Really random number?

Question

Mathematics

Let's say we have a thousand lottery tickets and we need to choose one or N winners. Each participant has a name and a unique ticket number (in the form of a number from 1 to 1000). The lottery is played when reaching a thousand participants.
Is it realistic to select winners in such a way that neither the organizer nor the participant could fabricate/cheat the winner selection system?
That is, you need to generate one or a series of random numbers (numbers are winners), the generation method of which would be non-falsifiable and transparent for each of the participants.
I apologize in advance for the crooked wording, I will be glad for any answers

Answer 1

Easily.
Let you need a number in the range 0..63 (I took a simpler example).
Each of the participants brings their own generated "random" number in an envelope, after which the final random number is somehow calculated. For example:

участник   число
A            7
B           13
C           42
D           49
итого      7⊕13⊕42⊕49=17

Falsification here is possible only with peeping by one of the participants of the numbers of all the others and giving them their number last.