The surprising part of STARKS and SNARKS comes down to the nature of polynomials. It's surprisingly easy to tell two polynomials apart with a small number of random checks (Schwartz Zippel lemma). In light of this it's not surprising there is good reading comparing them to erasure codes which rely on exactly this property of polynomials.
The non-interactive piece is pretty straightforward you just simulate challenge response conversation with unbiasible public randomness and show the transcript (Fiat Shamir transform).
Another area worth exploring is how some of these proof systems can have such incredibly small proofs (192 bytes for any computation in groth16 zk snarks). That relies on the much more difficult to intuit theory of elliptic curve pairing functions.
The non-interactive piece is pretty straightforward you just simulate challenge response conversation with unbiasible public randomness and show the transcript (Fiat Shamir transform).
Another area worth exploring is how some of these proof systems can have such incredibly small proofs (192 bytes for any computation in groth16 zk snarks). That relies on the much more difficult to intuit theory of elliptic curve pairing functions.