# Zero Knowledge Proofs | Knowledge Base *Nexus Labs - 2023* ## Cryptography Fundamentals **Basics** - [Introduction to Modern Cryptography](http://www.cs.umd.edu/~jkatz/imc.html) [Katz & Lindell] - [A Graduate Course in Applied Cryptography](http://toc.cryptobook.us/book.pdf) [Boneh & Shoup] **Optional** - [Providing Sound Foundations for Cryptography](https://dl.acm.org/doi/pdf/10.1145/3335741) [Goldreich] - [Mathematics and Computation](https://www.math.ias.edu/files/Book-online-Aug0619.pdf#page=1) [Widgerson] ## ## History of Zero-Knowledge Proofs - [GMR85] [The Knowledge Complexity of Interactive Proof Systems](https://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Proof%20Systems/The_Knowledge_Complexity_Of_Interactive_Proof_Systems.pdf) - [GMW86] [How to prove all NP-statements in zero-knowledge](https://link.springer.com/content/pdf/10.1007/3-540-47721-7_11.pdf) - [FS86] [How To Prove Yourself: Practical Solutions to Identification and Signature Problems](https://link.springer.com/content/pdf/10.1007/3-540-47721-7_12.pdf) - [BFM88] [Non-interactive zero-knowledge and its applications](https://dl.acm.org/doi/pdf/10.1145/62212.62222) - [BG92] [On Defining Proofs of Knowledge](https://www.wisdom.weizmann.ac.il/~oded/PSX/pok.pdf) ## Recent ZKP Advancements - [BCTV13] [Succinct non-interactive zero knowledge for a von Neumann Architecture](https://eprint.iacr.org/2013/879.pdf) - [GGPR13] [Quadratic span programs and succinct NIZKs without PCPs](https://eprint.iacr.org/2012/215.pdf) - Introduces Quadratic Arithmetic Programs (QAP) - Shows that circuit satisfiability can be efficiently reduced to QAP satisfiability - [KS22] [SuperNova: Proving universal machine executions without universal circuits](https://eprint.iacr.org/2022/1758.pdf) ## Zero-Knowledge Rollups - [LNS20] [Replicated state machines without replicated execution](https://eprint.iacr.org/2020/195.pdf) - A zk-rollup architecture, showing how to transform a generic replicated state machine (RSM) into another RSM through zk-SNARK based delegation that preserves safety and liveness. Implemented on Ethereum. - Addresses liveness (unlike many others zk-rollups and has no *data availability* issues, as it uses set accumulators instead or Merkle Trees to maintain state. ## Conferences - [ACM Symposium on Theory of Computing (STOC)](http://acm-stoc.org/) - [IEEE Symposium on Foundations of Computer Science (FOCS)](http://ieee-focs.org/) ## Knowledge Bases - [Zero Knowledge Canon (a16z)](https://a16zcrypto.com/zero-knowledge-canon/) - [Zero Knowledge Proofs MOOC (Berkeley)](https://zk-learning.org/) - [zkp.science](https://zkp.science/)