What is the meaning of the UNPREDICTABLE in random function?

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Linguistically I understand the meaning of unpredictable. But, during this time I often find the word predictable in some cases. I usually find these words if I enter an area with several topics, for example:

  1. Math.random vs crypto.getRandomValues in Javascript
  2. Random vs Secure Random numbers
  3. Etc

So what exactly does unpredictable mean in random functions? Then what are the conditions for a random function to be called "unpredictable random function"?

random-seed semantics cryptography random
2 Answers

If a value is random, then it means that knowing the previous values in the sequence provides you no information about the next value.

If a value is unpredictable, then there is no "practical" means of determining the next value. It is generally a stronger claim than random.

(The word "practical" here is doing some work. It generally means "within some set of rules about what the attacker may do." If the attacker has full access to the CPU and RAM, then nothing is "unpredictable," but we are generally interested in cases where they do not have this.)

As an example of the difference, the digits of pi are believed to be random (we don't actually know this, but it appears to be true). That means that there is no way to guess, better than chance, the 10,000th digit of pi. It's random. But it's perfectly predictable. Anyone can easily determine its value. So the digits of pi are a perfectly good random sequence, and could even be used effectively to drive a game's behavior where randomness is sufficient, but it won't be a secure random sequence and is useless for cryptographic purposes.

If I went to random.org (which provides very good random numbers), and generated a value, but then used it repeatedly, it would be a random value but also completely predictable.

This predictability can occur when producing the seed of a PRNG. While the PRNG may generate excellent random values, if its seed is predictable then the entire sequence will be known. ("Predictable" here doesn't mean with 100% certainty; any level of certainty better than chance is sufficient.)

As an example of this problem, networking gear has a significant challenge generating an unpredictable seed when first booted, particularly if the networking gear nearby is rebooted at the same time. Whatever process you use to create a random value can easily fall into a small set of likely values ("small" compared to all the possible values; it may still be in the millions, but that's not many values in cryptography). This is a problem that can require significant effort to resolve in high-security systems.

Most cryptographic systems do not define how these initial, unpredictable values are to be generated. They're just an assumed input to the system.

user_973370

Predictable is when the seed itself is from something that can be predicted, like the time for example in python random library:

import random, time

random.seed(time.time())
r1 = random.randrange(1e49, 1e50-1)

random.seed(time.time())
r2 = random.randrange(1e49, 1e50-1)

print(r1)
print(r2)

The output here will be the same.

Unpredictable would be when a random number has really high entropy, so that none could really find the initial seed and track down the random algorithm that was used.

user_135964340
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