In my exploration of zero-knowledge proofs, I have encountered various perspectives on the operational disparities among zk-SNARKs, zk-STARKs, and Bulletproofs, as documented in different blogs and discussions (such as the ones referenced in the provided links).

How do ZK-STARKs, ZK-SNARKs, and Bulletproofs compare in size and speed for range proofs?

Why it is said that “zk-SNARKs need a trusted setup” to work?

zk-SNARKs vs. Zk-STARKs vs. Bulletproofs: definitions

The provided links offer valuable insights into the differences in size, speed, and reliance on trusted setups for these cryptographic protocols. However, a notable gap remains in the availability of systematically written algorithms for zk-STARKs and Bulletproofs, comparable to the clarity found in the Petkus paper for zk-SNARKs. While the Petkus paper here offers a comprehensible explanation of zk-SNARKs using polynomial commitments and elucidates the proving and verification phases, I have encountered challenges in finding similarly well-documented constructions and instantiations for zk-STARKs and Bulletproofs. I found the paper on zk-STARKs here by Eli Ben-Sasson but it is so complex to understand the zk-STARKs.

I seek a detailed explanation, complete with mathematical formulations, of the proving and verification phases in zk-STARKs and Bulletproofs.

Thank you.



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