Where can I learn about proven methods for sharing cryptographic keys?

Question

Suppose that a group wants to encrypt some information, then share the encryption key among the group members in a way that requires the consensus of the group to decrypt th

Answer 1

What you describe sounds a lot like "secret splitting" (Section 12.1. Introduction to Cyptography. Trappe & Washington. 2nd ed) The basic idea is you can come up with a polynomial that includes your "secret" (a key) as a point on the line. You can give out "shares" by picking other points on this polynomial. Two points define a line of the form f(x) = ax + b, three points define a polynomial of the form f(x) = ax^2 + bx + c, and four points define something of the form f(x) = ax^3 + bx^2 + cx + d, and so on. You can choose a polynomial that includes your secret as a point, and a degree for the polynomial sufficient so that any N people can reconstruct it.

This is the basic idea that is known as the "Shamir threshold scheme."

See wikipedia on Secret Splitting and Shamir's Secret Sharing The wikipedia page has some links to implementations of this idea, including GPL'd code for Windows and UNIX.