CTF toolkit: lib (net, crypto_utils), templates per category, scaffold, cheatsheet, ps_and_qs example

examples/ps_and_qs.py

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+"""
+EXAMPLE: SECCON 2017 Quals — "Ps and Qs" (Crypto, 200p)
+https://github.com/p4-team/ctf/tree/master/2017-12-09-seccon-quals/crypto_ps_and_qs
+
+VULN: Two RSA public keys (pub1.pub, pub2.pub) share a prime (common factor).
+FACT: gcd(n1, n2) = p  -> recover q1 = n1/p, q2 = n2/p -> private keys -> decrypt.
+
+Run:
+    cd /home/code/ctfkit
+    python3 examples/ps_and_qs.py
+Expected flag: SECCON{1234567890ABCDEF}
+"""
+import sys
+from Crypto.PublicKey import RSA
+from Crypto.Util.number import long_to_bytes
+
+sys.path.insert(0, "/home/code/ctfkit")
+from lib.crypto_utils import gcd, modinv
+
+HERE = __file__.rsplit("/", 1)[0]
+
+
+def main():
+    pub1 = RSA.importKey(open(f"{HERE}/pub1.pub").read())
+    pub2 = RSA.importKey(open(f"{HERE}/pub2.pub").read())
+    p = gcd(pub1.n, pub2.n)
+    q1 = pub1.n // p
+    q2 = pub2.n // p
+    assert p * q1 == pub1.n and p * q2 == pub2.n, "common-factor failed"
+    msg = int.from_bytes(open(f"{HERE}/cipher", "rb").read(), "big")
+
+    d1 = modinv(pub1.e, (p - 1) * (q1 - 1))
+    pt = long_to_bytes(pow(msg, d1, pub1.n)).decode(errors="replace")
+    import re
+    m = re.search(r"SECCON\{[^}]+\}", pt)
+    flag = m.group(0) if m else pt
+    print("shared prime p =", p)
+    print("FLAG =", flag)
+    return flag
+
+
+if __name__ == "__main__":
+    main()