GH#90. New ElGamal generators were not square residues.

Changelog.rst

@@ -1,6 +1,16 @@
 Changelog
 =========
 
+3.4.10 (2 February 2018)
+++++++++++++++++++++++++
+
+Resolved issues
+---------------
+
+* When creating ElGamal keys, the generator wasn't a square residue:
+  ElGamal encryption was not secure under the DDH assumption.
+  Thanks to Weikeng Chen.
+
 3.4.9 (1 February 2018)
 +++++++++++++++++++++++
 

README.rst

@@ -71,7 +71,8 @@ All the code can be downloaded from `GitHub`_.
 News
 ----
 
-* **1 Feb 2018 (NEW)**. Bugfix release 3.4.9.
+* **2 Feb 2018 (NEW)**. Bugfix release 3.4.10.
+* 1 Feb 2018. Bugfix release 3.4.9.
 * 27 Jan 2018. Bugfix release 3.4.8.
 * 26 Aug 2017. Bugfix release 3.4.7.
 * 17 May 2017. Bugfix release 3.4.6.

lib/Crypto/PublicKey/ElGamal.py

@@ -58,33 +58,33 @@ def generate(bits, randfunc):
     q = (obj.p - 1) >> 1
 
     # Generate generator g
-    # See Algorithm 4.80 in Handbook of Applied Cryptography
-    # Note that the order of the group is n=p-1=2q, where q is prime
     while 1:
+        # Choose a square residue; it will generate a cyclic group of order q.
+        obj.g = pow(Integer.random_range(min_inclusive=2,
+                                     max_exclusive=obj.p,
+                                     randfunc=randfunc), 2, obj.p)
+
         # We must avoid g=2 because of Bleichenbacher's attack described
         # in "Generating ElGamal signatures without knowning the secret key",
         # 1996
-        #
-        obj.g = Integer.random_range(min_inclusive=3,
-                                     max_exclusive=obj.p,
-                                     randfunc=randfunc)
-        safe = 1
-        if pow(obj.g, 2, obj.p)==1:
-            safe=0
-        if safe and pow(obj.g, q, obj.p)==1:
-            safe=0
+        if obj.g in (1, 2):
+            continue
+
         # Discard g if it divides p-1 because of the attack described
         # in Note 11.67 (iii) in HAC
-        if safe and (obj.p-1) % obj.g == 0:
-            safe=0
+        if (obj.p - 1) % obj.g == 0:
+            continue
+
         # g^{-1} must not divide p-1 because of Khadir's attack
         # described in "Conditions of the generator for forging ElGamal
         # signature", 2011
         ginv = obj.g.inverse(obj.p)
-        if safe and (obj.p-1) % ginv == 0:
-            safe=0
-        if safe:
-            break
+        if (obj.p - 1) % ginv == 0:
+            continue
+
+        # Found
+        break
+
     # Generate private key x
     obj.x = Integer.random_range(min_inclusive=2,
                                  max_exclusive=obj.p-1,

lib/Crypto/__init__.py

@@ -1,4 +1,4 @@
 __all__ = ['Cipher', 'Hash', 'Protocol', 'PublicKey', 'Util', 'Signature',
            'IO', 'Math']
 
-version_info = (3, 4, 9)
+version_info = (3, 4, 10)