Exploring SNARK Interoperability in Rust and Go

SNARKs represent a groundbreaking cryptographic tool that enables the verification of computations without revealing the inputs or the intermediate steps. SNARK is deeply rooted in mathematical principles, leveraging concepts like hashes, and curve operations, which are language-agnostic. While many discussions around SNARK implementations often revolve around Rust due to its popularity in the cryptographic community, it's important to note that SNARKs can be implemented and utilized in various programming languages, including Go. In this article, we'll explore SNARK interoperability, demonstrating how proofs can be generated and validated in both Go and Rust.

SNARK in Go: gnark

One prominent library for implementing SNARKs in Go is gnark. Gnark is a powerful library designed specifically for Go that facilitates the creation and verification of zero-knowledge proofs using the zk-SNARK protocol. It supports various proving schemes, with Groth16 and Plonk being ones of the most used due to their efficiency and shorter proof sizes. The library is optimized for performance and ease of use, making it accessible even to those new to cryptographic protocols.

To illustrate the capabilities of Gnark, consider a zero-knowledge proof for a Sudoku puzzle. Similar to the approach taken in the Rust and Bellman article, a Sudoku solution can be verified without revealing the solution itself. Here's a basic example of how to use Gnark to generate and verify a Sudoku solution: 

package main

import (
    "fmt"
    "github.com/ConsenSys/gnark/backend/groth16"
    "github.com/ConsenSys/gnark/frontend"
    "github.com/ConsenSys/gnark/std/algebra/bls12381"
)

type SudokuCircuit struct {
    Cells [3][3]frontend.Variable `gnark:",private"` // Define all cells as private variables
}

func (circuit *SudokuCircuit) Define(curveID frontend.ID, cs *frontend.ConstraintSystem) error {
    // Constraints to ensure each number is between 1 and 3
    for i := 0; i < 3; i++ {
        for j := 0; j < 3; j++ {
            cell := circuit.Cells[i][j]
            cs.AssertIsLessOrEqual(cell, 3)
            cs.AssertIsGreaterThan(cell, 0)
        }
    }
    // Further constraints to ensure row, column, and the single block's uniqueness would be added here

    return nil
}

func main() {
    var circuit SudokuCircuit

    // Example 3x3 Sudoku solution setup
    solution := [3][3]int{
        {1, 2, 3},
        {3, 1, 2},
        {2, 3, 1},
    }

    // Initialize circuit.Cells with these values
    for i := 0; i < 3; i++ {
        for j := 0; j < 3; j++ {
            circuit.Cells[i][j] = frontend.Value(solution[i][j])
        }
    }

    r1cs, err := frontend.Compile(bls12381.ID, groth16.NewScheme(), &circuit)
    if err != nil {
        fmt.Println("Compile error:", err)
        return
    }

    pk, vk, err := groth16.Setup(r1cs)
    if err != nil {
        fmt.Println("Setup error:", err)
        return
    }

    // Assuming the witness matches the solution
    witness := circuit // Typically, you'd construct a separate witness structure
    proof, err := groth16.Prove(r1cs, pk, &witness)
    if err != nil {
        fmt.Println("Prove error:", err)
        return
    }
    
    fmt.Println("Proof created")
}

The code demonstrates a Zero-Knowledge Proof (ZKP) for a 3x3 Sudoku grid using the Gnark library in Go. In this ZKP application, we focus on ensuring that each cell in the Sudoku grid contains a number from 1 to 3 and that each number appears exactly once per row, column, and the single block of the grid.

Firstly, the `SudokuCircuit` struct is defined, which includes a 3x3 array of private variables. Each variable represents a cell in the Sudoku grid. The struct implements a `Define` method where the constraints for the Sudoku are set up: each cell must contain a value between 1 and 3. This setup doesn't explicitly include unique constraints for rows, columns, and blocks due to simplification but in a full implementation, these would be necessary to enforce the rules of Sudoku fully.

The main function initializes the Sudoku solution directly into `circuit.Cells`, compiling the circuit with the BLS12-381 curve using Gnark's `frontend.Compile` function. The code example utilizes the BLS12-381 cryptographic curve, chosen for its strong security properties and efficiency in pairing operations, making it highly suitable for constructing robust and succinct zero-knowledge proofs in applications. Due to its efficient pairing characteristics and higher security, BLS12-381 is commonly used in blockchain technologies and systems requiring strong security guarantees, like Zcash and Ethereum.

Post-compilation, cryptographic setup is performed with Groth16's `Setup` function, which generates both proving and verifying keys. A proof is then generated using `groth16.Prove`, which effectively demonstrates that the submitted Sudoku solution adheres to the predefined constraints without revealing the solution itself. This proof can be verified independently, confirming the solution's validity without exposing any specific details of the solution, thus maintaining privacy.

By initializing the circuit this way, you're essentially feeding the problem statement (in this case, the Sudoku board) into the SNARK setup to prepare it for proof generation and verification, while demonstrating that the solution meets the constraints defined in the Define method without revealing the actual solution in clear text.

The verification part of the Sudoku circuit assumes that you are loading a previously generated proof and verification key. Here’s how to do it: 

package main

import (
    "fmt"
    "github.com/ConsenSys/gnark/backend/groth16"
)

func main() {
    // Assuming proof and verification keys are loaded properly
    proof := // Load proof here
    vk := // Load verification key here

    // No public witness in this specific case
    publicWitness := // Set up the public inputs (if any, likely none in this case)

    err := groth16.Verify(proof, vk, publicWitness)
    if err != nil {
        fmt.Println("Verification failed:", err)
    } else {
        fmt.Println("Proof verified successfully")
    }
}

Cross-Language Interoperability

Go Generation, Rust Proof

To demonstrate cross-language interoperability, first, generate a proof in Go using Gnark and then verify it in Rust using the Bellman library. This approach emphasizes the flexibility and practical utility of SNARKs across different ecosystems.

For a proof system to function correctly across different programming languages or libraries (e.g., between Go and Rust), both the proof generation and verification stages must use the same cryptographic curve. If the Go code uses BLS12-381 for generating a proof, the Rust code must also use BLS12-381 for verifying this proof to ensure compatibility and correctness. Using different curves across these stages will lead to verification failures because the mathematical properties and security assumptions of the curves differ significantly.

extern crate bellman_ce;
use bellman_ce::pairing::bls12_381::Bls12;
use bellman_ce::groth16::{verify_proof, prepare_verifying_key, Proof, VerifyingKey};

fn main() {
    // Assume verification key and proof are loaded correctly
    let vk: VerifyingKey<Bls12> = // Load or deserialize the verifying key here
    let proof: Proof<Bls12> = // Load or deserialize the proof here

    // Public inputs would be set here if any were used in the proof
    let public_inputs = vec![];

    let pvk = prepare_verifying_key(&vk);

    assert!(verify_proof(&pvk, &proof, &public_inputs).is_ok());
    println!("Proof verified in Rust using BLS12-381");
}

Rust Generation, Go Proof

Conversely, generate a proof in Rust using the Bellman library and then verify it in Go using Gnark. This reverse scenario showcases the bi-directional nature of SNARK interoperability.

We will utilize the code from the previous article for generating the proof. The code from the article provides a comprehensive guide on setting up a circuit, generating the proof, and the necessary steps to prepare both proving and verifying keys using Bellman. Since the original article uses the BN256 curve and we want to use the BLS12-381 curve for enhanced security and compatibility with our Go implementation, we'll need to adjust the Rust code accordingly. 

extern crate bellman;
extern crate rand;
use bellman::{Circuit, ConstraintSystem, SynthesisError};
use bellman::groth16::{create_random_proof, generate_random_parameters, prepare_verifying_key, verify_proof};
use rand::thread_rng;
use bellman::pairing::bls12_381::{Bls12, Fr};

struct Sudoku {
    solution: Option<Vec<u32>>,
}

impl Circuit<Fr> for Sudoku {
    fn synthesize<CS: ConstraintSystem<Fr>>(self, cs: &mut CS) -> Result<(), SynthesisError> {
        let mut grid = Vec::with_capacity(9);

        // Allocate variables and enforce constraints
        for i in 0..9 {
            let value = self.solution
                .as_ref()
                .map(|sol| Fr::from(sol[i]))
                .unwrap_or(Fr::zero());

            let variable = cs.alloc(|| format!("grid_{}", i), || Ok(value))?;

            // Enforce that each cell is between 1 and 3
            cs.enforce(|| format!("cell_{}_range", i),
                |lc| lc + variable,
                |lc| lc + variable,
                |lc| lc + CS::one() - variable - Fr::from(3)
            );

            grid.push(variable);
        }

        // Add Sudoku-specific constraints here
        // For example, different rows, columns, and blocks should have distinct values

        Ok(())
    }
}

fn generate_sudoku_proof() -> Result<(Parameters<Bn256>, Proof<Bn256>), SynthesisError> {
	let rng = &mut thread_rng();

    // Example Sudoku solution (only known to the server)
    let solution = vec![1, 2, 3, 3, 1, 2, 2, 3, 1];

    // Create parameters (publicly verifiable)
    let params = {
        let c = Sudoku { solution: None };
        generate_random_parameters::<Bls12, _, _>(c, rng).unwrap()
    };

    // Create a proof
    let proof = {
        let c = Sudoku { solution: Some(solution) };
        create_random_proof(c, &params, rng).unwrap()
    };
    
    Ok((params, proof))
}

fn main() {
	// Server generates the proof
    let (params, proof) = generate_sudoku_proof().expect("Proof generation failed");   
 }

This section demonstrates how to verify the proof that was generated in the previous section. It uses the verification key and the proof to confirm the validity of the assertions made in the Sudoku circuit. 

package main

import (
    "fmt"
    "github.com/ConsenSys/gnark/backend/groth16"
)

func main() {
    // Load proof and verification keys generated from the above code
    proof := // Proof loaded here
    vk := // Verification key loaded here

    // Public inputs would be set here if there are any
    publicWitness := // Public witness setup

    err := groth16.Verify(proof, vk, publicWitness)
    if err != nil {
        fmt.Println("Verification failed:", err)
    } else {
        fmt.Println("Proof verified successfully")
    }
}

Conclusion

This exploration into zero-knowledge proofs shows their flexibility and potential to work across different programming languages. By using tools designed for both Go and Rust, we've demonstrated that SNARKs can be integrated seamlessly into various parts of a system or even across entirely different systems. This proves that with the right approach, the technical details can adapt to meet broad security and interoperability needs and points towards a future where secure, versatile applications can be developed using ZKPs, no matter the programming language.

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