Add support for sage modules via subprocess. Adds boneh_durfee() and …

…smallfractions() attacks.

.gitignore

@@ -61,3 +61,6 @@ target/
 
 # PyCharm
 .idea/
+
+# Sage stuff
+*.sage.py

README.md

@@ -5,14 +5,16 @@ Automatic selection of best attack for the given public key
 Attacks :
  - Weak public key factorization
  - Wiener's attack
- - Hastad's attack (Small exponent attack)
- - Small q (q<100,000)
+ - Hastad's attack (Small public exponent attack)
+ - Small q (q < 100,000)
  - Common factor between ciphertext and modulus attack
  - Fermat's factorisation for close p and q
  - Gimmicky Primes method
  - Past CTF Primes method
- - Self-Initializing Quadratic Sieve (SIQS) using Yafu - NEW
- - Common factor attacks across multiple keys - NEW
+ - Self-Initializing Quadratic Sieve (SIQS) using Yafu
+ - Common factor attacks across multiple keys
+ - Small fractions method when p/q is close to a small fraction
+ - Boneh Durfee Method when the private exponent d is too small compared to the modulus (i.e d < n^0.292)
 
 ## Usage:
 usage: RsaCtfTool.py [-h] \(--publickey PUBLICKEY | --createpub | --dumpkey\)
@@ -49,21 +51,25 @@ Mode 3 - Dump the public and/or private numbers from a PEM/DER format public or
 #### Examples :
  - weak\_public.pub, weak\_public.cipher : weak public key
  - wiener.pub, wiener.cipher : key vulnerable to Wiener's attack
- - small\exponent.pub, small\_exponent.cipher : key with e=3, vulnerable to Hastad's attack
+ - small\_exponent.pub, small\_exponent.cipher : key with e=3, vulnerable to Hastad's attack
  - small\_q.pub, small\_q.cipher : public key with a small prime
  - close\_primes.pub, close\_primes.cipher : public key with primes suceptible to fermat factorization
  - elite\_primes.pub : public key with a gimmick prime
  - fermat.pub : public key with another vulnerability to fermat factorization
  - pastctfprimes.pub : public key with a prime from a past CTF
  - siqs.pub: 256bit public key that is factored in 30 seconds with SIQS
  - factordb_parsing.pub: a public key with a prime that is described as an expression on factordb.com
+ - smallfraction.pub: a public key where p/q is close to a small fraction
+ - boneh\_durfee.pub: a public key factorable using boneh\_durfee method
+ - multikey-0.pub and multikey-1.pub: Public keys that share a common factor
 
 #### Requirements:
  - GMPY
  - SymPy
  - libnum (https://github.com/hellman/libnum.git)
  - PyCrypto
  - Requests
+ - SageMath - optional but advisable
 
 ### MacOS-specific Instructions
 If `pip install -r "requirements.txt"` fails to install requirements accessible within environment, the following command may work.

RsaCtfTool.py

@@ -21,6 +21,7 @@
 import requests
 import re
 import argparse
+import subprocess
 from glob import glob
 
 
@@ -91,12 +92,18 @@ def __init__(self, args):
             self.args = args
             self.unciphered = None
             self.attackobjs = None  # This is how we'll know this object represents 1 key
+
+            # Test if sage is working and if so, load additional sage based attacks
+            if args.sageworks:
+                self.implemented_attacks.append(self.smallfraction)
+                self.implemented_attacks.append(self.boneh_durfee)
+
             # Load ciphertext
             if args.uncipher is not None:
                 self.cipher = open(args.uncipher, 'rb').read().strip()
             else:
                 self.cipher = None
-        return 
+        return
 
     def hastads(self):
         # Hastad attack for low public exponent, this has found success for e = 3, and e = 5 previously
@@ -114,9 +121,9 @@ def hastads(self):
     def factordb(self):
         # if factordb returns some math to derive the prime, solve for p without using an eval
         def solveforp(equation):
-            if '^' in equation: k,j = equation.split('^')
-            if '-' in j: j,sub = j.split('-')
             try:
+                if '^' in equation: k,j = equation.split('^')
+                if '-' in j: j,sub = j.split('-')
                 eq = map(int, [k,j,sub])
                 return pow(eq[0],eq[1])-eq[2]
             except Exception as e:
@@ -169,6 +176,25 @@ def wiener(self):
 
         return
 
+    def boneh_durfee(self):
+        # use boneh durfee method, should return a d value, else returns 0
+        # only works if the sageworks() function returned True
+        # many of these problems will be solved by the wiener attack module but perhaps some will fall through to here
+        # TODO: get an example public key solvable by boneh_durfee but not wiener
+        sageresult = int(subprocess.check_output(['sage','boneh_durfee.sage',str(self.pub_key.n),str(self.pub_key.e)]))
+
+        if sageresult > 0:
+            # use PyCrypto _slowmath rsa_construct to resolve p and q from d
+            from Crypto.PublicKey import _slowmath
+            tmp_priv = _slowmath.rsa_construct(long(self.pub_key.n), long(self.pub_key.e), d=long(sageresult))
+
+            self.pub_key.p = tmp_priv.p
+            self.pub_key.q = tmp_priv.q
+            self.priv_key = PrivateKey(long(self.pub_key.p), long(self.pub_key.q),
+                                       long(self.pub_key.e), long(self.pub_key.n))
+
+        return
+
     def smallq(self):
         # Try an attack where q < 100,000, from BKPCTF2016 - sourcekris
         for prime in primes(100000):
@@ -180,6 +206,17 @@ def smallq(self):
 
         return
 
+    def smallfraction(self):
+        # Code/idea from Renaud Lifchitz's talk 15 ways to break RSA security @ OPCDE17
+        # only works if the sageworks() function returned True
+        sageresult = int(subprocess.check_output(['sage', 'smallfraction.sage',str(self.pub_key.n)]))
+        if sageresult > 0:
+            self.pub_key.p = sageresult
+            self.pub_key.q = self.pub_key.n / self.pub_key.p
+            self.priv_key = PrivateKey(long(self.pub_key.p), long(self.pub_key.q),
+                                       long(self.pub_key.e), long(self.pub_key.n))
+        return
+
     def fermat(self, fermat_timeout=60):
         # Try an attack where the primes are too close together from BKPCTF2016 - sourcekris
         # this attack module can be optional
@@ -343,7 +380,6 @@ def attack(self):
                     print "[-] Sorry, cracking failed"
 
     implemented_attacks = [ nullattack, hastads, factordb, pastctfprimes, noveltyprimes, smallq, wiener, comfact_cn, fermat, siqs ]
-
 
 # source http://stackoverflow.com/a/22348885
 class timeout:
@@ -361,6 +397,19 @@ def __enter__(self):
     def __exit__(self, type, value, traceback):
         signal.alarm(0)
 
+def sageworks():
+    # Check if sage is installed and working
+    try:
+        sageversion = subprocess.check_output(['sage', '-v'])
+    except OSError:
+        return False
+
+    if 'SageMath version' in sageversion:
+
+        return True
+    else:
+        return False
+
 if __name__ == "__main__":
     parser = argparse.ArgumentParser(description='RSA CTF Tool Continued')
     group = parser.add_mutually_exclusive_group(required=True)
@@ -398,6 +447,11 @@ def __exit__(self, type, value, traceback):
             print "[*] q: " + str(key.q)
         quit()
 
+    if sageworks():
+        args.sageworks = True
+    else:
+        args.sageworks = False
+
     attackobj = RSAAttack(args)
     attackobj.attack()