Is there an algorithm to securely split a message into x parts requiring at least y parts to reassemble? Obviously, y <= x.
An example:
Say that I have a secret message that I only want to be read in the event of my death. As a way to ensure this, I give a fraction of the message to ten friends. Now, I can’t guaranty that all my friends will be able to put their messages together to recover the original. So, I construct each message fraction in such a way so as to only require any 5 friends to put their parts together to reconstruct the whole. However, owning less than 5 parts will not give anything away about the message, except possibly the length.
My question is, is this possible? What algorithms might I look at to accomplish this?
Clarification edit: The important part of this is the cryptographic strength. An attacker should not be able to recover the message, either in whole or in part with less than y parts.
Shamir Secret Sharing and Blakley’s scheme are two well-established, provably secure means of sharing a secret so that it can be recovered only when a pre-determined number of “shares” are combined.