Zero-Knowledge Proof Systems

zk-SNARKs, zk-STARKs, and Bulletproofs.


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Zero-Knowledge Proof Systems. zk-SNARKs, zk-STARKs, and Bulletproofs.

Foundations and canonical references

The standard treatments of zero-knowledge proof systems approach the subject from complementary angles. Goldreich, Foundations of Cryptography (2004) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Supporting and adjacent work

A number of supporting contributions sharpen specific aspects of zero-knowledge proof systems or connect it to neighbouring problems. The knowledge complexity of interactive proof systems (Goldwasser et al., 1989) contributes to this area as one of the supporting references that inform current practice.

Open methodological questions for zero-knowledge proof systems include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

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