Essay CSI2108: Cryptographic Concepts – Rigorous Mathematical Argument – Cyber Security Assignment Help

Assignment Task:

Task 1:

A graph is a network of lines joining points. We say that two graphs are isomorphic if they are structurally the same aside from a re-ordering of the labels. That is, the two graphs should have the same number of edges and vertices, and the same connectivity between the edges. 
 
A graph isomorphism is a mapping between the vertices of the first graph to the vertices of the second graph that preserves the structure of the graphs. [In mathematical language, we say that an isomorphism between graphs G and H is a function f: G → H such that whenever e is an edge in G between vertices v₁ and v₂ then there is a corresponding edge in H between vertices f(v₁) and f(v₂).] 
 
Are the two graphs below isomorphic? Construct another graph with vertices u₁,u₂,u₃,u₄ and u₅ isomorphic to either of these two graphs. 

Task 2:

In the Week 1 workshop, we came across a problem where a colour blind person was convinced by their partner that they had two apples – one red and the other green.  
 
Outline what a zero-knowledge proof is and how the story of the colour blind person qualifies to be a zero-knowledge proof.

Task 3:

Outline how the Graph Isomorphism Problem can be used to construct zero-knowledge proof. 

Marking Key:

Task 1: Brief justification of your answer and correct graph. (You do not need to give a rigorous mathematical argument or provide an isomorphism, but your answer should convince somebody why the graphs are or are not isomorphic.) 
 
Task 2: Brief explanation of what a zero-knowledge proof is.

Justification of why the story of the colour blind person meets the requirements for being a zero-knowledge proof. 
 
Task 3: Description of the setup of the Graph Isomorphism Problem is a zero-knowledge proof.  

Justification for why your scenario meets the requirements for being a zero-knowledge proof.