crypto/even_rsa_can_be_broken

crypto/even_rsa_can_be_broken/encrypt.py

@@ -0,0 +1,34 @@
+from sys import exit
+from Crypto.Util.number import bytes_to_long, inverse
+from setup import get_primes
+
+e = 65537
+
+def gen_key(k):
+    """
+    Generates RSA key with k bits
+    """
+    p,q = get_primes(k//2)
+    N = p*q
+    d = inverse(e, (p-1)*(q-1))
+
+    return ((N,e), d)
+
+def encrypt(pubkey, m):
+    N,e = pubkey
+    return pow(bytes_to_long(m.encode('utf-8')), e, N)
+
+def main(flag):
+    pubkey, _privkey = gen_key(1024)
+    encrypted = encrypt(pubkey, flag) 
+    return (pubkey[0], encrypted)
+
+if __name__ == "__main__":
+    flag = open('flag.txt', 'r').read()
+    flag = flag.strip()
+    N, cypher  = main(flag)
+    print("N:", N)
+    print("e:", e)
+    print("cyphertext:", cypher)
+    exit()
+

crypto/even_rsa_can_be_broken/solve.py

@@ -0,0 +1,53 @@
+#!/usr/bin/env nix-shell
+#!nix-shell -i sage -p sage python3Packages.pwntools python3Packages.pycryptodome
+
+import time
+import sys
+
+from sage.all import *
+
+from pwn import *
+from Crypto.Util.number import long_to_bytes
+
+ADDR, PORT, *_ = "verbal-sleep.picoctf.net 56956".split()
+
+def factor_n(n) -> (int, int):
+  print('Factoring N')
+  start = time.time()
+  factors = ZZ(n).factor()
+  stop = time.time()
+  print(f"Took: {stop - start}")
+
+  p, q, *rest = [x[0] for x in list(factors)]
+  assert len(rest) == 0
+
+  return p, q
+
+def decrypt(p: int, q: int, e: int, n: int, enc: int) -> bytes:
+  phi = (p - 1) * (q - 1)
+  d = inverse_mod(e, phi)
+  m = power_mod(enc, d, n)
+  return long_to_bytes(m)
+
+def main():
+  r = remote(ADDR, PORT)
+
+  n = int(r.recvline().split(b' ')[1].strip())
+  e = int(r.recvline().split(b' ')[1].strip())
+  enc = int(r.recvline().split(b' ')[1].strip())
+
+  r.close()
+
+  print(f"{n=}")
+  print(f"{e=}")
+  print(f"{enc=}")
+
+  p, q = factor_n(n)
+
+  print(f"{p=}")
+  print(f"{q=}")
+
+  print(decrypt(p, q, e, n, enc).decode())
+
+if __name__ == '__main__':
+    main()