Do you know of a m of n security algorithm?

I've tried Googling this and can't figure how to phrase the query.

In security there is the concept of M of N (M < N) where M executives (of a total group of N) can authorize certain action.

If one has an encryption key one can divide it into three parts, give each of three people two out of the three parts and have 2 of 3 people can be used to recover the original key.

It there a general algorithm for doing this? I can figure 2 out of 4 or 5.