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A Mastermind game with zk-SNARKs

This is an implementation of the Mastermind board game which uses zk-SNARKs instead of a trusted third party to enforce game rules.

It uses the snarkjs and circom JavaScript libraries from iden3.

Image source

About zk-SNARKS

zk-SNARKs allow you to cryptographically prove knowledge of some secret data without revealing said data. For a simple explanation of zk-SNARKs, read this blog post by Christian Lundkvist.

The rules of Mastermind

There are two players: the codebreaker and the codemaster.

The codemaster creates a secret four-digit sequence of coloured pegs, limited to red, blue, green, and yellow.

To win, the codebreaker must guess the secret sequence of pegs within a set number of attempts. After each guess, if the codebreaker does not yet have the correct solution, the codemaster must tell the codebreaker the following clue:

  1. How many exact matches of colour and position there are — these are are black pegs

  2. How many pegs have matching colours, but are in the wrong position — these are white pegs.

For example, if the solution is R R B Y, and the guess is Y R B G, the codemaster must provide this clue: 2 black pegs and 1 white peg.

Solution       : Y R B G
Guess          : R R B Y

Exact matches  : 0 1 1 0 -> 2 black pegs
Inexact matches: 0 0 0 1 -> 1 white peg

Inexact matches do not overlap; for instance:

Solution       : R R Y B
Guess          : G G R B

Exact matches  : 0 0 0 1 -> 1 black peg
Inexact matches: 0 0 1 0 -> 1 white peg (not two, even though there are two red 
                                         pegs in the solution)

An illustrated example:

Image source

The protocol

1. Prepare the circuit

Create an arithmetic circuit C which is essentially this function:

C (pubGuess, pubClue, pubSolutionHash, privSolution):
    hash(privSolution) === pubSolutionHash
    genClue(pubGuess, privSolution) === pubClue

That is, given the secret sequence privSolution, the guess pubGuess, the clue pubClue, and a cryptographic hash of the secret sequence, the circuit:

a) calculates the correct clue and the cryptographic hash of the secret sequence, and

b) declares two constraints: that the cryptographic hash is correct and that the clue is correct.

In a later step, the codebreaker can cryptographically verify that (a) and/or (b) does not hold; more on that later.

2. Trusted setup

Generate the proving key, verifiying key, and toxic waste. Discard the toxic waste. Make the proving key and verifying key public. For simplicity, we assume that whoever did so can be trusted.

3. Generate a random salt

Using a commit-reveal scheme, the codemaster and codebreaker should arrive at a random salt. This is not part of the zk-SNARK, but helps to prevent a rainbow attack on the solution by the codebreaker.

4. Start the game

Before each game, the codemaster should generate the following:

a) the secret solution to the puzzle — e.g. G R Y B

b) the SHA256 hash of the solution and the salt

The codemaster should then send the hash to the codebreaker.

5. Make a guess

For each turn, the codebreaker should send their guess to the codemaster, who should then generate the following:

a) the clue which corresponds to the secret solution and the guess;

b) a proof that the clue is correct, which is the result of computing:

proof = Prover(provingKey, pubGuess, pubClue, pubSolutionHash, privSolution)

The codemaster must then send the clue and the proof back to the codemaster, who can verify that the clue is valid by computing:

Verify(verifyingKey, pubGuess, pubClue, pubSolutionHash, proof)

6. Repeat

Perform step 5 until the codebreaker guesses the correct solution. Note that this implementation of Mastermind lets you make as many guesses as you want, and even after you reach the correct solution.

Running the game

You need the TypeScript compiler tsc v2.7.2 or higher, and Node v10 or higher.

You may use yarn or npm as your package manager, but the following instructions will use yarn.

Setting up the circuit

1. Install dependencies

cd mastermind && \
yarn install && \

2. Compile the circuit

node build/mastermind/src/compile.js \
  -i mastermind/circuits/mastermind.circom \
  -o mastermind/circuits/mastermind.json -r

3. Perform the trusted setup

This takes about 30 seconds if you use Node 10 or greater. Note that it will take about ten times longer to complete if you use Node 9, as Node 10 has more optimised BigInt support.

mkdir -p mastermind/setup && \
node build/mastermind/src/trustedsetup.js \
  -i mastermind/circuits/mastermind.json \
  -pk mastermind/setup/ \
  -vk mastermind/setup/mastermind.vk.json -r

5. Generate a sample proof and public signals in JS

Generate the proof and public signals for a sample input:

mkdir -p mastermind/proofs mastermind/signals && \
node build/mastermind/src/generateproof.js \
  -c mastermind/circuits/mastermind.json \
  -vk mastermind/setup/mastermind.vk.json \
  -pk mastermind/setup/ \
  -po mastermind/proofs/mastermind.proof.json \
  -so mastermind/signals/testsignals.json

6. Verify a sample proof in JS

To verify it, run:

node build/mastermind/src/test_js_verification.js \
  -c mastermind/circuits/mastermind.json \
  -vk mastermind/setup/mastermind.vk.json \
  -p mastermind/proofs/mastermind.proof.json \
  -s mastermind/signals/testsignals.json

Run the Mastermind game in your browser

First, build the frontend

cd frontend && \
yarn install && \
yarn build:prod

You may also run the frontend development server using yarn dev.

In a different terminal, set up virtualenv:

cd backend && \
virtualenv -p python3 venv && \
source venv/bin/activate && \
pip3 install -r requirements.txt

Next, run the backend server in a separate terminal. Note that you have to set the NODE_PATH environment variable to a Node binary of version 10 or above.

export NODE_PATH='/path/to/node/10+' 
cd zkmm/backend && \
source venv/bin/activate && \
python3 migrate && \
python3 collectstatic -c --noinput && \
python3 runserver

Launch http://localhost:9000 for the development frontend environment, or http://localhost:8000 for the production frontend environment.

Make a guess and click on the Verify button to have the backend generate a proof, so that the frontend can verify the clue in the browser:

The proof takes about 18 seconds generate on an Intel i5 processor, and about 1 second to verify in the browser.

Bonus: verify a sample proof in Solidity

Generate the Solidity code of the verifier, and deploy it to a Ethereum network, like Ropsten.

If you wish to deploy it yourself, you can use Remix. Avoid using the Javascript VM to execute the verifyProof function as your browser may freeze up. Instead, get some Ropsten ether, deploy your contract to the testnet, and use that to verify the proof.

Alternatively, you can connect to a working verifier contract on Ropsten here.

mkdir -p mastermind/contracts && \
node build/mastermind/src/generateverifier.js \
  -i mastermind/setup/mastermind.vk.json \
  -o mastermind/contracts/mastermindverifier.sol -r

Next, generate the contract call parameters and paste the output into Remix:

node build/mastermind/src/generatecall.js \
  -p mastermind/proofs/mastermind.proof.json \
  -s mastermind/signals/testsignals.json

Example output:

["0x204fbb7755e152c2368ad1df3bb8f5cfa95f39adc6222f42ab138e70b92850af", "0x01aef8e7b8a5c1205abf51c7c91bef1eaba5b1046c61d761c7a03d316dc0185d"],[["0x24c698c2dd423d7df4455dee12783e51ecd281cb82139c9439311b015af50189", "0x19e0cac361ebd59dbf365492e823c7c02022774a9882282e00b5df912d291a02"],["0x023219cbe60a4d8bac7068e92a05486ec877608c4eb7897273863bf32c2ad2cf", "0x022ed9097142b1009e021cef3afd7778eec3a0aa65f74cdd21830283c44ada2c"]],["0x2dc657c7ee0f4c325dfb24562733d355d9bb4d01010967544467fe44eef8e8f9", "0x2d5b9b3bcefa2e0d31de45202a29355ef70994ec911d443cf804823a4dd09177"],["0x16425edee78f5b01f5e18b132ce10936bd2e08d222c6f298ed121d498689915b","0x0000000000000000000000000000000000000000000000000000000000000001","0x0000000000000000000000000000000000000000000000000000000000000002","0x0000000000000000000000000000000000000000000000000000000000000002","0x0000000000000000000000000000000000000000000000000000000000000001","0x0000000000000000000000000000000000000000000000000000000000000001","0x0000000000000000000000000000000000000000000000000000000000000002","0x16425edee78f5b01f5e18b132ce10936bd2e08d222c6f298ed121d498689915b"]

Click the verifyProof button to execute the function.


A Mastermind game using zk-snarks




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