Hashing mechanisms,

Python hashing codes,

Cryptography studying notes,

Mods, Euclidian Theorem

Diffie Hellman

Zero knowledge related studies, videos explanations, documentations.

Cracking CryptoCurrencies Studies

Video 1

EB116 – Eli Ben-Sasson: Zero Knowledge Proofs

https://www.youtube.com/watch?v=1GTRfZ0m7M8&t=3365s

zero knowledge protocols

computational zero knowledge

non-interectactive zkp

80s interactive zk

Now snarks

Quadratic span programs

Quadratic arithmetic programs

Pinnoccio

Lib snark

Short random scripts

Asymmetric encryption

Additively homo

Lib snark

Pinoccio

Hob

Zero cash

In old systems

The setup phase picking a short string

First 256 words for example

Asymmetric encryption

Public key cryptography

Lib snark

Pinoccio

Hob

Zero cash

Setup phase is critical

Destroy the laptop who creates the initial phase

Zero Knowledge Proofs are methods of providing cryptographic proofs to another party while keeping some information secret. The simple concept of ZKP offer tantalizing possibilities: Banks could prove solvency without revealing depositors. Governments could prove the fairness of an election without compromising privacy.

Computer science professor Eli Ben-Sasson joined us to discuss where blockchains and cryptocurrencies intersect with Zero Knowledge Proofs and related technologies such as zkSNARKs. It offered a fascinating view into what will surely become a core part of blockchain tech in the future.

Topics covered included:

- What are proof systems?

- Zero Knowledge Proofs (ZKP) and other terminology such as SNARKs and zkSNARKs

- The mechanics of Zero Knowledge Proofs

- The role of performance in Zero Knowledge Proofs

- Applications of ZKPs

- The widespread potential impact of ZKP to verify processes

Links mentioned in this episode:

- Eli Ben-Sasson's Website http://bit.ly/1PbbK9O

- SNARKs for C talk by Madars Virza http://bit.ly/1PQFoah

- Stackexchange: What are SNARKs http://bit.ly/1UEcqbq

- SNARKs for C paper [PDF] http://bit.ly/20Cse26

- Zerocash Talk http://bit.ly/1Puy2He

All the blockchains from genesis till now is 288 KB.

Blockchainb Zero Knowledge Proof

Playlist

2. video

Introduction zk SNARKs STARKs Eli Ben Sasson Technion Cyber and Computer Security Summer School

https://www.youtube.com/watch?v=VUN35BC11Qw&list=PLYFBvOluduluKLChUkDmnI8l-9kw3CQST&index=2&t=1248s

Introduction to zk SNARKs STARKs by Prof. Eli Ben Sasson of Technion. The lecture was presented at the 6th Technion Summer School on Cyber and Computer Security held Sept. 10 – 14, 2017 at Technion. The summer school theme was Decentralized Cryptographic Currencies and Blockchains.

Quasi linear – almost linear

Video 3

https://www.youtube.com/watch?v=9VuZvdxFZQo&list=PLYFBvOluduluKLChUkDmnI8l-9kw3CQST&index=3&t=1236s

STARKS I - Arithmetization Eli Ben Sasson Technion Cyber Computer Security

If Bob is cheating?

PCP promistable checkable proofs

Starks 2 video

https://www.youtube.com/watch?v=L7tZeO8ihcQ&t=1753s

STARKs II - Low Degree Testing Eli Ben Sasson Technion Cyber and Computer Security Summer School

The cryptography comes in the proof parts.

Fast Fourier Transform FFT

Recursive Algoritm

Fast fourier transfor

IFFT is the inverse of FFT

Fast Reed Solomon interactive oracle proof of proximity

https://eccc.weizmann.ac.il/report/2017/134/

Another video

https://www.youtube.com/watch?v=HJ9K_o-RRSY

Transparent scalable computational integrity - Eli Ben Sasson, Silicon Valley ethereum meetup

Non deterministic input

finance password

non deterministic exponontions

Prover efficiency, biggest problem, very large

Soundness, what is the probability of error

Engineering, how do you build it in a good way?

ZK-PCP Zero Knowledge, Privacy Preserving Proof

SCIP (Scalable Computational Integrity and Privacy) -> STARK (Succinct Transparent ARgument of Knowledge)

FFT needs very large space

And large memory

Starks are more efficient then Snarks

Non of the systems are constant if you leave them to go to infinity

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Another Video, Same Content Another Seminar

Towards Transparent and Scalable Computational Integrity and Privacy

https://www.youtube.com/watch?v=kYmnXxs9kUM&t=36s

Moon math – Elliptic Curves – Quadratic Arithmetic Programs

Adding zk make it scalable

Interpolation

Butterfly

Pcpp provisticly checkable proof preduction

Stark uses over Snark, Transparency and Scalability

Snarky uses Eliiptic Curve

Starky uses Hashes

PCP Probabilistically Checkable Proof System

Based on math, no cryptography on it, no zk, , just proof system.

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ECC is used for redundancy to protect from prover’s cheating attempts

Because of this problem that prover can cheat

In the execution space, ecc is used.

ECC protect the memory from malicious noises

Error correcting code

We are adding redundancy with ecc

The setup is coding is really needed

Prover picks a point in 1000 points. And cheat in there

You use ECC to protect from that.

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Perfect Zero Knowledge

Video

https://www.youtube.com/watch?v=kltostJdnNU

Zero Knowledge Proofs in Node.JS - London Node User Group - August 2018

https://medium.com/@argongroup/on-zero-knowledge-proofs-in-blockchains-14c48cfd1dd1

Video

Sigma Protocols and Zero Knowledge

https://www.youtube.com/watch?v=nwsmG3S9wIc&list=PLYFBvOluduluKLChUkDmnI8l-9kw3CQST&index=8&t=0s

ZK Proof of Knowledge

Prover P, verifier V, relation R

P proves that it knows a witness w for which (x,w) E R without revealing anything

Prover always convinces the verifier, we always obtain witness for the prover

The verifier not supposed to learn anything

Know the dlog

Zero knowledge is not blackbox, zero knowledge is three rounds

Prove that something in zero knowledge is hard

Proof of knowledge even harder

Diffie Hellman Tuples

W is random

If H is not generator then this is not a diffie hellman tuple

The proof is half a page, it is really short.

Soundness property

Prover don’t have any freedom here

https://www.youtube.com/watch?v=mNfeO0F_zLg

Zero-Knowledge Supply Chain Blockchain, MediLedger, Responsible Gold at Consensus 2018

Transaction is broadcasted to the blockchain

Fake transactions can be understood by blockchain.

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Vitalik Buterin: Zero Knowledge Proofs and Ethereum Update @ Ethereum HK Meetup

https://www.youtube.com/watch?v=n8zsPf4FzO4&t=3395s

Another video

Greg Maxwell: A Deep Dive Into Bitcoin Core 0.15

https://www.youtube.com/watch?v=nSRoEeqYtJA