OpenSSL Security Advisory [10 July 2001]

WEAKNESS OF THE OpenSSL PRNG IN VERSIONS UP TO OpenSSL 0.9.6a
-------------------------------------------------------------

CONTENTS:
 - Synopsis
 - Detailed problem description
 - Solution
 - Impact
 - Source code patch [*]
 - Acknowledgement

[*] OpenSSL 0.9.6b has been corrected and does not require this patch.

The source code of OpenSSL 0.9.6b is available as file openssl-0.9.6b.tar.gz
from <URL: ftp://ftp.openssl.org/source;type=d>.
If you were previously using the "engine" release of OpenSSL 0.9.6 or
0.9.6a, obtain file openssl-engine-0.9.6b.tar.gz instead.

MD5 checksums:
     openssl-0.9.6b.tar.gz          bd8c4d8c5bafc7a4d55d152989fdb327
     openssl-engine-0.9.6b.tar.gz   ab5ca5b157459c49bdab06a7db8a5a47

OpenSSL source code can also be obtained from a number of mirror sites.
For a list, see <URL: http://www.openssl.org/source/mirror.html>.

If you are using a pre-compiled OpenSSL package, please look for update
information from the respective software distributor.  The OpenSSL
group itself does not distribute OpenSSL binaries.


SYNOPSIS
--------

The pseudo-random number generator (PRNG) in SSLeay/OpenSSL versions
up to 0.9.6a is weakened by a design error.  Knowing the output of
specific PRNG requests (including a number of consecutive very short
PRNG requests) would allow an attacker to determine the PRNG's
internal state and thus to predict future PRNG output.

Typical applications (including applications using OpenSSL's SSL/TLS
library) are not vulnerable to this attack because PRNG requests
usually happen in larger chunks.  However, we strongly recommend
upgrading to OpenSSL 0.9.6b, which includes a fixed PRNG.
If upgrading to 0.9.6b is not immediately possible, the source
code patch contained at the end of this advisory should be applied.



DETAILED PROBLEM DESCRIPTION
----------------------------

Recently a cryptographic flaw in OpenSSL's built-in pseudo-random
number generator (PRNG) was pointed out to us by Markku-Juhani
O. Saarinen <markku-juhani.saarinen@nokia.com>, who showed how
an attacker could reconstruct the PRNG's internal state from
the output of a couple of hundred 1-byte PRNG requests.  This problem
dates back to SSLeay, which OpenSSL is based on, and was found in other
SSLeay-based toolkits as well.  While a number of enhancements have
been done to the original PRNG during the development of OpenSSL, this
design error was overlooked so far.

The PRNG (implemented in source code file crypto/md_rand.c) uses a
hash function, by default SHA-1, to update its internal secret state
and to generate output.  The secret state consists of two components:
A chaining variable 'md', sized according to the hash function's
output (160 bits for SHA-1), and a large buffer 'state'.  'md' is
always replaced by a hash function output during the PRNG's operation.
'state' is accessed circularly and is used for storing additional
entropy.

When generating output bytes, OpenSSL versions up to 0.9.6a set 'md'
to the hash of one half of its previous value and some other data,
including bytes from 'state'.  The design error was that the half of
'md' input to the hash function was the same half that was also used
as PRNG output, meaning that it in general cannot be considered
secret.  Also the number of bytes used from 'state' depended on the
number of bytes requested as PRNG output and could be as small as one,
allowing for easy brute-force analysis of all possible cases.
The combination of these effects made it possible to reconstruct
the complete internal PRNG state from the output of one PRNG request
appropriately sized to gain knowledge on 'md' followed by enough
consecutive 1-byte PRNG requests to traverse all of 'state'.


SOLUTION
--------

OpenSSL 0.9.6b changes the PRNG implementation as follows to give the
PRNG its intended strength:

1. When updating 'md' during PRNG output generation, all of the
   previous 'md' value is hashed, including the secret half.

2. Also, the number of bytes from 'state' included into the hash is
   now independent from the number of PRNG bytes requested.

The first measure alone would be sufficient to solve the problem.  The
second measure makes sure that additional data from 'state' is never
mixed in in small portions; this heuristically further strengthens the
PRNG.


IMPACT
------

It is unlikely for applications to request PRNG bytes in a pattern
allowing for the attack against the OpenSSL PRNG.  Typically,
applications will request PRNG bytes in larger chunks.
No applications is known to us which is actually vulnerable.

However, the PRNG design flaw is a significant weakness: The PRNG does
not provide the intended strength under all circumstances.  Therefore,
we strongly recommend that all users upgrade to OpenSSL 0.9.6b as soon
as possible.


SOURCE CODE PATCH
-----------------

If upgrading to OpenSSL 0.9.6b is not immediately possible, the
following patch should be applied to file crypto/rand/md_rand.c in the
OpenSSL source code tree.  (The patch is compatible with OpenSSL
versions 0.9.5 up to 0.9.6a.)  This changes the PRNG in two ways, as
discussed above.

--- md_rand.c
+++ md_rand.c
@@ -313,6 +313,7 @@
 	{
 	static volatile int stirred_pool = 0;
 	int i,j,k,st_num,st_idx;
+	int num_ceil;
 	int ok;
 	long md_c[2];
 	unsigned char local_md[MD_DIGEST_LENGTH];
@@ -333,6 +334,12 @@
 		}
 #endif
 
+	if (num <= 0)
+		return 1;
+	
+	/* round upwards to multiple of MD_DIGEST_LENGTH/2 */
+	num_ceil = (1 + (num-1)/(MD_DIGEST_LENGTH/2)) * (MD_DIGEST_LENGTH/2);
+
 	/*
 	 * (Based on the rand(3) manpage:)
 	 *
@@ -418,11 +425,11 @@
 	md_c[1] = md_count[1];
 	memcpy(local_md, md, sizeof md);
 
-	state_index+=num;
+	state_index+=num_ceil;
 	if (state_index > state_num)
 		state_index %= state_num;
 
-	/* state[st_idx], ..., state[(st_idx + num - 1) % st_num]
+	/* state[st_idx], ..., state[(st_idx + num_ceil - 1) % st_num]
 	 * are now ours (but other threads may use them too) */
 
 	md_count[0] += 1;
@@ -434,6 +441,7 @@
 
 	while (num > 0)
 		{
+		/* num_ceil -= MD_DIGEST_LENGTH/2 */
 		j=(num >= MD_DIGEST_LENGTH/2)?MD_DIGEST_LENGTH/2:num;
 		num-=j;
 		MD_Init(&m);
@@ -444,27 +452,28 @@
 			curr_pid = 0;
 			}
 #endif
-		MD_Update(&m,&(local_md[MD_DIGEST_LENGTH/2]),MD_DIGEST_LENGTH/2);
+		MD_Update(&m,local_md,MD_DIGEST_LENGTH);
 		MD_Update(&m,(unsigned char *)&(md_c[0]),sizeof(md_c));
 #ifndef PURIFY
 		MD_Update(&m,buf,j); /* purify complains */
 #endif
-		k=(st_idx+j)-st_num;
+		k=(st_idx+MD_DIGEST_LENGTH/2)-st_num;
 		if (k > 0)
 			{
-			MD_Update(&m,&(state[st_idx]),j-k);
+			MD_Update(&m,&(state[st_idx]),MD_DIGEST_LENGTH/2-k);
 			MD_Update(&m,&(state[0]),k);
 			}
 		else
-			MD_Update(&m,&(state[st_idx]),j);
+			MD_Update(&m,&(state[st_idx]),MD_DIGEST_LENGTH/2);
 		MD_Final(local_md,&m);
 
-		for (i=0; i<j; i++)
+		for (i=0; i<MD_DIGEST_LENGTH/2; i++)
 			{
 			state[st_idx++]^=local_md[i]; /* may compete with other threads */
-			*(buf++)=local_md[i+MD_DIGEST_LENGTH/2];
 			if (st_idx >= st_num)
 				st_idx=0;
+			if (i < j)
+				*(buf++)=local_md[i+MD_DIGEST_LENGTH/2];
 			}
 		}
 
*** END OF PATCH ***


ACKNOWLEDGEMENT
---------------

We thank Markku-Juhani O. Saarinen <markku-juhani.saarinen@nokia.com>
for discovering the PRNG problem and bringing it to our attention.


URL for this Security Advisory:
http://www.openssl.org/news/secadv_prng.txt