I think this chapter just proves GP's point, rather than refuting it. It's much cleaner than the Wikipedia article and it mentions the zero share problem, but it doesn't mention any other concern like constant time implementations, cache side channel attacks or the leading zero coefficient that I pointed to at the other post.
It's a good guide to learn about Secret Sharing, but it doesn't give you even 1% of what you need to know implement it safely by yourself.
> or the leading zero coefficient that I pointed to at the other post.
That isn't actually a problem, although I've seen a lot of people that think it is.
The problem is framed as "if you have a leading zero coefficient, it's equivalent to a threshold of t-1", but you'd need a zero leading coefficient for every polynomial.
With a 32 byte secret and GF(2^8), you expect at least 1 leading zero coefficient in 11% of random secrets, but a threshold reduction from t to t-1 only occurs with 2^-256 probability (that is, every leading coefficient has to be 0).
You might think you can detect this condition, but SSS is kind of like a one-time pad if you don't have sufficient shares.
> it doesn't mention any other concern like constant time implementations, cache side channel attacks
These are table stakes for secure cryptography. ZKDocs is a guide to algorithms, not implementations.
It's a good guide to learn about Secret Sharing, but it doesn't give you even 1% of what you need to know implement it safely by yourself.