class1

Class 1 - Feb 19

Lesson 1

Homework 1

Links

Zero Knowledge Cryptography Introduction - Solidity Fridays

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Main applications of Zero Knowledge

• obscure data
• condense data
• provide data

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Home work for class 1

Maths Introduction

Some modular arithmetic

1. Working with the following set of Integers S = {0,1,2,3,4,5,6}

   What is

   a) 4 + 4

   = 2

   print((4 + 4) % 6)

   b) 3 x 5

   = 3

   print((3 * 5) % 6)

   c) what is the inverse of 3 ?

   0.3333333

   print((1 / 3) % 6)

2. For S = {0,1,2,3,4,5,6}

   Can we consider 'S' and the operation '+' to be a group ?

   No conditions to be a group:

   • Closure: addition is not closed within $S$. $2 + 5 = 7$, which is not an element of $S$.
   • Associativity: addition is associative. $(a + b) + c = a + (b + c)$ for all elements $a$, $b$, and $c$ in $S$.
   • Identity: there is no identity. An identity element would need to satisfy $a + e = e$ and $e + a = a$ for all elements $a$ in $S$, but no such element exists in $S$.
   • Inverse: not all elements have inverses in $S$. There is no element $x$ such that $6 + x = 0$.

3. What is

   -13 mod 5 ?

   2

   print(-13 % 5)

4. Polynomials

   For the polynomial $x^{3}-x^{2}+4x-12$

   Find a the positive root ?

   cannot find only one positive root

   What is the degree of this polynomial ?

   3 (highest exponent of the variable)

Use cases

In your teams discuss any systems you have used that involved zero knowledge proofs.

I studied Starknet.

Have you seen any applications of zero knowledge proofs other than with a blockchain ?

An Anonymous Verifiable Voting algorithm (Using ZKPs, eligible voters can prove their right to cast a ballot without revealing their identity).

Zero Knowledge Technology as a future of Banking and Verifiable Autonomous Financial Protocols

Checks and balances: Machine learning and zero-knowledge proofs

3 Real World Applications of Zero Knowledge Proofs

What is to you, the most important feature of zkp technology ?

The ability to prove something is TRUE without showing the data for the computation.

Think of some use cases of zero knowledge proofs that you would like to see developed.

Create verifiable and ownable machine learning app.