The Secret Sharing Problem
Understand why splitting a secret naively is insecure.
The Problem
You have a master key that must survive, be accessible in emergencies, yet never be compromised by a single person. How do you store it? Giving the full key to multiple people means any one of them can misuse it. Keeping one copy creates a single point of failure.
Naive Splitting Fails
Splitting a 128-bit key into two 64-bit halves and giving each half to two people seems clever but is insecure: each half reduces the brute-force cost from 2^128 to 2^64. An adversary who compromises one person gains a 64-bit head start.