Sorry if this question's a bit basic, but I don't know of any way to ask it concisely enough for a search... What I'm looking for is a proven means of doing the following:
Create x number of strings so that any combination of at least y of those x can be used to recreate a message.
For example: if I have "this is my message" (the message), I'd like to split it up in some way where I can give 10 people (x) part of the message, but ensure that the message can be reconstructed accurately as soon as any 7 of those people (y) combine their individual components.
In reality this message would be a public key for encryption, although I don't see how that would really matter. Ideally, both x and y would be as variable as possible (one algorithm/approach which works when x=10 and y=7, as well as when x=50 and y=1, as well as when x=5 and y=5, etc).