john_pollard

john_pollard/sol.py

@@ -0,0 +1,48 @@
+#!python3
+from pwn import *
+import re
+
+def pollard_rho(n):
+    x0 = 2
+    d = 1
+    while True:
+        if x0 == n:
+            return -1
+        x = x0
+        y = x
+        g = lambda x: (pow(x, 2, n) + 1)%n
+        while d == 1:
+            x = g(x)
+            y = g(g(y))
+            d = math.gcd(abs(x-y), n)
+        if d == n:
+            x0 += 1
+        else:
+            return d
+
+with open("cert.plaintext", 'r') as f:
+    lines = f.readlines()
+
+modulus = lines[13].strip()
+modulus = int(re.findall("\(.*\)", modulus)[0][3:-1], 16)
+log.info("modulus: {}".format(modulus))
+
+exponent = lines[14].strip()
+exponent = int(re.findall("\(.*\)", exponent)[0][3:-1], 16)
+log.info("exponent: {}".format(exponent))
+
+signature = lines[17:-13]
+signature = int(''.join(map(lambda l: l.strip(), signature)).replace(':', ''), 16)
+log.info("signature:")
+log.hexdump(pack(signature, 'all', 'big', False))
+
+log.info("factoring modulus")
+p = pollard_rho(modulus)
+q = modulus//p
+assert p*q == modulus
+log.success("p: {}".format(p))
+log.success("q: {}".format(q))
+
+log.success("flag1: picoCTF{{{},{}}}".format(p, q))
+log.success("flag2: picoCTF{{{},{}}}".format(q, p))
+