Are there algorithms for secure secret sharing such that the algorithm depends solely on the value being secured, relying on no randomness in its calculations.
If there aren't, is such an algorithm an impossibility? If there are, what are some examples?
I ask because I've come up with a secret sharing scheme (which is probably littered with flaws ;-)), and I'd like try and prove certain properties about it. If deterministic secret sharing schemes are a no-go, I'd very much appreciate a heads up.
I'm not entirely certain this question is well defined. If it is not, I would greatly appreciate any information on why it is ill defined and how to make it more rigorous if possible.