Threshold Chunking

The Problem

How do you distribute a file in pieces such that you need exactly a given number of the pieces to rebuild the entire file?

This article was inspired by the Shamir Secret Sharing Scheme (SSSS), a cryptographic scheme (process) by which a secret key is shared between $n$ fragments, any $m$ of which can be used to recreate the entire key (n and $m$ being determined at the beginning of the process). Recreating the key from fragments is automatic and requires no further password or other. If you can find $m$ fragments and know which index they each have, you can recreate the key in its entirety.