(Shamir’s scheme is delightfully straightforward, but if polynomial interpolation over finite fields isn’t a thing you feel in your bones, try inventing an n-of-n-shares scheme that only uses xor and a random-number generator. Gb nyy ohg bar bs gur cnegvpvcnagf, tvir n puhax bs enaqbz qngn nf ybat nf gur frperg; gb gur ynfg bar, tvir gur kbe bs gur frperg naq gur enaqbz puhaxf. You probably don’t want that in production, but it’s nice to figure it out and even utterly simple to prove it secure, provided you understand the proof for one-time pads.)