I was wondering why Randomized Algorithm were often more efficient than non-randomized algorithm.

Then I looked at a list of random number generators (or RNG).

Of course we usually talk about PRNG (Pseudo Random Number Generator) since “truly random” is impossible/hard to achieve.

An interesting thing I stumbled into is that you can create a PRNG using a block cipher in counter mode, by iterating the counter and always encrypting the same thing, if the block cipher used is good, it should look random.

This sounds solid since ciphers sometimes need to have Ciphertext Indistinguishability from random noise.

To support such deniable encryption systems, a few cryptographic algorithms are specifically designed to make ciphertext messages indistinguishable from random bit strings

Also under the Ciphertext indistinguishability property that a cipher should respect, you shouldn’t be able to find any relations between the ciphertexts coming from the same input but encrypted with an increasing counter.