[Cryptography] Proper Entropy Source

[Mansour Moufid]

On Thu, Jan 23, 2020 at 5:42 AM John Denker <jsd at av8n.com> wrote:

> Software can increase randomness, as defined below, even
> though it does not increase entropy.

A contradiction.

>   The word means different things to different people,
>   but in crypto context the following definition is
>   often close enough:
>         random means "not guessable by adversaries"

False. According to the uniqueness theorem, there is one and only one
definition of entropy.

See Khinchin for the proof (theorem 1, page 9):

    https://b-ok.cc/book/3360302/7a70ca

> > You mean source of randomness,
> > entropy is the measure of randomness. [a]
>
> 1) Even if that were true, it would be silly.  How to you
> propose to increase a thing without increasing the measure
> of the thing?

It is not possible to "increase" entropy with a deterministic scheme (software).

Again, see Khinchin for the proof (page 6).

These proofs are the foundation of probability theory. If you find an
error in them, let the world know.