/ :: bitbashing

On Syllable’s /dev/random

Inspired by the recent FreeBSDarc4random vulnerability, I’ve been taking a look at the random number generators used by various libraries and operating systems.

Syllable is a desktop OS based on AtheOS that provides what seems like a pretty decent desktop experience along with POSIX APIs and the GNU toolchain.

Crypto is pretty much entirely a userspace operation - but one area where system interaction is vital is in the gathering of hard to guess data used to seed a cryptographically secure PRNG. This is, unfortunately, difficult to do well in most environments, because of course direct hardware access is restricted in any modern operating system, and above the hardware level a computer system is quite deterministic. On many older systems, the only recourse is to collect system statistics (for example using Win32’s Tooltip API to grab heap statistics, or running programs like ‘netstat’ or ‘who’ on Unix and capturing the output), and hope there is not a local attacker who is capturing the same set of statistics and using it to guess the seed information that was collected.

To help make this process easier and safer for applications, the Linux kernel introduced /dev/random, which is a PRNG seeded with data like interrupt timings - data which is accessible to the kernel but not userspace. This concept of an OS provided RNG was quickly adopted by most other Unix systems like the BSDs and Solaris.

Botan uses /dev/random, among other sources, to provide seed information for a PRNG based on the HMAC-KDF design of Hugo Krawczyk. Before relying on Syllable’s implemementation, I wanted to check out the code to be sure additional sources were not required (which, when porting to a completely new OS, typically means writing new code to access whatever system statistics information the OS might provide).

I am glad I did so, since it turns out that Syllable’s kernel RNG is a MT13397 Mersenne twister.

A Mersenne twister is a fine random number generator for general use, with good statistical properties, but it is not a particularly good choice for cryptographic applications.

Most troubling is the implementation of seed(), which I have reproduced here:

 96 /* initializes state[N] with a seed */
 97 void seed(int32 s)
 98 {
 99     int j;
100     state[0]= s & 0xffffffffUL;
101     for (j=1; j<N; j++) {
102         state[j] = (1812433253UL * (state[j-1] ^ (state[j-1] >> 30)) + j);
103         /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
104         /* In the previous versions, MSBs of the seed affect   */
105         /* only MSBs of the array state[].                        */
106         /* 2002/01/09 modified by Makoto Matsumoto             */
107         state[j] &= 0xffffffffUL;  /* for >32 bit machines */
108     }
109     left = 1; initf = 1;
110 }

The array state is a 624 word array that contains the internal state of the twister. However, all of these words are overwritten on each call to seed, and thus only depends on the single 32-bit word which was last given as a seed value, plus the number of times the PRNG has been stepped since it was last seeded.

The device code that provides userspace access to the PRNG also does some pretty funky stuff:

26 static int random_read(void* node, void* cookie, \
                          off_t pos, void* buf, size_t length)
27 {
28   char* buffer = (char*)buf;
29   int i, j, k;
30
31   j = k = 0;
32
33   for( i = 0;  i < length;  i++ )
34   {
35           j = rand();
36
37           if( j != k )
38                   buffer[i] = j % 256;
39
40           k = j;
41   }
42
43   return( length );
44 }

Here rand() is a call that produces the next 32 bits of output from the twister. I’m not sure exactly about the logic on lines 37 and 38, but it appears the idea was to ensure that no two consecutive bytes have the same value. However this occurring is actually fine, and in a uniform random distribution of bytes one would expect to see it about .4% of the time. Instead, when this occurs, no value at all is written to that index in the output array, leaving it unaltered.

A (citation-less) sentence in the current version of the Wikipedia article on the Mersenne twister states that “Observing a sufficient number of iterates (624 in the case of MT19937) allows one to predict all future iterates”. Since only the low 8 bits of each output are visible outside the kernel, it is not clear to me if this would allow a practical attack against Syllable’s /dev/random or not.

There seem to be several ways this could be easily improved without an excessive amount of effort. Instead of wiping out the previous seed information, new calls to seed() should supplement the previously set seeds. Exchanging the twister for a cryptographically secure PRNG, even a relatively weak one like RC4 (discarding the first few thousand bytes of output to avoid the known statistical biases), would also seem to be a compelling win here.