Shamir's Secret Sharing on non-prime GF I am implementing Shamir's secret sharing scheme on arbitrary binary files.  I don't intend to use this; this is a project to help me explore cryptography.  In setting up the finite field arithmetic, I chose my field to be GF(257).  

My understanding is that a prime GF is needed to ensure that a single modular inverse exists for each value in the field (this conflicts with the answer to How can Shamir&#39;s method for secret sharing work in the GF(256)?).

Can someone explain this discrepancy?
You appear to be confused by the sentence in the answer:


  If you use simple modular reduction they won't work (e.g. you can't just compute the operations mod 256).


This sentence is true, but doesn't mean what you think it does.

It doesn't mean that you can't compute inverses in $GF(256)$; instead, what it means is that you can't compute the addition and multiplication as $A + B \bmod 256$ and $A \times B \bmod 256$; other algorithms need to be used.

It happens that addition is easy; you can do it by doing a bitwise exclusive or; in C, that's A ^ B

Multiplication and inverses are a bit trickier; however, I can point you to the answer here that addresses how to do with with a few table lookups