agree w waxwing!

Similar to Shamirs secret sharing, having T-1 shares actually provides you zero information. There is no information leakage. Using a finite field with "wrapping around" is fundamental for this property. The wiki page on SSS is really solid:

https://en.wikipedia.org/wiki/Shamir%27s_secret_sharing

And thanks! It used to be more nuts but i slimmed it down a bit