Are there any pseudo random number generator based on Galois fields? The source of the AES randomness lies in the GF, so GF should be capable of generating random bits.
Why are there no such generators?
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Sign up to join this communityAre there any pseudo random number generator based on Galois fields? The source of the AES randomness lies in the GF, so GF should be capable of generating random bits.
Why are there no such generators?
There are several generators that use finite fields. Blum Blum Shub uses one directly, but is very slow. AES-CTR-DRBG is a CSPRNG that uses AES-128 in CTR mode, thereby indirectly using a finite field. It's fast enough for practical use, particularly with the hardware accelerated AES instructions many modern processors have.
I don't understand what you mean by The source of AES randomness lies in the G(alois) F(ield).
A field is an algebraic structure, it has no randomness. You can think of classical information theoretic randomness, which is a property of a probabilistic source. The source is used to generate a seed, and the seed can be taken to be an element of the field, with an update mapping based on the algebraic structure of the field.
Even if you wanted to think in terms of Kolmogorov complexity as a measure of "randomness" and took a binary extension Galois field and thought of its individual elements as bitstrings, some of those elements will have short descriptions, some not, but the field is just a passive structure.
In addition to the nice examples in the other answer of generators making use of finite fields, the following also use finite fields: