How to convince users of the honesty of the number generator?

Question

random numbers

There is a site where prize draws are held. Winners are chosen by the usual random() function, which is present in one form or another in the standard libraries of almost all languages. Due to the specifics of the site, there are a large number of people who do not believe in randomness and believe that everything is rigged, as a result they pass by draws. Question: how to prove/demonstrate honesty and transparency in order to involve, among other things, the audience that does not believe?

Answer 1

Ask to encrypt a number from 1 to 1000 (for example) plus some text with the private key. The cipher is sent to you, but you can't do anything with it. Then you post which number is the winning number without knowing who might have won. Then users send you their public key (if they win, otherwise there is no point). The prize is divided among the winners in equal proportions.
You can change the scheme to suit your needs, but the essence is the same. The chip with encryption proves that rigging is impossible, because. you can't know who guessed what number. And at the same time, users cannot change the number after you announce the winner, that is, the winning number.