[marzell]

The second point, yeah that's relevant.

On the first point, just give each person n-1 shards, each missing a different one. Then any 2 can decrypt. Or configure it for however many participants there are and they minimum number needed to encrypt.

[d-z-m]

The key part about Shamir is that having any number of shards short of the threshold doesn't reveal anything about the secret. Let's say you split your 256 bit encryption key into 4 64-bit pieces with each person getting 3 of the 4. Each person now knows 3/4 of the secret. Now any one person simply has to brute force the remaining 64 bits of the key in order to decrypt.