lognorman20 / circom_three_coloring

Verifying if a graph has a valid Three Coloring in Circom

Circom Three Coloring

Verifying if a graph has a valid Three Coloring in Circom.

An edge list of different integers as nodes is used to represent a graph. For example,

"graph": [[0,1],[0,2],[1,2]],

creates the following graph:

   0
  / \
 1---2

To reprsesent the colors of each node, a separate colors array is used

"colors": [0,1,2]

where each number in colors represents a different color. The index in the array maps to the color of the ith node. For example, colors[1] will give you the color of the node labeled 1.

Combining these two inputs, a colored graph is represented programmatically.

Run

First, clone this repo using the following command:

git clone https://github.com/lognorman20/circom_three_coloring.git

Next, ensure that you've installed Circom and SnarkJS.

Use the Makefile to run core operations. A description of each option is as follows:

make all: Cleans the directory, compiles the Circom circuit, generates witnesses, fully runs the Powers of Tau Ceremony, and finally generates and verifies a proof for the circuit given a set of witnesses. The witnesses used are in circuits/input.json.

make circuit: Compiles the Circom circuit and generates witnesses. The output can be found in artifacts/compilation.

make ptau: Runs the Powers of Tau Ceremony. make circuit must be ran before this command. The output can be found in artifacts/setup.

make proof: Generates and verifies a proof for the circuit given the inputs in circuits/input.json. The output can be found in artifacts/proof.

make clean: Cleans the repository of all files relating to the compilation, setup, or proving stage.

To change the inputs of the proof, alter the circuits/input.json file's contents. The file contains two keys:

{
    "graph": [[0,1],[1,2],[2,3],[2,4],[3,4],[4,0]],
    "colors": [0,1,0,1,2]
}

Additionally, change the inputs to circuits/main.circom need to be changed.

component main {public [ graph ]} = ThreeColoring(N,M);

Set N (number of nodes) and M (number of edges) according to the graph in input.json.