Random Number Generation on low entropy computer systems

Lately, I got interested in random number generation. Generating random numbers securely so they are suitable for cryptographic use is hard.

Linux introduced /dev/random, a block device to a random number generator in the kernel. The generator keeps an estimate of the number of bits of noise in the entropy pool. From this entropy pool, random numbers are created by using a secure hash function on the data in the pool . When read, the /dev/random device will only return random bytes within the estimated number of bits of noise in the entropy pool. The Operating System adds entropy from all sorts of sources, such as disk latency. However, if you are running Linux on an embedded device (or “internet of things”) or in a cloud instance, there may not be a “real” disk drive, and whatever latency is measured may not contain good enough entropy. Another important source of entropy is the clock-cycle timer (rdtsc) that is called at various instances to measure the time between interrupts and other frequently and somewhat randomly occurring events. The rdtsc instruction is often virtualized in cloud-machines which could make it harder to get good entropy.  Anyways… the problem of getting random numbers in low-entropy situations is important enough that Intel added an on-chip random number generator to their new processors (rdrand), but many cloud instances emulate older CPUs and embedded system don’t necessarily run with x86 chips that have rdrand.

So far, so good. For now, I don’t have an embedded system to experiment with, but a similar problem is with servers in the cloud. Can the rdtsc instruction still be used to get entropy in a virtual machine? I found this, played around a bit with the program listed and also learned about the existence of haveged (I’ll get back to that). I started a micro-instance (1 CPU, 512Mb RAM) in a popular cloud service and found that, yes indeed, the rdtsc instruction seems to be virtualized. The average tick count between millions of two consecutive rdtsc instructions is far too small to account for whatever else is going on on the machine (unless, of course, I somehow got a 512MB machine all by myself – which is unlikely). On the other hand, the output of the least significant bit of the difference of two consecutive rdtsc calls looked pretty random, but didn’t pass randomness tests. Adding von-Neumann whitening on the LSB obtained from two rdtsc calls is actually sufficiently random to pass FIPS 140-2 randomness tests (I used the implementation in rngtest) and only fails about 1 in 1000 (comparison: a test-run with entropy from /dev/random failed 1:10000). So in theory, this should be okay to use as an entropy source, but maybe it should still be combined with other sources of entropy.

Coming back to other already existing solutions. It turns out there’s an entropy gathering demon called haveged that can add entropy to the pool to remedy low-entropy conditions that can occur in servers, but possibly also on embedded devices and in cloud instance. The method exploits the modifications of the internal volatile hardware states as a source of uncertainty. Modern superscalar processors feature various hardware mechanisms which aim to improve performance: caches, branch predictors, TLBs and much more. The state of these components is also volatile and cannot be directly monitored in software. On the other hand, every invocation of the operating system modifies thousands of these binary volatile states. The general idea of extracting entropy from rdtsc still works, however the only thing that still makes me wonder a bit is that the full timer (not just the LSB) is used and that the whitening method is rather complex.

I learned a lot, but there’s still more to explore. Cloud machines probably have more going on than embedded systems, so I’m still not convinced that this will work on embedded devices. I’ll try to wrap my head around the whitening function in haveged. It’s still being developed and maybe ARM support will be added some day. Then the demon could be used on smart phones to improve the security of the random number generation.



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