One generation, multiple puzzles

[SonahtQ]

Is it possible for current (time-lock puzzle) algorithm to have multiple maybe infinite count of solutions per one puzzle?

That would be very handy, for example server generates puzzle for each client session ones and when client send request for something, request has to be along with puzzle solution, then server keeps all previous solutions and checks if the new one is truely new and only then fullfil request response.

[fabiospampinato]

I'm not sure but I think technically a single puzzle always has infinite solutions, because I'm assuming there are just going to be an infinite number of decryption keys that just happen to work the same way, though the probability of even finding two of these would be astronomical.

Looking more at the algorithm the encryption key is essentially encrypted by summing the product of two large prime numbers to it, so there is only going to be one pair of prime numbers that when subtracted to the encrypted key reveals the key, though I guess there could be an infinite number of non-prime pairs that sum to the same number or something.

More specifically for your use case I think it might be doable, what we really want for that use case is not really many solutions to one puzzle, but many puzzles with the same primes, which are the relatively expensive part of the generation.

I'm not exactly sure what the best way to do this would be, there are some interesting ideas from HashCash also, where the user basically gives you a solution to a puzzle without requesting a puzzle first, or without requesting a puzzle for each request, which could simplify things a lot.