ZK proofs have a number of good explainers, mostly using graph colorings. Non-interactive versions, however, require quite a bit more than that explanation allows - and despite asking experts, I still haven't found a good, basic explanation.
Maybe the blog of Prof. Matthew Green of JHU is of use. Specifically, the two-part series about zero-knowledge proofs. Part II discusses non-interactive ZK proofs. Part I is really required to grasp the extension to non-interactive ZKP's, so you may need to read that first.
https://blog.cryptographyengineering.com/2017/01/21/zero-kno...
I liked this PDF that starts with using modular arithmetic to prove knowledge of polynomial, using bilinear EC pairings to make it self and then, finally, encoding computations as polynomials: https://arxiv.org/pdf/1906.07221.pdf
ZK proofs have a number of good explainers, mostly using graph colorings. Non-interactive versions, however, require quite a bit more than that explanation allows - and despite asking experts, I still haven't found a good, basic explanation.