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With your clarification edits it is clear what you are looking for. Generated Value = SHA512(A || B || C) Where A = 512 bit secret Where B = x bits server seed and can be attacker chosen Where C = x bits client seed and can be attacker chosen The thing I am curious about is if it's possible for end-user to guess secret seed if he is given ability to ...


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generate a random number that users can later verify was not fixed/influenced in any way by me. There's no way to do that on your own. But you can ask users to contribute to the seed, eg. Generate a seed $s$ Commit to $s$ and send commitment to the user User generates his own seed, $s'$ and sends it to you Combine (eg. XOR) the two seeds together. ...


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By inventing your own random number generator, you are chasing a red herring. There is no need whatsoever for you to invent your own RNG. Combining cryptographic primitives on your own is exceedingly dangerous, and worse, there's no actual need to do so. Unfortunately, if you are only choosing 10 numbers between 1-100, there are only $100^{10}$ possible ...



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