY-----

TP-Link/read_n_e_from_rsa_key.py

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+from Crypto.PublicKey import RSA
+import argparse
+
+def main(filename):
+    try:
+        with open(filename, "r") as file:
+            key = RSA.importKey(file.read())
+            print("Modulus (n):", key.n)
+            print("Public Exponent (e):", key.e)
+    except FileNotFoundError:
+        print(f"Error: File '{filename}' not found.")
+    except ValueError:
+        print(f"Error: Could not import key from '{filename}'. Ensure it's a valid RSA public key.")
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description="Display RSA public key parameters (n and e).")
+    parser.add_argument("filename", type=str, help="Path to the RSA public key file.")
+    args = parser.parse_args()
+
+    main(args.filename)