The chapter delves into the intricacies of building cryptographic proofs from hash functions, discussing the evolution from Interactive Oracle Proofs to succinct non-interactive arguments. It explores the concept of 'snargs' and contrasts hash-based SNARKs with other types of SNARKs, emphasizing the importance of ideal hash functions for security. The chapter also highlights the significance of systematizing cryptographic proofs for long-term security and optimizing hash-based proving systems for efficiency.

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