triple-secure

triple_secure/sol.py

@@ -0,0 +1,43 @@
+#!python3
+from sage.all import *
+import pwn
+
+pwn.log.info("reading file")
+with open("public-key.txt", 'r') as f:
+    lines = f.readlines()
+    n1 = Integer(lines[0][4:].strip())
+    n2 = Integer(lines[1][4:].strip())
+    n3 = Integer(lines[2][4:].strip())
+    e = Integer(lines[3][3:].strip())
+    c = Integer(lines[4][3:].strip())
+
+pwn.log.info("calculating p, q, r")
+p = gcd(n1, n2)
+q = gcd(n1, n3)
+r = gcd(n2, n3)
+assert p*q == n1
+assert p*r == n2
+assert q*r == n3
+pwn.success("p: {:x}".format(p))
+pwn.success("q: {:x}".format(q))
+pwn.success("r: {:x}".format(r))
+
+pwn.log.info("calculating d1, d2, d3")
+_p = p-1
+_q = q-1
+_r = r-1
+d1 = pow(e, -1, _p*_q).lift()
+d2 = pow(e, -1, _p*_r).lift()
+d3 = pow(e, -1, _q*_r).lift()
+pwn.log.success("d1: {:x}".format(d1))
+pwn.log.success("d2: {:x}".format(d2))
+pwn.log.success("d3: {:x}".format(d3))
+
+pwn.log.info("decrypting message...")
+m2 = pow(c, d3, n3).lift()
+m1 = pow(m2, d2, n2).lift()
+m = pow(m1, d1, n1).lift()
+pwn.log.info("decrypted message!")
+m_literal = pwn.pack(int(m), 'all', 'big', False)
+pwn.log.success("flag: {}".format(m_literal.decode()))
+