Let’s start off with one of my favorite quotes from John von Neumann: “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.”
What von Neumann is getting at is that the “pseudo” in pseudorandom number generator (PRNG) is really a synonym for “not at all”. Granted, if you come in the middle of a good PRNG sequence, guessing the next number is nearly impossible. But if you know, or can guess, the seed that started the PRNG off, you know all past and future values nearly instantly; it’s a purely deterministic mathematical function. This shouldn’t be taken as a rant against PRNGs, but merely as a reminder that when you use one, the un-guessability of the numbers that it spits out is only as un-guessable as the seed. And while “un-guessability” isn’t a well-defined mathematical concept, or even a real word, entropy is.
That’s why entropy matters to you. Almost anything that your computer wants to keep secret will require the generation of a secret random number at some point, and any series of “random” numbers that a computer generates will have only as much entropy, and thus un-guessability, as the seed used. So how does a computer, a deterministic machine, harvest entropy for that seed in the first place? And how can you make sure you’ve got enough? And did you know that your Raspberry Pi can be turned into a heavy-duty source of entropy? Read on!
Continue reading “What is Entropy and How Do I Get More of It?”
One of the standout talks at the 33rd Chaos Communications Congress concerned pseudo-random-number generators (PRNGs). [Vladimir Klebanov] (right) and [Felix Dörre] (left) provided a framework for making sure that PRNGs are doing what they should. Along the way, they discovered a flaw in Libgcrypt/GNUPG, which they got fixed. Woot.
Cryptographically secure random numbers actually matter, a lot. If you’re old enough to remember the Debian OpenSSL debacle of 2008, essentially every Internet service was backdoorable due to bad random numbers. So they matter. [Vladimir] makes the case that writing good random number generators is very, very hard. Consequently, it’s very important that their output be tested very, very well.
So how can we test them? [Vladimir] warns against our first instinct, running a statistical test suite like DIEHARD. He points out (correctly) that running any algorithm through a good enough hash function will pass statistical tests, but that doesn’t mean it’s good for cryptography.
Continue reading “33C3: How Can You Trust Your Random Numbers?”
How can you generate random bits? Some people think it’s not easy, others will tell you that it’s pretty damn hard, and then there are those who wonder if it is possible at all. Of course, it is easy to create a very long pseudorandom sequence in software, but even the best PRNG (Pseudorandom Number Generator) needs a good random seed, as we don’t want to get the same sequence each time we switch on the unit, do we? That’s why we need a TRNG (True Random Number Generator), but that requires special hardware.
Some high-end microprocessors are equipped with an internal hardware TRNG, but it is, unfortunately, not true for most low-cost microcontrollers. There are a couple of tricks hackers use to compensate. They usually start the internal free running counter and fetch its contents when some external event occurs (user presses a button, or so). This works, but not without disadvantages. First, there is the danger of “locking” those two events, as a timer period may be some derivative of input scan routine timing. Second, the free running time (between switching on and the moment the unit requests a random number) is often too short, resulting in the seed being too close to the sequence start, and thus predictable. In some cases even, there is no external input before the unit needs a random seed!
Despite what has already been discussed, microcontrollers do have a source of true randomness inside them. While it might not be good enough for crypto applications, it still generates high enough entropy for amusement games, simulations, art gadgets, etc.
Continue reading “True Random Number Generator for a True Hacker”
Most toolchains for embedded system include support for random number generation. But if you’ve read the manual you’ll know that this is really just pseudo random number generation (PRNG). When calling this function the same numbers will always return in the same order unless a different random number seed is supplied in advance. [Gardner] put together a simple and cheap solution for deriving better random number seeds. He reads a voltage from a 555 timer using the ADC on the microcontroller. At first glance it may not seem like a great source of randomness, but he performed some testing and the results look quite promising.
The project is aimed at Arduino-based circuits, but any chip with an ADC will work. The 555 timer is used as a free running oscillator. We know that this not be very stable when compared to even the worst of crystal oscillators, but that’s what makes it work so well as a random seed source. Add to this the low parts count and small size of the additional circuitry and you’ve got a winning combination. So keep this in mind when you need a random number but don’t necessarily need rock solid entropy.
[via Reddit and Freetronics]
[MS3FGX] has done an interesting study about using Bluetooth adapters as a source for Pseudorandom Number Generation (PRNG). As it turns out, the Bluez package has a function that calls a remote Bluetooth adapter to return a random number. He picked up 10 compatible adapters for about $30 from DealExtreme and set about assembling some numbers to see how this compares to an OS-based PRNG.
Because millions of samples are needed for an accurate comparison, time became a problem. The adapters are a little bit slow responding to a request, sending just 4800 numbers in the first 30-second test. This can be overcome with multiple adapters being accessed by multiple computers for hours at a time. What can this be used for? Your guess is as good as ours, but [MS3FGX] has done a great job of writing up his tests. He’s also made a set of 20.7 million randomly generated values available if you want to generate your own statistical analysis.