Refreshed documentation for ElGamal. Small corrections to DSA and RSA.

lib/Crypto/PublicKey/DSA.py

@@ -25,9 +25,9 @@
 """DSA public-key signature algorithm.
 
 DSA_ is a widespread public-key signature algorithm. Its security is
-based on the discrete logarithm problem, that is, given a multiplicative
-group, a generator *g*, and an element *h*, the difficulty
-of finding another element *x* such that *g^x = h*. The problem is believed
+based on the discrete logarithm problem (DLP_). Given a cyclic
+group, a generator *g*, and an element *h*, it is hard
+to find an integer *x* such that *g^x = h*. The problem is believed
 to be difficult, and it has been proved such (and therefore secure) for
 more than 30 years.
 
@@ -36,15 +36,17 @@
 The algorithm can only be used for authentication (digital signature).
 DSA cannot be used for confidentiality (encryption).
 
-The group is actually a sub-group over a finite finite field of prime order *p*.
-The sub-group order is *q*, and it always holds that *(p-1)* is a multiple of *q*. 
+The group is actually a sub-group over the integers modulo *p*, with *p* prime.
+The sub-group order is *q*, which is prime too; it always holds that *(p-1)* is a multiple of *q*.
 The cryptographic strength is linked to the magnitude of *p* and *q*.
 In 2012, a sufficient size is deemed to be 2048 bits for *p* and 256 bits for *q*.
 For more information, see the most recent ECRYPT_ report.
 
-The actual value of *g* is not important. *(p,q,g)* are called *domain
-parameters*; they are not sensitive but must be shared by both parties (the
-signer and the verifier).
+The values *(p,q,g)* are called *domain parameters*;
+they are not sensitive but must be shared by both parties (the signer and the verifier).
+
+The DSA signature is twice as big the size of *q* (64 bytes if *q* is 256 bit
+long).
 
 This module provides facilities for generating new DSA keys and for constructing
 them from known components. DSA keys allows you to perform basic signing and
@@ -66,6 +68,7 @@
     >>>     print "Incorrect signature"
 
 .. _DSA: http://en.wikipedia.org/wiki/Digital_Signature_Algorithm
+.. _DLP: http://www.cosic.esat.kuleuven.be/publications/talk-78.pdf
 .. _ECRYPT: http://www.ecrypt.eu.org/documents/D.SPA.17.pdf
 """
 
@@ -130,14 +133,18 @@ def sign(self, M, K):
         :attention: selection of *K* is crucial for security. Generating a
          random number larger than *q* and taking the modulus by *q* is
          **not** secure, since smaller values will occur more frequently.
-         Generating a random larger systematically smaller than *q-1*
-         (e.g. *floor((q-1)/8)* bytes) is also **not** secure. In general,
+         Generating a random number systematically smaller than *q-1*
+         (e.g. *floor((q-1)/8)* random bytes) is also **not** secure. In general,
          it shall not be possible for an attacker to know the value of `any
          bit of K`__.
 
         :attention: The number *K* shall not be reused for any other
          operation and shall be discarded immediately.
 
+        :attention: It is strongly recommended to have M be a digest created
+         via a cryptographic hash, otherwise an attacker may mount an
+         existential forgery attack.
+
         :Return: A tuple with 2 longs.
 
         .. __: http://www.di.ens.fr/~pnguyen/pub_NgSh00.htm

lib/Crypto/PublicKey/ElGamal.py

@@ -23,10 +23,83 @@
 # SOFTWARE.
 # ===================================================================
 
-"""ElGamal public-key algorithm (encryption and signature)."""
+"""ElGamal public-key algorithm (randomized encryption and signature).
+
+Signature algorithm
+-------------------
+The security of the ElGamal signature scheme is based (like DSA) on the discrete
+logarithm problem (DLP_). Given a cyclic group, a generator *g*,
+and an element *h*, it is hard to find an integer *x* such that *g^x = h*.
+
+The group is the largest multiplicative sub-group of the integers modulo *p*,
+with *p* prime.
+The signer holds a value *x* (*0<x<p-1*) as private key, and its public
+key (*g*, *p*, *y* where *y=g^x mod p*) is distributed.
+
+The ElGamal signature is twice as big as *p*.
+
+Encryption algorithm
+--------------------
+The security of the ElGamal encryption scheme is based on the computational
+Diffie-Hellman problem (CDH_). Given a cyclic group, a generator *g*,
+and two integers *a* and *b*, it is difficult to find
+the element *g^{ab}* when only *g^a* and *g^b* are known, and not *a* and *b*. 
+
+As before, the group is the largest multiplicative sub-group of the integers
+modulo *p*, with *p* prime.
+The receiver holds a value *a* (*0<a<p-1*) as private key, and its public key
+(*g*, *p*, *b* where *b*=g^a*) is given to the sender.
+
+The ElGamal ciphertext is twice as big as *p*.
+
+Security
+--------
+Both DLP and CDH problem are believed to be difficult, and they have been proved
+such (and therefore secure) for more than 30 years.
+
+The cryptographic strength is linked to the magnitude of *p*.
+In 2012, a sufficient size for *p* is deemed to be 2048 bits.
+For more information, see the most recent ECRYPT_ report.
+
+Even though ElGamal algorithms are in theory reasonably secure for new designs,
+in practice there are no real good reasons for using them.
+The signature is four times larger than the equivalent DSA, and the ciphertext
+is two times larger than the equivalent RSA.
+
+Functionality
+-------------
+This module provides facilities for generating new ElGamal keys and for constructing
+them from known components. ElGamal keys allows you to perform basic signing,
+verification, encryption, and decryption.
+
+    >>> from Crypto import Random
+    >>> from Crypto.Random import random
+    >>> from Crypto.PublicKey import ElGamal
+    >>> from Crypto.Util.number import GCD
+    >>> from Crypto.Hash import SHA
+    >>>
+    >>> message = "Hello"
+    >>> key = ElGamal.generate(1024, Random.new().read)
+    >>> h = SHA.new(message).digest()
+    >>> while 1:
+    >>>     k = random.StrongRandom().randint(1,key.p-1)
+    >>>     if GCD(k,key.p-1)==1: break
+    >>> sig = key.sign(h,k)
+    >>> ...
+    >>> if key.verify(h,sig):
+    >>>     print "OK"
+    >>> else:
+    >>>     print "Incorrect signature"
+
+.. _DLP: http://www.cosic.esat.kuleuven.be/publications/talk-78.pdf
+.. _CDH: http://en.wikipedia.org/wiki/Computational_Diffie%E2%80%93Hellman_assumption
+.. _ECRYPT: http://www.ecrypt.eu.org/documents/D.SPA.17.pdf
+"""
 
 __revision__ = "$Id$"
 
+__all__ = ['generate', 'construct', 'error', 'ElGamalobj']
+
 from Crypto.PublicKey.pubkey import *
 from Crypto.Util import number
 
@@ -35,11 +108,27 @@ class error (Exception):
 
 # Generate an ElGamal key with N bits
 def generate(bits, randfunc, progress_func=None):
-    """generate(bits:int, randfunc:callable, progress_func:callable)
+    """Randomly generate a fresh, new ElGamal key.
+
+    :Parameters:
+        bits : int
+            Key length, or size (in bits) of the modulus *p*.
+            Recommended value is 2048.
+        randfunc : callable
+            Random number generation function; it should accept
+            a single integer N and return a string of random data
+            N bytes long.
+        progress_func : callable
+            Optional function that will be called with a short string
+            containing the key parameter currently being generated;
+            it's useful for interactive applications where a user is
+            waiting for a key to be generated.
 
-    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.
+    :attention: You should always use a cryptographically secure random number generator,
+        such as the one defined in the ``Crypto.Random`` module; **don't** just use the
+        current time and the ``random`` module.
+
+    :Return: An ElGamal key object (`ElGamalobj`).
     """
     obj=ElGamalobj()
     # Generate prime p
@@ -78,10 +167,29 @@ def generate(bits, randfunc, progress_func=None):
     obj.y = pow(obj.g, obj.x, obj.p)
     return obj
 
-def construct(tuple):
-    """construct(tuple:(long,long,long,long)|(long,long,long,long,long)))
-             : ElGamalobj
-    Construct an ElGamal key from a 3- or 4-tuple of numbers.
+def construct(tup):
+    """Construct an ElGamal key from a tuple of valid ElGamal components.
+
+    The modulus *p* must be a prime.
+
+    The following conditions must apply:
+
+    - 1 < g < p-1
+    - g^{p-1} = 1 mod p
+    - 1 < x < p-1
+    - g^x = y mod p
+
+    :Parameters:
+        tup : tuple
+            A tuple of long integers, with 3 or 4 items
+            in the following order:
+
+            1. Modulus (*p*).
+            2. Generator (*g*).
+            3. Public key (*y*).
+            4. Private key (*x*). Optional.
+
+    :Return: An ElGamal key object (`ElGamalobj`).
     """
 
     obj=ElGamalobj()
@@ -93,8 +201,106 @@ def construct(tuple):
     return obj
 
 class ElGamalobj(pubkey):
+    """Class defining an ElGamal key.
+
+    :undocumented: __getstate__, __setstate__, __repr__, __getattr__
+    """
+
+    #: Dictionary of ElGamal parameters.
+    #:
+    #: A public key will only have the following entries:
+    #:
+    #:  - **y**, the public key.
+    #:  - **g**, the generator.
+    #:  - **p**, the modulus.
+    #:
+    #: A private key will also have:
+    #:
+    #:  - **x**, the private key.
     keydata=['p', 'g', 'y', 'x']
 
+    def encrypt(self, plaintext, K):
+        """Encrypt a piece of data with ElGamal.
+
+        :Parameter plaintext: The piece of data to encrypt with ElGamal.
+         It must be numerically smaller than the module (*p*).
+        :Type plaintext: byte string or long
+
+        :Parameter K: A secret number, chosen randomly in the closed
+         range *[1,p-2]*.
+        :Type K: long (recommended) or byte string (not recommended)
+
+        :Return: A tuple with two items. Each item is of the same type as the
+         plaintext (string or long).
+
+        :attention: selection of *K* is crucial for security. Generating a
+         random number larger than *p-1* and taking the modulus by *p-1* is
+         **not** secure, since smaller values will occur more frequently.
+         Generating a random number systematically smaller than *p-1*
+         (e.g. *floor((p-1)/8)* random bytes) is also **not** secure.
+         In general, it shall not be possible for an attacker to know
+         the value of any bit of K.
+
+        :attention: The number *K* shall not be reused for any other
+         operation and shall be discarded immediately.
+        """
+        return pubkey.encrypt(self, plaintext, K)
+
+    def decrypt(self, ciphertext):
+        """Decrypt a piece of data with ElGamal.
+
+        :Parameter ciphertext: The piece of data to decrypt with ElGamal.
+        :Type ciphertext: byte string, long or a 2-item tuple as returned
+         by `encrypt`
+
+        :Return: A byte string if ciphertext was a byte string or a tuple
+         of byte strings. A long otherwise.
+        """
+        return pubkey.decrypt(self, ciphertext)
+
+    def sign(self, M, K):
+        """Sign a piece of data with ElGamal.
+
+        :Parameter M: The piece of data to sign with ElGamal. It may
+         not be longer in bit size than *p-1*.
+        :Type M: byte string or long
+
+        :Parameter K: A secret number, chosen randomly in the closed
+         range *[1,p-2]* and such that *gcd(k,p-1)=1*.
+        :Type K: long (recommended) or byte string (not recommended)
+
+        :attention: selection of *K* is crucial for security. Generating a
+         random number larger than *p-1* and taking the modulus by *p-1* is
+         **not** secure, since smaller values will occur more frequently.
+         Generating a random number systematically smaller than *p-1*
+         (e.g. *floor((p-1)/8)* random bytes) is also **not** secure.
+         In general, it shall not be possible for an attacker to know
+         the value of any bit of K.
+
+        :attention: The number *K* shall not be reused for any other
+         operation and shall be discarded immediately.
+
+        :attention: It is strongly recommended to have M be a digest created
+         via a cryptographic hash, otherwise an attacker may mount an
+         existential forgery attack.
+
+        :Return: A tuple with 2 longs.
+        """
+        return pubkey.sign(self, M, K)
+
+    def verify(self, M, signature):
+        """Verify the validity of an ElGamal signature.
+
+        :Parameter M: The expected message.
+        :Type M: byte string or long
+
+        :Parameter signature: The ElGamal signature to verify.
+        :Type signature: A tuple with 2 longs as return by `sign`
+
+        :Return: True if the signature is correct, False otherwise.
+        """
+        return pubkey.verify(self, M, signature)
+
     def _encrypt(self, M, K):
         a=pow(self.g, K, self.p)
         b=( M*pow(self.y, K, self.p) ) % self.p
@@ -128,19 +334,15 @@ def _verify(self, M, sig):
         return 0
 
     def size(self):
-        "Return the maximum number of bits that can be handled by this key."
         return number.size(self.p) - 1
 
     def has_private(self):
-        """Return a Boolean denoting whether the object contains
-        private components."""
         if hasattr(self, 'x'):
             return 1
         else:
             return 0
 
     def publickey(self):
-        """Return a new key object containing only the public information."""
         return construct((self.p, self.g, self.y))
 
 

lib/Crypto/PublicKey/RSA.py

@@ -32,10 +32,13 @@
 The algorithm can be used for both confidentiality (encryption) and
 authentication (digital signature). It is worth noting that signing and
 decryption are significantly slower than verification and encryption.
-The cryptograhic strength is primarily linked to the length of the modulus.
+The cryptograhic strength is primarily linked to the length of the modulus *n*.
 In 2012, a sufficient length is deemed to be 2048 bits. For more information,
 see the most recent ECRYPT_ report.
 
+Both RSA ciphertext and RSA signature are as big as the modulus *n* (256
+bytes if *n* is 2048 bit long).
+
 This module provides facilities for generating fresh, new RSA keys, constructing
 them from known components, exporting them, and importing them.