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How was early randomness generated?

Many programs make use of randomness, from BASIC guess-the-number games to encryption key generators. This randomness could have been generated in many, many different ways: hardware, software, software seeded by hardware...

What techniques were used to generate randomness in early computers, and were cryptographically secure sources of randomness commonly used?

Answer*

The one-word answer to your question is "badly".

The way to create random numbers quickly is via a [Pseudorandom number generator][1] (PRNG). That Wikipedia page gives the history of PRNGs and in particular notes that [linear congruential generators][2] are/were common, with quite a few failings including periodicity (i.e. it cycles through the same sequence of values), poor distribution, predictability, and quite a few other faults that make them poor choices for use in cryptography. That page also describes [linear-feedback shift registers][3] but I don't recall them being used in the BASICs of my youth.

The first decent PRNG is the [Mersenne Twister][4], which was invented in 1997. It requires 2.5 KiB of RAM to store its state, and is relatively computationally intensive, so it would be ludicrous to provide it as the standard random number source of a BASIC running on a machine with only a few tens of kilobytes of RAM and a slow CPU even if the algorithm had been known at the time.

Cryptographically-secure random numbers need the aid of a hardware device that contains true randomness, such as interrupt timings from I/O devices, or even a dedicated quantum noise source. Again, older machines tended not to have much in the way of interrupt-driven I/O, commonly using a vertical blank interrupt to trigger a polling process instead. 

For a concrete example, look at the [source of the Sinclair ZX Spectrum's `RND` function][5]. In case that link goes bad, I'll also summarise it. There is a 16 bit system variable `SEED` which unsurprisingly contains the current random number seed. When you call `RND`, it computes `(SEED+1)*75 mod 65537 - 1` which it stores in `SEED`, and returns `SEED / 65536`, i.e. a value in the range [0, 1).

Because `SEED` is just 16 bits, it's clear that this PRNG can't have more than 65,536 possible states. Mathematical analysis of the function it uses to generate the next `SEED` will show that it has exactly 65,536 states, and thus will repeat and generate the same values after that many calls. It's alright for deciding where to put aliens on the screen, but I wouldn't trust my online banking to it...


  [1]: https://en.wikipedia.org/wiki/Pseudorandom_number_generator
  [2]: https://en.wikipedia.org/wiki/Linear_congruential_generator
  [3]: https://en.wikipedia.org/wiki/Linear-feedback_shift_register
  [4]: https://en.wikipedia.org/wiki/Mersenne_Twister
  [5]: http://skoolkit.ca/disassemblies/rom/asm/9720.html

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12

"dedicated quantum noise source". Hooking up with a Geiger Counter was not unknown.

PCARR
– PCARR

2017-02-05 13:05:30 +00:00
Commented Feb 5, 2017 at 13:05
27

This is a bit too harsh IMO. What's a good and what's a bad PRNG depends on what you need the numbers for. Sure, some cryptographical applications won't be satisfied with any results that can be deterministically predicted, but for many other purposes like games or most Monte Carlo algorithms it makes absolutely no difference whether you use a simple LCG (as long as you don't choose ridiculously bad parameters) or a true quantum randomness source.

leftaroundabout
– leftaroundabout

2017-02-06 14:13:50 +00:00
Commented Feb 6, 2017 at 14:13
23

As a minor quibble, Mersenne Twister was not "the first decent PRNG"; it was just the first that became widespread outside crypto-specific applications. ISAAC, for example, was published in 1993, and produces considerably better randomness than MT. RC4 (which is usually called a stream cipher rather than a PRNG, but those are effectively the same thing) was developed in 1987, although it remained a trade secret until 1994. And the DES block cipher, which can be easily used as a crypto-quality PRNG (far better than MT, anyway), dates from 1975.

Ilmari Karonen
– Ilmari Karonen

2017-02-06 17:11:42 +00:00
Commented Feb 6, 2017 at 17:11
9

Badly indeed. On my first job in 1989, I implemented one RNG algorithm from a textbook of mine, and added the wrinkle that the client could specify the range of numbers returned. Should be no problem with random output, right? Well, one user tried it with Boolean (0..1), and discovered the algorithm merely alternated.

T.E.D.
– T.E.D.

2017-02-06 18:49:18 +00:00
Commented Feb 6, 2017 at 18:49
11

The Mersenne Twister was not the first decent PRNG, not even outside cryptography. RANLUX produces a much higher quality, predates it by at least 3 years and was widely used in things like Monte Carlo simulations. Ranshi predates it by at least 3 years, is faster and also produces better randomness.

LKlevin
– LKlevin

2017-02-07 06:29:40 +00:00
Commented Feb 7, 2017 at 6:29

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