--- PublicKey/ElGamal.py
+++ PublicKey/ElGamal.py
@@ -25,39 +25,54 @@
     Generate an ElGamal key of length 'bits', using 'randfunc' to get
     random data and 'progress_func', if present, to display
     the progress of the key generation.
+
+    The key will be safe for use for both encryption and signature
+    (although it should be used for **only one** purpose).
+
     """
     obj=ElGamalobj()
-    # Generate prime p
+    # Generate a safe prime p
+    # See Algorithm 4.86 in Handbook of Applied Cryptography
     if progress_func:
         progress_func('p\n')
-    obj.p=bignum(getPrime(bits, randfunc))
-    # Generate random number g
+    while 1:
+        q = bignum(getPrime(bits-1, randfunc))
+        obj.p = 2*q+1
+        if number.isPrime(obj.p, randfunc=randfunc):
+            break
+    # 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
     if progress_func:
         progress_func('g\n')
-    size=bits-1-(ord(randfunc(1)) & 63) # g will be from 1--64 bits smaller than p
-    if size<1:
-        size=bits-1
-    while (1):
-        obj.g=bignum(getPrime(size, randfunc))
-        if obj.g < obj.p:
+    while 1:
+        # We must avoid g=2 because of Bleichenbacher's attack described
+        # in "Generating ElGamal signatures without knowning the secret key",
+        # 1996
+        #
+        obj.g = number.getRandomRange(3, obj.p, 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
+        # Discard g if it divides p-1 because of the attack described
+        # in Note 11.67 (iii) in HAC
+        if safe and divmod(obj.p-1, obj.g)[1]==0:
+            safe=0
+        # g^{-1} must not divide p-1 because of Khadir's attack
+        # described in "Conditions of the generator for forging ElGamal
+        # signature", 2011
+        ginv = number.inverse(obj.g, obj.p)
+        if safe and divmod(obj.p-1, ginv)[1]==0:
+            safe=0
+        if safe:
             break
-        size=(size+1) % bits
-        if size==0:
-            size=4
-    # Generate random number x
+    # Generate private key x
     if progress_func:
         progress_func('x\n')
-    while (1):
-        size=bits-1-ord(randfunc(1)) # x will be from 1 to 256 bits smaller than p
-        if size>2:
-            break
-    while (1):
-        obj.x=bignum(getPrime(size, randfunc))
-        if obj.x < obj.p:
-            break
-        size = (size+1) % bits
-        if size==0:
-            size=4
+    obj.x=number.getRandomRange(2, obj.p-1, randfunc)
+    # Generate public key y
     if progress_func:
         progress_func('y\n')
     obj.y = pow(obj.g, obj.x, obj.p)
@@ -105,6 +120,8 @@
         return (a, b)
 
     def _verify(self, M, sig):
+        if sig[0]<1 or sig[0]>p-1:
+            return 0
         v1=pow(self.y, sig[0], self.p)
         v1=(v1*pow(sig[0], sig[1], self.p)) % self.p
         v2=pow(self.g, M, self.p)