college-rowing-team

college_rowing_team/sol.py

@@ -0,0 +1,52 @@
+#!python3
+from sage.all import *
+import pwn
+
+e = 3
+pairs = []
+pwn.log.info("reading file")
+with open("encrypted-messages.txt", 'r') as f:
+    lines = f.readlines()
+
+    for i in range(12):
+        j = 4*i
+        N = Integer(lines[j][3:].strip())
+        e = Integer(lines[j+1][3:].strip())
+        c = Integer(lines[j+2][3:].strip())
+        pairs.append((N, c))
+
+# filter other messages
+pwn.log.info("filtering non-flag messages")
+msgs = [
+    b'I just cannot wait for rowing practice today!',
+    b'I hope we win that big rowing match next week!',
+    b'Rowing is such a fun sport!'
+        ]
+flag_pairs = []
+for N, c in pairs:
+    is_flag = True
+    for msg in msgs:
+        m = pwn.unpack(msg, 'all', endian='big', sign=False)
+        if pow(m, e, N) == c:
+            is_flag = False
+    if is_flag:
+        flag_pairs.append((N, c))
+
+pwn.log.debug("found {} flag pairs".format(len(flag_pairs)))
+
+# chinese remainder theorem
+pwn.log.info("computing m")
+a = []
+b = []
+for N, c in flag_pairs:
+    a.append(c)
+    b.append(N)
+m_e = crt(a, b)
+pwn.log.info("found m^e")
+pwn.log.debug("m_e: {}".format(m_e))
+pwn.log.info("calculating m")
+m = m_e.nth_root(e)
+pwn.log.debug("m: {}".format(m))
+m_literal = pwn.pack(int(m), 'all', 'big', False)
+pwn.log.success("found flag: {}".format(m_literal.decode()))
+