[myself248]

Could you make one equivalent to the other, by R-S encoding a key? And if you have less than the whole key (assuming it's large enough that the missing portion is still bruteforce-resistant), then even a partial reconstruction of the key still gives you none of the data.

[lowercase1]

Yes you can! Apply an All or Nothing Transform before RS encoding so that you need all of the original data to decrypt. Then you can only decrypt if you have k of n pieces. You save by a factor of k in piece size over SSS.

http://web.eecs.utk.edu/~plank/plank/papers/FAST-2011.pdf