https://github.com/samuelschlesinger/graph-iso-nizkp

NIZKPs of Graph Isomorphism.
https://github.com/samuelschlesinger/graph-iso-nizkp

Last synced: 20 days ago
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NIZKPs of Graph Isomorphism.

• Host: GitHub
• URL: https://github.com/samuelschlesinger/graph-iso-nizkp
• Owner: SamuelSchlesinger
• Created: 2023-11-04T15:51:23.000Z (about 1 year ago)
• Default Branch: dev
• Last Pushed: 2023-11-04T17:26:01.000Z (about 1 year ago)
• Last Synced: 2024-10-27T19:10:17.929Z (2 months ago)
• Language: Rust
• Size: 3.91 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Non-Interactive Proof of Graph Isomorphism

To create a non-interactive proof of graph isomorphism, we can use

the Fiat-Shamir transform.

## Prover

Given graphs A and B, we begin by generating M random isomorphic graphs to A, a

vector C of graphs. We create a binary string S consisting of the binary

representation of A, B, and all of the Cs. We use a one-way function to map

this into a bit-vector V such that if V[i] then we reveal an isomorphism from

C[i] to A, else we reveal an isomorphism from C[i] to B. In the proof, we

include A, B, all of the Cs, and the array of isomorphisms in question, I.

## Verifier

The verifier generates V, then confirms that if V[i], then I[i] maps C[i] to A,

else I[i] maps C[i] to B.

## Correctness

If the prover does know the isomorphism between A and B, then the resulting

proof is correct with probability 1. If the prover does not know the isomorphism,

then they will need to choose their Cs such that the string V allows them to show

an isomorphism.