gnark/examples arithmetization and proof

[ANNMAINAWANGARI]

How's proving done in the cubic example since the circuit isn't compiled. Per the docs, gnark follows a typical workflow and it is recommended to execute a circuit without running a zk-SNARK prover. Is that the case in the gnark/examples?

[ivokub]

Hi, the online playground at https://play.gnark.io/ doesn't run the full prover to output a proof, but only runs until solving stage and then stops. There are some performance problems with compiling the full Groth16/PLONK prover.

For testing locally, I would recommend setting up a Go environment, doing:

go mod init example
go get github.com/consensys/gnark@master

And then start implementing the circuits in main.go for example. As an example on how to run the full Groth16 prover, see https://pkg.go.dev/github.com/consensys/[email protected]/std/math/emulated#example-Field:

	circuit := ExampleFieldCircuit[emulated.BN254Fp]{}
	witness := ExampleFieldCircuit[emulated.BN254Fp]{
		In1: emulated.ValueOf[emulated.BN254Fp](3),
		In2: emulated.ValueOf[emulated.BN254Fp](5),
		Res: emulated.ValueOf[emulated.BN254Fp](15),
	}
	ccs, err := frontend.Compile(ecc.BN254.ScalarField(), r1cs.NewBuilder, &circuit)
	if err != nil {
		panic(err)
	} else {
		fmt.Println("compiled")
	}
	witnessData, err := frontend.NewWitness(&witness, ecc.BN254.ScalarField())
	if err != nil {
		panic(err)
	} else {
		fmt.Println("secret witness parsed")
	}
	publicWitnessData, err := witnessData.Public()
	if err != nil {
		panic(err)
	} else {
		fmt.Println("public witness parsed")
	}
	pk, vk, err := groth16.Setup(ccs)
	if err != nil {
		panic(err)
	} else {
		fmt.Println("setup done")
	}
	proof, err := groth16.Prove(ccs, pk, witnessData, backend.WithSolverOptions(solver.WithHints(emulated.GetHints()...)))
	if err != nil {
		panic(err)
	} else {
		fmt.Println("proved")
	}
	err = groth16.Verify(proof, vk, publicWitnessData)
	if err != nil {
		panic(err)
	} else {
		fmt.Println("verified")
	}

[ANNMAINAWANGARI]

Thanks. Does the emulated package implement recursive snarks? Or the example above and is that a solution being used for performance optimization?

[ivokub]

Emulated package itself doesn't implement recursive snarks. We have recursive PLONK in std/recursion/plonk package. We also have Groth16 recursive verifier, but it is incomplete.