but you can also just use Reed-Solomon and split the payload, the difference with Shamir is that you lose information-theoretic security (you lose it the moment you use encryption anyway) and the payload also needs to undergo an all-or-nothing-transform (AONT).

AONT transforms the entire payload into an encrypted blob which also serves as its own key, a withheld piece is a de facto encryption key. this is required because Reed-Solomon can have pathological cases where pieces leak information.