# 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/)

Nexus Labs
Nexus Labs is a scientific organization hyperscaling Ethereum compute.

A collection of examples of how to use the Nexus Network as a platform for verifiable cloud computing.

3/24/2023Nexus Labs Research Blog

3/2/2023We introduce Nexus Zero, a decentralized zero-knowledge cloud computing network.

2/10/2023Shamir's Secret Sharing Scheme was introduced in [S79] How to Share a Secret by Adi Shamir from MIT. A secret sharing scheme serves the following goal. A dealer has a secret $\alpha \in Z$ for some finite set $Z$. He wishes to generate $n$ shares $\alpha_1, \dots, \alpha_n \in Z$ such that: Any $t$-sized subset of shares are sufficient to recover $\alpha$. Every subset of size at most $t-1$ does not reveal any information about $\alpha$. Defining a Secret Sharing Scheme We assume there are $n$ parties $P_1, \dots, P_n$ and a dealer, who keeps a secret $\alpha \in Z$, all of which can be modeled as polynomial-time randomized Turing machines.

2/5/2023
Published on ** HackMD**