Archive repository

follow whitespace rule of strings.TrimSpace

.travis.yml

@@ -5,3 +5,6 @@ go:
 
 env:
   - GO111MODULE=on
+
+before_install: rm wasm/go-snark-wasm-wrapper.go
+

README.md

@@ -1,17 +1,17 @@
-# go-snark [![Go Report Card](https://goreportcard.com/badge/github.com/arnaucube/go-snark)](https://goreportcard.com/report/github.com/arnaucube/go-snark) [![Build Status](https://travis-ci.org/arnaucube/go-snark.svg?branch=master)](https://travis-ci.org/arnaucube/go-snark) [![Gitter](https://badges.gitter.im/go-snark/community.svg)](https://gitter.im/go-snark/community?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge)
+### Warning
+Implementation of the zkSNARK [Pinocchio protocol](https://eprint.iacr.org/2013/279.pdf) and [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) from scratch in Go done in my free time to understand the concepts. Do not use in production.
+
+If you want to generate proofs & verify them from Go, you can try https://github.com/vocdoni/go-snark, which is implemented using the [bn256](https://github.com/ethereum/go-ethereum/tree/master/crypto/bn256/cloudflare) for the Pairing curve operations for the Groth16 zkSNARK, and it is compatible with [circom](https://github.com/iden3/circom).
+
+# go-snark-study [![Go Report Card](https://goreportcard.com/badge/github.com/arnaucube/go-snark-study)](https://goreportcard.com/report/github.com/arnaucube/go-snark-study) [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study)
 
 zkSNARK library implementation in Go
 
-
 - `Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture`, Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza https://eprint.iacr.org/2013/879.pdf
 - `Pinocchio: Nearly practical verifiable computation`, Bryan Parno, Craig Gentry, Jon Howell, Mariana Raykova https://eprint.iacr.org/2013/279.pdf
 - `On the Size of Pairing-based Non-interactive Arguments`, Jens Groth https://eprint.iacr.org/2016/260.pdf
 
-## Caution & Warning
+## Features
-Implementation of the zkSNARK [Pinocchio protocol](https://eprint.iacr.org/2013/279.pdf) and [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) from scratch in Go to understand the concepts. Do not use in production.
-
-Not finished, implementing this in my free time to understand it better, so I don't have much time.
-
 Currently allows to do the complete path with [Pinocchio protocol](https://eprint.iacr.org/2013/279.pdf) and [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) :
 
 0. write circuit
@@ -33,22 +33,16 @@ Minimal complete flow implementation:
 - [x] generate proofs
 - [x] verify proofs with BN128 pairing
 
-Improvements from the minimal implementation:
+## WASM usage
-- [x] allow to call functions in circuits language
+Experimentation with go-snark-study compiled to wasm: https://github.com/arnaucube/go-snark-study/tree/master/wasm
-- [x] allow `import` in circuits language
-- [ ] allow `for` in circuits language
-- [ ] move witness values calculation outside the setup phase
-- [x] Groth16
-- [ ] multiple optimizations
-
 
 ## Usage
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark?status.svg)](https://godoc.org/github.com/arnaucube/go-snark) zkSnark
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study) zkSnark
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/groth16?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/groth16) zkSnark Groth16
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/groth16?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/groth16) zkSnark Groth16
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/bn128) bn128 (more details: https://github.com/arnaucube/go-snark/tree/master/bn128)
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/bn128) bn128 (more details: https://github.com/arnaucube/go-snark-study/tree/master/bn128)
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/fields?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/fields) Finite Fields operations
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/fields?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/fields) Finite Fields operations
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/r1csqap) R1CS to QAP (more details: https://github.com/arnaucube/go-snark/tree/master/r1csqap)
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/r1csqap) R1CS to QAP (more details: https://github.com/arnaucube/go-snark-study/tree/master/r1csqap)
-- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/circuitcompiler?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/circuitcompiler) Circuit Compiler
+- [![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/circuitcompiler?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/circuitcompiler) Circuit Compiler
 
 ### CLI usage
 *The cli still needs some improvements, such as seting input files, etc.*
@@ -87,6 +81,10 @@ In the command line, execute:
 ```
 > ./go-snark-cli compile test.circuit
 ```
+If you want to have the wasm input ready also, add the flag `wasm`
+```
+> ./go-snark-cli compile test.circuit wasm
+```
 
 This will output the `compiledcircuit.json` file.
 
@@ -97,6 +95,10 @@ Having the `compiledcircuit.json`, now we can generate the `TrustedSetup`:
 ```
 This will create the file `trustedsetup.json` with the TrustedSetup data, and also a `toxic.json` file, with the parameters to delete from the `Trusted Setup`.
 
+If you want to have the wasm input ready also, add the flag `wasm`
+```
+> ./go-snark-cli trustedsetup wasm
+```
 
 #### Generate Proofs
 Assumming that we have the `compiledcircuit.json`, `trustedsetup.json`, `privateInputs.json` and the `publicInputs.json` we can now generate the `Proofs` with the following command:
@@ -192,6 +194,16 @@ publicSignalsVerif := []*big.Int{b35Verif}
 assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
 ```
 
+##### Verify Proof generated from [snarkjs](https://github.com/iden3/snarkjs)
+Is possible with `go-snark-study` to verify proofs generated by `snarkjs`
+
+Example:
+```go
+verified, err := VerifyFromCircom("circom-test/verification_key.json", "circom-test/proof.json", "circom-test/public.json")
+assert.Nil(t, err)
+assert.True(t, verified)
+```
+
 
 ## Versions
 History of versions & tags of this project:
@@ -205,7 +217,7 @@ go test ./... -v
 ```
 
 ## vim/nvim circuit syntax highlighter
-For more details and installation instructions see https://github.com/arnaucube/go-snark/tree/master/vim-syntax
+For more details and installation instructions see https://github.com/arnaucube/go-snark-study/tree/master/vim-syntax
 
 ---
 

bn128/README.md

@@ -1,5 +1,5 @@
 ## Bn128
-[![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/bn128) bn128
+[![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/bn128?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/bn128) bn128
 Implementation of the bn128 pairing in Go.
 
 

bn128/bn128.go

@@ -4,7 +4,7 @@ import (
 	"errors"
 	"math/big"
 
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
 )
 
 // Bn128 is the data structure of the BN128

bn128/g1.go

@@ -3,7 +3,7 @@ package bn128
 import (
 	"math/big"
 
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
 )
 
 type G1 struct {

bn128/g2.go

@@ -3,7 +3,7 @@ package bn128
 import (
 	"math/big"
 
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
 )
 
 type G2 struct {

circuitcompiler/circuit.go

@@ -5,7 +5,7 @@ import (
 	"math/big"
 	"strconv"
 
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
 )
 
 // Circuit is the data structure of the compiled circuit

circuitcompiler/lexer.go

@@ -32,7 +32,7 @@ const (
 var eof = rune(0)
 
 func isWhitespace(ch rune) bool {
-	return ch == ' ' || ch == '\t' || ch == '\n'
+	return ch == ' ' || ch == '\t' || ch == '\n' || ch == '\r' || ch == '\v' || ch == '\f'
 }
 
 func isLetter(ch rune) bool {

circuitexamples/factor.circuit

@@ -1,4 +1,4 @@
-func test(private a, private b, public c):
+func main(private a, private b, public c):
 	d = a * b
 	equals(c, d)
 	out = 1 * 1

circuitexamples/function.circuit

@@ -1,4 +1,4 @@
-func test(private s0, public s1):
+func main(private s0, public s1):
 	s2 = s0 * s0
 	s3 = s2 * s0
 	s4 = s3 + s0

cli/main.go

@@ -11,10 +11,11 @@ import (
 	"math/big"
 	"os"
 
-	snark "github.com/arnaucube/go-snark"
+	snark "github.com/arnaucube/go-snark-study"
-	"github.com/arnaucube/go-snark/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
-	"github.com/arnaucube/go-snark/groth16"
+	"github.com/arnaucube/go-snark-study/groth16"
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
+	"github.com/arnaucube/go-snark-study/utils"
 	"github.com/urfave/cli"
 )
 
@@ -96,6 +97,11 @@ func CompileCircuit(context *cli.Context) error {
 
 	circuitPath := context.Args().Get(0)
 
+	wasmFlag := false
+	if context.Args().Get(1) == "wasm" {
+		wasmFlag = true
+	}
+
 	// read circuit file
 	circuitFile, err := os.Open(circuitPath)
 	panicErr(err)
@@ -185,10 +191,48 @@ func CompileCircuit(context *cli.Context) error {
 	jsonFile.Close()
 	fmt.Println("Compiled Circuit data written to ", jsonFile.Name())
 
+	if wasmFlag {
+		circuitString := utils.CircuitToString(*circuit)
+		jsonData, err := json.Marshal(circuitString)
+		panicErr(err)
+		// store setup into file
+		jsonFile, err := os.Create("compiledcircuitString.json")
+		panicErr(err)
+		defer jsonFile.Close()
+		jsonFile.Write(jsonData)
+		jsonFile.Close()
+	}
+
+	// store px
+	jsonData, err = json.Marshal(px)
+	panicErr(err)
+	// store setup into file
+	jsonFile, err = os.Create("px.json")
+	panicErr(err)
+	defer jsonFile.Close()
+	jsonFile.Write(jsonData)
+	jsonFile.Close()
+	fmt.Println("Px data written to ", jsonFile.Name())
+	if wasmFlag {
+		pxString := utils.ArrayBigIntToString(px)
+		jsonData, err = json.Marshal(pxString)
+		panicErr(err)
+		// store setup into file
+		jsonFile, err = os.Create("pxString.json")
+		panicErr(err)
+		defer jsonFile.Close()
+		jsonFile.Write(jsonData)
+		jsonFile.Close()
+	}
+
 	return nil
 }
 
 func TrustedSetup(context *cli.Context) error {
+	wasmFlag := false
+	if context.Args().Get(0) == "wasm" {
+		wasmFlag = true
+	}
 	// open compiledcircuit.json
 	compiledcircuitFile, err := ioutil.ReadFile("compiledcircuit.json")
 	panicErr(err)
@@ -230,8 +274,7 @@ func TrustedSetup(context *cli.Context) error {
 	var tsetup snark.Setup
 	tsetup.Pk = setup.Pk
 	tsetup.Vk = setup.Vk
-	tsetup.G1T = setup.G1T
+	tsetup.Pk.G1T = setup.Pk.G1T
-	tsetup.G2T = setup.G2T
 
 	// store setup to json
 	jsonData, err := json.Marshal(tsetup)
@@ -243,6 +286,17 @@ func TrustedSetup(context *cli.Context) error {
 	jsonFile.Write(jsonData)
 	jsonFile.Close()
 	fmt.Println("Trusted Setup data written to ", jsonFile.Name())
+	if wasmFlag {
+		tsetupString := utils.SetupToString(tsetup)
+		jsonData, err := json.Marshal(tsetupString)
+		panicErr(err)
+		// store setup into file
+		jsonFile, err := os.Create("trustedsetupString.json")
+		panicErr(err)
+		defer jsonFile.Close()
+		jsonFile.Write(jsonData)
+		jsonFile.Close()
+	}
 	return nil
 }
 
@@ -289,10 +343,10 @@ func GenerateProofs(context *cli.Context) error {
 	hx := snark.Utils.PF.DivisorPolynomial(px, trustedsetup.Pk.Z)
 
 	fmt.Println(circuit)
-	fmt.Println(trustedsetup.G1T)
+	fmt.Println(trustedsetup.Pk.G1T)
 	fmt.Println(hx)
 	fmt.Println(w)
-	proof, err := snark.GenerateProofs(circuit, trustedsetup, w, px)
+	proof, err := snark.GenerateProofs(circuit, trustedsetup.Pk, w, px)
 	panicErr(err)
 
 	fmt.Println("\n proofs:")
@@ -319,13 +373,6 @@ func VerifyProofs(context *cli.Context) error {
 	json.Unmarshal([]byte(string(proofsFile)), &proof)
 	panicErr(err)
 
-	// open compiledcircuit.json
-	compiledcircuitFile, err := ioutil.ReadFile("compiledcircuit.json")
-	panicErr(err)
-	var circuit circuitcompiler.Circuit
-	json.Unmarshal([]byte(string(compiledcircuitFile)), &circuit)
-	panicErr(err)
-
 	// open trustedsetup.json
 	trustedsetupFile, err := ioutil.ReadFile("trustedsetup.json")
 	panicErr(err)
@@ -340,7 +387,7 @@ func VerifyProofs(context *cli.Context) error {
 	err = json.Unmarshal([]byte(string(publicInputsFile)), &publicSignals)
 	panicErr(err)
 
-	verified := snark.VerifyProof(circuit, trustedsetup, proof, publicSignals, true)
+	verified := snark.VerifyProof(trustedsetup.Vk, proof, publicSignals, true)
 	if !verified {
 		fmt.Println("ERROR: proofs not verified")
 	} else {
@@ -451,7 +498,7 @@ func Groth16GenerateProofs(context *cli.Context) error {
 	fmt.Println(trustedsetup.Pk.PowersTauDelta)
 	fmt.Println(hx)
 	fmt.Println(w)
-	proof, err := groth16.GenerateProofs(circuit, trustedsetup, w, px)
+	proof, err := groth16.GenerateProofs(circuit, trustedsetup.Pk, w, px)
 	panicErr(err)
 
 	fmt.Println("\n proofs:")
@@ -478,13 +525,6 @@ func Groth16VerifyProofs(context *cli.Context) error {
 	json.Unmarshal([]byte(string(proofsFile)), &proof)
 	panicErr(err)
 
-	// open compiledcircuit.json
-	compiledcircuitFile, err := ioutil.ReadFile("compiledcircuit.json")
-	panicErr(err)
-	var circuit circuitcompiler.Circuit
-	json.Unmarshal([]byte(string(compiledcircuitFile)), &circuit)
-	panicErr(err)
-
 	// open trustedsetup.json
 	trustedsetupFile, err := ioutil.ReadFile("trustedsetup.json")
 	panicErr(err)
@@ -499,7 +539,7 @@ func Groth16VerifyProofs(context *cli.Context) error {
 	err = json.Unmarshal([]byte(string(publicInputsFile)), &publicSignals)
 	panicErr(err)
 
-	verified := groth16.VerifyProof(circuit, trustedsetup, proof, publicSignals, true)
+	verified := groth16.VerifyProof(trustedsetup.Vk, proof, publicSignals, true)
 	if !verified {
 		fmt.Println("ERROR: proofs not verified")
 	} else {

externalVerif/README.md

@@ -0,0 +1,12 @@
+# go-snark-study /externalVerif
+Utilities to verify zkSNARK proofs generated by other tools.
+
+## Verify Proof generated from [snarkjs](https://github.com/iden3/snarkjs)
+Is possible with `go-snark-study` to verify proofs generated by `snarkjs`
+
+Example:
+```go
+verified, err := VerifyFromCircom("circom-test/verification_key.json", "circom-test/proof.json", "circom-test/public.json")
+assert.Nil(t, err)
+assert.True(t, verified)
+```

externalVerif/circom-test/circuit.circom

@@ -0,0 +1,8 @@
+template Multiplier() {
+   signal private input a;
+   signal private input b;
+   signal output c;
+   c <== a*b;
+}
+
+component main = Multiplier();

externalVerif/circom-test/circuit.json

@@ -0,0 +1,74 @@
+{
+ "mainCode": "{\n}\n",
+ "signalName2Idx": {
+  "one": 0,
+  "main.a": 2,
+  "main.b": 3,
+  "main.c": 1
+ },
+ "components": [
+  {
+   "name": "main",
+   "params": {},
+   "template": "Multiplier",
+   "inputSignals": 2
+  }
+ ],
+ "componentName2Idx": {
+  "main": 0
+ },
+ "signals": [
+  {
+   "names": [
+    "one"
+   ],
+   "triggerComponents": []
+  },
+  {
+   "names": [
+    "main.c"
+   ],
+   "triggerComponents": []
+  },
+  {
+   "names": [
+    "main.a"
+   ],
+   "triggerComponents": [
+    0
+   ]
+  },
+  {
+   "names": [
+    "main.b"
+   ],
+   "triggerComponents": [
+    0
+   ]
+  }
+ ],
+ "constraints": [
+  [
+   {
+    "2": "21888242871839275222246405745257275088548364400416034343698204186575808495616"
+   },
+   {
+    "3": "1"
+   },
+   {
+    "1": "21888242871839275222246405745257275088548364400416034343698204186575808495616"
+   }
+  ]
+ ],
+ "templates": {
+  "Multiplier": "function(ctx) {\n    ctx.setSignal(\"c\", [], bigInt(ctx.getSignal(\"a\", [])).mul(bigInt(ctx.getSignal(\"b\", []))).mod(__P__));\n    ctx.assert(ctx.getSignal(\"c\", []), bigInt(ctx.getSignal(\"a\", [])).mul(bigInt(ctx.getSignal(\"b\", []))).mod(__P__));\n}\n"
+ },
+ "functions": {},
+ "nPrvInputs": 2,
+ "nPubInputs": 0,
+ "nInputs": 2,
+ "nOutputs": 1,
+ "nVars": 4,
+ "nConstants": 0,
+ "nSignals": 4
+}

externalVerif/circom-test/input.json

@@ -0,0 +1 @@
+{"a": 3, "b": 11}

externalVerif/circom-test/proof.json

@@ -0,0 +1,27 @@
+{
+ "pi_a": [
+  "18388960469390566286541775203573681018272060202314500468244373257908579233056",
+  "7618815753031896296145768956584956596571516464117106968297323458939823682730",
+  "1"
+ ],
+ "pi_b": [
+  [
+   "17050824088966017765399151386329118398626450147519924253020767437783796544260",
+   "19912572158122217836152914282050675315049542075120224143747749799495268338155"
+  ],
+  [
+   "20465264120227255663865054937863503553147947378051666554617444700075602812731",
+   "18655251778322805691388473632530173510779859979743695956359151230786651584957"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "pi_c": [
+  "1422784641124790360586256228365363101120672643204565045434023905594849706813",
+  "8557716062509065082036904136615813135951258906799509331823365499907603810450",
+  "1"
+ ],
+ "protocol": "groth"
+}

externalVerif/circom-test/proving_key.json

@@ -0,0 +1,221 @@
+{
+ "protocol": "groth",
+ "nVars": 4,
+ "nPublic": 1,
+ "domainBits": 2,
+ "domainSize": 4,
+ "polsA": [
+  {
+   "1": "1"
+  },
+  {
+   "2": "1"
+  },
+  {
+   "0": "21888242871839275222246405745257275088548364400416034343698204186575808495616"
+  },
+  {}
+ ],
+ "polsB": [
+  {},
+  {},
+  {},
+  {
+   "0": "1"
+  }
+ ],
+ "polsC": [
+  {},
+  {
+   "0": "21888242871839275222246405745257275088548364400416034343698204186575808495616"
+  },
+  {},
+  {}
+ ],
+ "A": [
+  [
+   "16145916318196730299582072104388453231952213805668281741813587224450782397538",
+   "4434505318477484327659527264104806919103674231447634885054368605283938696207",
+   "1"
+  ],
+  [
+   "10618406967550056457559358662746625591602641004174976323307214433994084907915",
+   "1843236360452735081347085412539192450068665510574800388201121698908391533923",
+   "1"
+  ],
+  [
+   "1208972877970123411566574123860641832032384890981476033353526096830198333194",
+   "777503551507025252294438107100944741641946695980350712141258191590862204805",
+   "1"
+  ],
+  [
+   "0",
+   "1",
+   "0"
+  ]
+ ],
+ "B1": [
+  [
+   "0",
+   "1",
+   "0"
+  ],
+  [
+   "0",
+   "1",
+   "0"
+  ],
+  [
+   "0",
+   "1",
+   "0"
+  ],
+  [
+   "1208972877970123411566574123860641832032384890981476033353526096830198333194",
+   "21110739320332249969951967638156330347054364461317472950547779703054364003778",
+   "1"
+  ]
+ ],
+ "B2": [
+  [
+   [
+    "0",
+    "0"
+   ],
+   [
+    "1",
+    "0"
+   ],
+   [
+    "0",
+    "0"
+   ]
+  ],
+  [
+   [
+    "0",
+    "0"
+   ],
+   [
+    "1",
+    "0"
+   ],
+   [
+    "0",
+    "0"
+   ]
+  ],
+  [
+   [
+    "0",
+    "0"
+   ],
+   [
+    "1",
+    "0"
+   ],
+   [
+    "0",
+    "0"
+   ]
+  ],
+  [
+   [
+    "9283666785342556550467669770956850930982548182701254051508520248901282197973",
+    "11369378229277445316894458966429873744779877313900506577160370623273013178252"
+   ],
+   [
+    "10625777544326349817513295021482494426101347915428005055375725845993157551870",
+    "21401790227434807639472120486932615400751346915707967674912972446672152512583"
+   ],
+   [
+    "1",
+    "0"
+   ]
+  ]
+ ],
+ "C": [
+  null,
+  null,
+  [
+   "18545397130363256321926549041639729743141431075318462370025152832852939073307",
+   "2616861286119881509516846668252666108741377487742351180864484963773522850295",
+   "1"
+  ],
+  [
+   "2525636894222523143142808451978966577881491159416335121257094078801746645235",
+   "16535861715720884910945782094658684127457731006848459401043529763859412916301",
+   "1"
+  ]
+ ],
+ "vk_alfa_1": [
+  "16068200068882411629410035093795608526771554471937479213726134794660780102550",
+  "20501676791339890155108177259376873296876233680064261776170683533526889207340",
+  "1"
+ ],
+ "vk_beta_1": [
+  "5365573823291502335794132193185274277974617763863996013954364593194136465016",
+  "11644349101388223784378896360832586557929271772024496470708905460439243894584",
+  "1"
+ ],
+ "vk_delta_1": [
+  "15680151079584844532489259722917096938769907841931133291928746685613811358733",
+  "16784279394546603697881462850128771845781623009095957214568117820968443242506",
+  "1"
+ ],
+ "vk_beta_2": [
+  [
+   "13973091636763944887728510851169742544309374663995476311690518173988838518856",
+   "12903946180439304546475897520537621821375470264150438270817301786763517825250"
+  ],
+  [
+   "370374369234123593044872519351942112043402224488849374153134091815693350697",
+   "17423079115073430837335625309232513526393852743032331213038909731579295753224"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "vk_delta_2": [
+  [
+   "1192908377564945353343974763532707545526009748811618581810344379529229172159",
+   "10373868200341234689659697947697825014338252335089936445608341428888724327154"
+  ],
+  [
+   "6258644116885726740914814071115026921733331135830050167672544002787860516536",
+   "2784479362505735918824286514153638713518597314121639212447411360814573899319"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "hExps": [
+  [
+   "1137454402546542017796495169973321459788661791339116580816039119135416491226",
+   "10581992627412174102808274058339351114019966039682644500297077873241797449624",
+   "1"
+  ],
+  [
+   "3253811140290017934039655168718326971539049766532829948316663892796117200680",
+   "3496418280903365070403555364992889823060908616232765866481366503085657668823",
+   "1"
+  ],
+  [
+   "7426424892372059053157891943364774187577620238460342150964457392480230669997",
+   "14261604113665464620229095737623968407326243628348811684313201927885047569756",
+   "1"
+  ],
+  [
+   "14706800931196014592083141709960980909656368788497354451613143286705158867076",
+   "8321358240716309588423491516494287064322707776658072083979021495463106099808",
+   "1"
+  ],
+  [
+   "21560594640856118286219580794351895174554979903538723611152363886530011848778",
+   "15512645592267656573910252616175869133748229079507420222439452334013754939136",
+   "1"
+  ]
+ ]
+}

externalVerif/circom-test/public.json

@@ -0,0 +1,3 @@
+[
+ "33"
+]

externalVerif/circom-test/verification_key.json

@@ -0,0 +1,93 @@
+{
+ "protocol": "groth",
+ "nPublic": 1,
+ "IC": [
+  [
+   "13238385840837109667936052879696151554096578146827286302729161004449442572510",
+   "7229895880483697230987627368481585486229758623816305076929725978466335833042",
+   "1"
+  ],
+  [
+   "14970768730171390202518134018231251321095352434740566553215758534237407624223",
+   "11858341424183782282346697815973277820477089967861765360499368718702428507405",
+   "1"
+  ]
+ ],
+ "vk_alfa_1": [
+  "16068200068882411629410035093795608526771554471937479213726134794660780102550",
+  "20501676791339890155108177259376873296876233680064261776170683533526889207340",
+  "1"
+ ],
+ "vk_beta_2": [
+  [
+   "13973091636763944887728510851169742544309374663995476311690518173988838518856",
+   "12903946180439304546475897520537621821375470264150438270817301786763517825250"
+  ],
+  [
+   "370374369234123593044872519351942112043402224488849374153134091815693350697",
+   "17423079115073430837335625309232513526393852743032331213038909731579295753224"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "vk_gamma_2": [
+  [
+   "20123714298473938437207866646336289719062614610167653880378271328974655580609",
+   "13002533616763316572747276872341370962409012236118399865958073576789163874362"
+  ],
+  [
+   "9275552728819724842865155645402980221399400114914205138826048710506018574007",
+   "9767402488181356088371101345613657976874749415205606884811092820466492903357"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "vk_delta_2": [
+  [
+   "1192908377564945353343974763532707545526009748811618581810344379529229172159",
+   "10373868200341234689659697947697825014338252335089936445608341428888724327154"
+  ],
+  [
+   "6258644116885726740914814071115026921733331135830050167672544002787860516536",
+   "2784479362505735918824286514153638713518597314121639212447411360814573899319"
+  ],
+  [
+   "1",
+   "0"
+  ]
+ ],
+ "vk_alfabeta_12": [
+  [
+   [
+    "5808968930823264229923553886264093087733079723496081749582815497064726636649",
+    "15704206953123342065158329174314435955575427797267883688615695147218681260603"
+   ],
+   [
+    "2019376182570496317125733151845779676488434395598091282285101061771413397585",
+    "5033120379874305142732026662367866621873812132639805141544817513451132976303"
+   ],
+   [
+    "6413062281604814018100947958938305639421600365853645030429871508055751771332",
+    "16501101898595852943280641675936242756163761586970222679114350546638012990295"
+   ]
+  ],
+  [
+   [
+    "7994355756858823685828118366797930607512610071147093396079158087328554257367",
+    "12608941378902474737301318807093065779176013217938745808277102463837219428790"
+   ],
+   [
+    "7722352178656099663978033703115542396108273285932660670008724291332590018773",
+    "18402524427751774707431639562944919677540025075739837574780127622149131456184"
+   ],
+   [
+    "8237540863924877742345165686185155147152873047203223764861378545202201950314",
+    "885942718772685438966081900822373900701293300627890502324305030525329921651"
+   ]
+  ]
+ ]
+}

externalVerif/circom-test/witness.json

@@ -0,0 +1,6 @@
+[
+ "1",
+ "33",
+ "3",
+ "11"
+]

externalVerif/circomVerifier.go

@@ -0,0 +1,90 @@
+package externalVerif
+
+import (
+	"encoding/json"
+	"fmt"
+	"io/ioutil"
+
+	"github.com/arnaucube/go-snark-study/groth16"
+	"github.com/arnaucube/go-snark-study/utils"
+)
+
+type CircomProof struct {
+	PiA [3]string    `json:"pi_a"`
+	PiB [3][2]string `json:"pi_b"`
+	PiC [3]string    `json:"pi_c"`
+}
+type CircomVk struct {
+	IC          [][3]string     `json:"IC"`
+	Alpha1      [3]string       `json:"vk_alfa_1"`
+	Beta2       [3][2]string    `json:"vk_beta_2"`
+	Gamma2      [3][2]string    `json:"vk_gamma_2"`
+	Delta2      [3][2]string    `json:"vk_delta_2"`
+	AlphaBeta12 [2][3][2]string `json:"vk_alpfabeta_12"` // not really used, for the moment in go-snarks calculed in verification time
+}
+
+func VerifyFromCircom(vkPath, proofPath, publicSignalsPath string) (bool, error) {
+	// open verification_key.json
+	vkFile, err := ioutil.ReadFile(vkPath)
+	if err != nil {
+		return false, err
+	}
+	var circomVk CircomVk
+	json.Unmarshal([]byte(string(vkFile)), &circomVk)
+	if err != nil {
+		return false, err
+	}
+
+	var strVk utils.GrothVkString
+	strVk.IC = circomVk.IC
+	strVk.G1.Alpha = circomVk.Alpha1
+	strVk.G2.Beta = circomVk.Beta2
+	strVk.G2.Gamma = circomVk.Gamma2
+	strVk.G2.Delta = circomVk.Delta2
+	vk, err := utils.GrothVkFromString(strVk)
+	if err != nil {
+		return false, err
+	}
+	fmt.Println("vk parsed:", vk)
+
+	// open proof.json
+	proofsFile, err := ioutil.ReadFile(proofPath)
+	if err != nil {
+		return false, err
+	}
+	var circomProof CircomProof
+	json.Unmarshal([]byte(string(proofsFile)), &circomProof)
+	if err != nil {
+		return false, err
+	}
+
+	strProof := utils.GrothProofString{
+		PiA: circomProof.PiA,
+		PiB: circomProof.PiB,
+		PiC: circomProof.PiC,
+	}
+	proof, err := utils.GrothProofFromString(strProof)
+	if err != nil {
+		return false, err
+	}
+	fmt.Println("proof parsed:", proof)
+
+	// open public.json
+	publicFile, err := ioutil.ReadFile(publicSignalsPath)
+	if err != nil {
+		return false, err
+	}
+	var publicStr []string
+	json.Unmarshal([]byte(string(publicFile)), &publicStr)
+	if err != nil {
+		return false, err
+	}
+	publicSignals, err := utils.ArrayStringToBigInt(publicStr)
+	if err != nil {
+		return false, err
+	}
+	fmt.Println("publicSignals parsed:", publicSignals)
+
+	verified := groth16.VerifyProof(vk, proof, publicSignals, true)
+	return verified, nil
+}

externalVerif/circomVerifier_test.go

@@ -0,0 +1,13 @@
+package externalVerif
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestVerifyFromCircom(t *testing.T) {
+	verified, err := VerifyFromCircom("circom-test/verification_key.json", "circom-test/proof.json", "circom-test/public.json")
+	assert.Nil(t, err)
+	assert.True(t, verified)
+}

go.mod

@@ -1,4 +1,4 @@
-module github.com/arnaucube/go-snark
+module github.com/arnaucube/go-snark-study
 
 require (
 	github.com/davecgh/go-spew v1.1.1 // indirect

groth16/groth16.go

@@ -6,12 +6,42 @@ import (
 	"fmt"
 	"math/big"
 
-	"github.com/arnaucube/go-snark/bn128"
+	"github.com/arnaucube/go-snark-study/bn128"
-	"github.com/arnaucube/go-snark/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
 )
 
+type Pk struct { // Proving Key
+	BACDelta [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
+	Z        []*big.Int
+	G1       struct {
+		Alpha    [3]*big.Int
+		Beta     [3]*big.Int
+		Delta    [3]*big.Int
+		At       [][3]*big.Int // {a(τ)} from 0 to m
+		BACGamma [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to m
+	}
+	G2 struct {
+		Beta     [3][2]*big.Int
+		Gamma    [3][2]*big.Int
+		Delta    [3][2]*big.Int
+		BACGamma [][3][2]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to m
+	}
+	PowersTauDelta [][3]*big.Int // powers of τ encrypted in G1 curve, divided by δ
+}
+type Vk struct {
+	IC [][3]*big.Int
+	G1 struct {
+		Alpha [3]*big.Int
+	}
+	G2 struct {
+		Beta  [3][2]*big.Int
+		Gamma [3][2]*big.Int
+		Delta [3][2]*big.Int
+	}
+}
+
 // Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
 type Setup struct {
 	Toxic struct {
@@ -23,35 +53,8 @@ type Setup struct {
 	}
 
 	// public
-	Pk struct { // Proving Key
+	Pk Pk
-		BACDelta [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to l
+	Vk Vk
-		Z        []*big.Int
-		G1       struct {
-			Alpha    [3]*big.Int
-			Beta     [3]*big.Int
-			Delta    [3]*big.Int
-			At       [][3]*big.Int // {a(τ)} from 0 to m
-			BACGamma [][3]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
-		}
-		G2 struct {
-			Beta     [3][2]*big.Int
-			Gamma    [3][2]*big.Int
-			Delta    [3][2]*big.Int
-			BACGamma [][3][2]*big.Int // {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
-		}
-		PowersTauDelta [][3]*big.Int // powers of τ encrypted in G1 curve, divided by δ
-	}
-	Vk struct {
-		IC [][3]*big.Int
-		G1 struct {
-			Alpha [3]*big.Int
-		}
-		G2 struct {
-			Beta  [3][2]*big.Int
-			Gamma [3][2]*big.Int
-			Delta [3][2]*big.Int
-		}
-	}
 }
 
 // Proof contains the parameters to proof the zkSNARK
@@ -165,9 +168,9 @@ func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, al
 		bt := Utils.PF.Eval(betas[i], setup.Toxic.T)
 		g1bt := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, bt)
 		g2bt := Utils.Bn.G2.MulScalar(Utils.Bn.G2.G, bt)
-		// G1.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m in G1
+		// G1.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to m in G1
 		setup.Pk.G1.BACGamma = append(setup.Pk.G1.BACGamma, g1bt)
-		// G2.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m in G2
+		// G2.BACGamma: {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to m in G2
 		setup.Pk.G2.BACGamma = append(setup.Pk.G2.BACGamma, g2bt)
 	}
 
@@ -192,7 +195,7 @@ func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, al
 		)
 		g1c := Utils.Bn.G1.MulScalar(Utils.Bn.G1.G, c)
 
-		// Pk.BACDelta: {( βui(x)+αvi(x)+wi(x) ) / γ } from 0 to l
+		// Pk.BACDelta: {( βui(x)+αvi(x)+wi(x) ) / δ } from l+1 to m
 		setup.Pk.BACDelta = append(setup.Pk.BACDelta, g1c)
 	}
 
@@ -219,7 +222,7 @@ func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, al
 }
 
 // GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
-func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, w []*big.Int, px []*big.Int) (Proof, error) {
+func GenerateProofs(circuit circuitcompiler.Circuit, pk Pk, w []*big.Int, px []*big.Int) (Proof, error) {
 	var proof Proof
 	proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
 	proof.PiB = Utils.Bn.Fq6.Zero()
@@ -238,57 +241,57 @@ func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, w []*big.Int,
 	piBG1 := [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
 
 	for i := 0; i < circuit.NVars; i++ {
-		proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(setup.Pk.G1.At[i], w[i]))
+		proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(pk.G1.At[i], w[i]))
-		piBG1 = Utils.Bn.G1.Add(piBG1, Utils.Bn.G1.MulScalar(setup.Pk.G1.BACGamma[i], w[i]))
+		piBG1 = Utils.Bn.G1.Add(piBG1, Utils.Bn.G1.MulScalar(pk.G1.BACGamma[i], w[i]))
-		proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(setup.Pk.G2.BACGamma[i], w[i]))
+		proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(pk.G2.BACGamma[i], w[i]))
 	}
 	for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
-		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.BACDelta[i], w[i]))
+		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(pk.BACDelta[i], w[i]))
 	}
 
 	// piA = (Σ from 0 to m (pk.A * w[i])) + pk.Alpha1 + r * δ
-	proof.PiA = Utils.Bn.G1.Add(proof.PiA, setup.Pk.G1.Alpha)
+	proof.PiA = Utils.Bn.G1.Add(proof.PiA, pk.G1.Alpha)
-	deltaR := Utils.Bn.G1.MulScalar(setup.Pk.G1.Delta, r)
+	deltaR := Utils.Bn.G1.MulScalar(pk.G1.Delta, r)
 	proof.PiA = Utils.Bn.G1.Add(proof.PiA, deltaR)
 
 	// piBG1 = (Σ from 0 to m (pk.B1 * w[i])) + pk.g1.Beta + s * δ
 	// piB = piB2 = (Σ from 0 to m (pk.B2 * w[i])) + pk.g2.Beta + s * δ
-	piBG1 = Utils.Bn.G1.Add(piBG1, setup.Pk.G1.Beta)
+	piBG1 = Utils.Bn.G1.Add(piBG1, pk.G1.Beta)
-	proof.PiB = Utils.Bn.G2.Add(proof.PiB, setup.Pk.G2.Beta)
+	proof.PiB = Utils.Bn.G2.Add(proof.PiB, pk.G2.Beta)
-	deltaSG1 := Utils.Bn.G1.MulScalar(setup.Pk.G1.Delta, s)
+	deltaSG1 := Utils.Bn.G1.MulScalar(pk.G1.Delta, s)
 	piBG1 = Utils.Bn.G1.Add(piBG1, deltaSG1)
-	deltaSG2 := Utils.Bn.G2.MulScalar(setup.Pk.G2.Delta, s)
+	deltaSG2 := Utils.Bn.G2.MulScalar(pk.G2.Delta, s)
 	proof.PiB = Utils.Bn.G2.Add(proof.PiB, deltaSG2)
 
-	hx := Utils.PF.DivisorPolynomial(px, setup.Pk.Z) // maybe move this calculation to a previous step
+	hx := Utils.PF.DivisorPolynomial(px, pk.Z) // maybe move this calculation to a previous step
 
 	// piC = (Σ from l+1 to m (w[i] * (pk.g1.Beta + pk.g1.Alpha + pk.C)) + h(tau)) / δ) + piA*s + r*piB - r*s*δ
 	for i := 0; i < len(hx); i++ {
-		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.PowersTauDelta[i], hx[i]))
+		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(pk.PowersTauDelta[i], hx[i]))
 	}
 	proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(proof.PiA, s))
 	proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(piBG1, r))
 	negRS := Utils.FqR.Neg(Utils.FqR.Mul(r, s))
-	proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.G1.Delta, negRS))
+	proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(pk.G1.Delta, negRS))
 
 	return proof, nil
 }
 
 // VerifyProof verifies over the BN128 the Pairings of the Proof
-func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publicSignals []*big.Int, debug bool) bool {
+func VerifyProof(vk Vk, proof Proof, publicSignals []*big.Int, debug bool) bool {
 
-	icPubl := setup.Vk.IC[0]
+	icPubl := vk.IC[0]
 	for i := 0; i < len(publicSignals); i++ {
-		icPubl = Utils.Bn.G1.Add(icPubl, Utils.Bn.G1.MulScalar(setup.Vk.IC[i+1], publicSignals[i]))
+		icPubl = Utils.Bn.G1.Add(icPubl, Utils.Bn.G1.MulScalar(vk.IC[i+1], publicSignals[i]))
 	}
 
 	if !Utils.Bn.Fq12.Equal(
 		Utils.Bn.Pairing(proof.PiA, proof.PiB),
 		Utils.Bn.Fq12.Mul(
-			Utils.Bn.Pairing(setup.Vk.G1.Alpha, setup.Vk.G2.Beta),
+			Utils.Bn.Pairing(vk.G1.Alpha, vk.G2.Beta),
 			Utils.Bn.Fq12.Mul(
-				Utils.Bn.Pairing(icPubl, setup.Vk.G2.Gamma),
+				Utils.Bn.Pairing(icPubl, vk.G2.Gamma),
-				Utils.Bn.Pairing(proof.PiC, setup.Vk.G2.Delta)))) {
+				Utils.Bn.Pairing(proof.PiC, vk.G2.Delta)))) {
 		if debug {
 			fmt.Println("❌ groth16 verification not passed")
 		}

groth16/groth16_test.go

@@ -8,8 +8,8 @@ import (
 	"testing"
 	"time"
 
-	"github.com/arnaucube/go-snark/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -85,7 +85,7 @@ func TestGroth16MinimalFlow(t *testing.T) {
 	// check length of polynomials H(x) and Z(x)
 	assert.Equal(t, len(hx), len(px)-len(setup.Pk.Z)+1)
 
-	proof, err := GenerateProofs(*circuit, setup, w, px)
+	proof, err := GenerateProofs(*circuit, setup.Pk, w, px)
 	assert.Nil(t, err)
 
 	// fmt.Println("\n proofs:")
@@ -97,11 +97,11 @@ func TestGroth16MinimalFlow(t *testing.T) {
 	b35Verif := big.NewInt(int64(35))
 	publicSignalsVerif := []*big.Int{b35Verif}
 	before := time.Now()
-	assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
+	assert.True(t, VerifyProof(setup.Vk, proof, publicSignalsVerif, true))
 	fmt.Println("verify proof time elapsed:", time.Since(before))
 
 	// check that with another public input the verification returns false
 	bOtherWrongPublic := big.NewInt(int64(34))
 	wrongPublicSignalsVerif := []*big.Int{bOtherWrongPublic}
-	assert.True(t, !VerifyProof(*circuit, setup, proof, wrongPublicSignalsVerif, false))
+	assert.True(t, !VerifyProof(setup.Vk, proof, wrongPublicSignalsVerif, false))
 }

r1csqap/README.md

@@ -1,5 +1,5 @@
 ## R1CS to Quadratic Arithmetic Program
-[![GoDoc](https://godoc.org/github.com/arnaucube/go-snark/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark/r1csqap) R1CS to QAP
+[![GoDoc](https://godoc.org/github.com/arnaucube/go-snark-study/r1csqap?status.svg)](https://godoc.org/github.com/arnaucube/go-snark-study/r1csqap) R1CS to QAP
 - `Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture`, Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza https://eprint.iacr.org/2013/879.pdf
 - Vitalik Buterin blog post about QAP https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649
 - Ariel Gabizon in Zcash blog https://z.cash/blog/snark-explain5

r1csqap/r1csqap.go

@@ -4,7 +4,7 @@ import (
 	"bytes"
 	"math/big"
 
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
 )
 
 // Transpose transposes the *big.Int matrix

r1csqap/r1csqap_test.go

@@ -5,7 +5,7 @@ import (
 	"math/big"
 	"testing"
 
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
 	"github.com/stretchr/testify/assert"
 )
 

snark.go

@@ -7,12 +7,35 @@ import (
 	"math/big"
 	"os"
 
-	"github.com/arnaucube/go-snark/bn128"
+	"github.com/arnaucube/go-snark-study/bn128"
-	"github.com/arnaucube/go-snark/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
-	"github.com/arnaucube/go-snark/fields"
+	"github.com/arnaucube/go-snark-study/fields"
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
 )
 
+type Pk struct { // Proving Key pk:=(pkA, pkB, pkC, pkH)
+	G1T [][3]*big.Int // t encrypted in G1 curve, G1T == Pk.H
+	A   [][3]*big.Int
+	B   [][3][2]*big.Int
+	C   [][3]*big.Int
+	Kp  [][3]*big.Int
+	Ap  [][3]*big.Int
+	Bp  [][3]*big.Int
+	Cp  [][3]*big.Int
+	Z   []*big.Int
+}
+
+type Vk struct {
+	Vka   [3][2]*big.Int
+	Vkb   [3]*big.Int
+	Vkc   [3][2]*big.Int
+	IC    [][3]*big.Int
+	G1Kbg [3]*big.Int    // g1 * Kbeta * Kgamma
+	G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
+	G2Kg  [3][2]*big.Int // g2 * Kgamma
+	Vkz   [3][2]*big.Int
+}
+
 // Setup is the data structure holding the Trusted Setup data. The Setup.Toxic sub struct must be destroyed after the GenerateTrustedSetup function is completed
 type Setup struct {
 	Toxic struct {
@@ -28,28 +51,8 @@ type Setup struct {
 	}
 
 	// public
-	G1T [][3]*big.Int    // t encrypted in G1 curve, G1T == Pk.H
+	Pk Pk
-	G2T [][3][2]*big.Int // t encrypted in G2 curve
+	Vk Vk
-	Pk  struct {         // Proving Key pk:=(pkA, pkB, pkC, pkH)
-		A  [][3]*big.Int
-		B  [][3][2]*big.Int
-		C  [][3]*big.Int
-		Kp [][3]*big.Int
-		Ap [][3]*big.Int
-		Bp [][3]*big.Int
-		Cp [][3]*big.Int
-		Z  []*big.Int
-	}
-	Vk struct {
-		Vka   [3][2]*big.Int
-		Vkb   [3]*big.Int
-		Vkc   [3][2]*big.Int
-		IC    [][3]*big.Int
-		G1Kbg [3]*big.Int    // g1 * Kbeta * Kgamma
-		G2Kbg [3][2]*big.Int // g2 * Kbeta * Kgamma
-		G2Kg  [3][2]*big.Int // g2 * Kgamma
-		Vkz   [3][2]*big.Int
-	}
 }
 
 // Proof contains the parameters to proof the zkSNARK
@@ -242,13 +245,13 @@ func GenerateTrustedSetup(witnessLength int, circuit circuitcompiler.Circuit, al
 		// tEncr = Utils.Bn.Fq1.Mul(tEncr, setup.Toxic.T)
 		tEncr = Utils.FqR.Mul(tEncr, setup.Toxic.T)
 	}
-	setup.G1T = gt1
+	setup.Pk.G1T = gt1
 
 	return setup, nil
 }
 
 // GenerateProofs generates all the parameters to proof the zkSNARK from the Circuit, Setup and the Witness
-func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, w []*big.Int, px []*big.Int) (Proof, error) {
+func GenerateProofs(circuit circuitcompiler.Circuit, pk Pk, w []*big.Int, px []*big.Int) (Proof, error) {
 	var proof Proof
 	proof.PiA = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
 	proof.PiAp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
@@ -260,35 +263,35 @@ func GenerateProofs(circuit circuitcompiler.Circuit, setup Setup, w []*big.Int,
 	proof.PiKp = [3]*big.Int{Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero(), Utils.Bn.G1.F.Zero()}
 
 	for i := circuit.NPublic + 1; i < circuit.NVars; i++ {
-		proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(setup.Pk.A[i], w[i]))
+		proof.PiA = Utils.Bn.G1.Add(proof.PiA, Utils.Bn.G1.MulScalar(pk.A[i], w[i]))
-		proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(setup.Pk.Ap[i], w[i]))
+		proof.PiAp = Utils.Bn.G1.Add(proof.PiAp, Utils.Bn.G1.MulScalar(pk.Ap[i], w[i]))
 	}
 
 	for i := 0; i < circuit.NVars; i++ {
-		proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(setup.Pk.B[i], w[i]))
+		proof.PiB = Utils.Bn.G2.Add(proof.PiB, Utils.Bn.G2.MulScalar(pk.B[i], w[i]))
-		proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(setup.Pk.Bp[i], w[i]))
+		proof.PiBp = Utils.Bn.G1.Add(proof.PiBp, Utils.Bn.G1.MulScalar(pk.Bp[i], w[i]))
 
-		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(setup.Pk.C[i], w[i]))
+		proof.PiC = Utils.Bn.G1.Add(proof.PiC, Utils.Bn.G1.MulScalar(pk.C[i], w[i]))
-		proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(setup.Pk.Cp[i], w[i]))
+		proof.PiCp = Utils.Bn.G1.Add(proof.PiCp, Utils.Bn.G1.MulScalar(pk.Cp[i], w[i]))
 
-		proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(setup.Pk.Kp[i], w[i]))
+		proof.PiKp = Utils.Bn.G1.Add(proof.PiKp, Utils.Bn.G1.MulScalar(pk.Kp[i], w[i]))
 	}
 
-	hx := Utils.PF.DivisorPolynomial(px, setup.Pk.Z) // maybe move this calculation to a previous step
+	hx := Utils.PF.DivisorPolynomial(px, pk.Z) // maybe move this calculation to a previous step
 
 	// piH = pkH,0 + sum (  hi * pk H,i ), where pkH = G1T, hi=hx
-	// proof.PiH = Utils.Bn.G1.Add(proof.PiH, setup.G1T[0])
+	// proof.PiH = Utils.Bn.G1.Add(proof.PiH, pk.G1T[0])
 	for i := 0; i < len(hx); i++ {
-		proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(setup.G1T[i], hx[i]))
+		proof.PiH = Utils.Bn.G1.Add(proof.PiH, Utils.Bn.G1.MulScalar(pk.G1T[i], hx[i]))
 	}
 
 	return proof, nil
 }
 
 // VerifyProof verifies over the BN128 the Pairings of the Proof
-func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publicSignals []*big.Int, debug bool) bool {
+func VerifyProof(vk Vk, proof Proof, publicSignals []*big.Int, debug bool) bool {
 	// e(piA, Va) == e(piA', g2)
-	pairingPiaVa := Utils.Bn.Pairing(proof.PiA, setup.Vk.Vka)
+	pairingPiaVa := Utils.Bn.Pairing(proof.PiA, vk.Vka)
 	pairingPiapG2 := Utils.Bn.Pairing(proof.PiAp, Utils.Bn.G2.G)
 	if !Utils.Bn.Fq12.Equal(pairingPiaVa, pairingPiapG2) {
 		if debug {
@@ -301,7 +304,7 @@ func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publ
 	}
 
 	// e(Vb, piB) == e(piB', g2)
-	pairingVbPib := Utils.Bn.Pairing(setup.Vk.Vkb, proof.PiB)
+	pairingVbPib := Utils.Bn.Pairing(vk.Vkb, proof.PiB)
 	pairingPibpG2 := Utils.Bn.Pairing(proof.PiBp, Utils.Bn.G2.G)
 	if !Utils.Bn.Fq12.Equal(pairingVbPib, pairingPibpG2) {
 		if debug {
@@ -314,7 +317,7 @@ func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publ
 	}
 
 	// e(piC, Vc) == e(piC', g2)
-	pairingPicVc := Utils.Bn.Pairing(proof.PiC, setup.Vk.Vkc)
+	pairingPicVc := Utils.Bn.Pairing(proof.PiC, vk.Vkc)
 	pairingPicpG2 := Utils.Bn.Pairing(proof.PiCp, Utils.Bn.G2.G)
 	if !Utils.Bn.Fq12.Equal(pairingPicVc, pairingPicpG2) {
 		if debug {
@@ -327,16 +330,16 @@ func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publ
 	}
 
 	// Vkx, to then calculate Vkx+piA
-	vkxpia := setup.Vk.IC[0]
+	vkxpia := vk.IC[0]
 	for i := 0; i < len(publicSignals); i++ {
-		vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(setup.Vk.IC[i+1], publicSignals[i]))
+		vkxpia = Utils.Bn.G1.Add(vkxpia, Utils.Bn.G1.MulScalar(vk.IC[i+1], publicSignals[i]))
 	}
 
 	// e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2)
 	if !Utils.Bn.Fq12.Equal(
 		Utils.Bn.Pairing(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiB), // TODO Add(vkxpia, proof.PiA) can go outside in order to save computation, as is reused later
 		Utils.Bn.Fq12.Mul(
-			Utils.Bn.Pairing(proof.PiH, setup.Vk.Vkz),
+			Utils.Bn.Pairing(proof.PiH, vk.Vkz),
 			Utils.Bn.Pairing(proof.PiC, Utils.Bn.G2.G))) {
 		if debug {
 			fmt.Println("❌ e(Vkx+piA, piB) == e(piH, Vkz) * e(piC, g2), QAP disibility checked")
@@ -350,10 +353,10 @@ func VerifyProof(circuit circuitcompiler.Circuit, setup Setup, proof Proof, publ
 	// e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB)
 	// == e(piK, g2Kgamma)
 	piApiC := Utils.Bn.G1.Add(Utils.Bn.G1.Add(vkxpia, proof.PiA), proof.PiC)
-	pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, setup.Vk.G2Kbg)
+	pairingPiACG2Kbg := Utils.Bn.Pairing(piApiC, vk.G2Kbg)
-	pairingG1KbgPiB := Utils.Bn.Pairing(setup.Vk.G1Kbg, proof.PiB)
+	pairingG1KbgPiB := Utils.Bn.Pairing(vk.G1Kbg, proof.PiB)
 	pairingL := Utils.Bn.Fq12.Mul(pairingPiACG2Kbg, pairingG1KbgPiB)
-	pairingR := Utils.Bn.Pairing(proof.PiKp, setup.Vk.G2Kg)
+	pairingR := Utils.Bn.Pairing(proof.PiKp, vk.G2Kg)
 	if !Utils.Bn.Fq12.Equal(pairingL, pairingR) {
 		fmt.Println("❌ e(Vkx+piA+piC, g2KbetaKgamma) * e(g1KbetaKgamma, piB) == e(piK, g2Kgamma)")
 		return false

snark_test.go

@@ -8,9 +8,9 @@ import (
 	"testing"
 	"time"
 
-	"github.com/arnaucube/go-snark/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
-	"github.com/arnaucube/go-snark/groth16"
+	"github.com/arnaucube/go-snark-study/groth16"
-	"github.com/arnaucube/go-snark/r1csqap"
+	"github.com/arnaucube/go-snark-study/r1csqap"
 	"github.com/stretchr/testify/assert"
 )
 
@@ -86,7 +86,7 @@ func TestGroth16MinimalFlow(t *testing.T) {
 	// check length of polynomials H(x) and Z(x)
 	assert.Equal(t, len(hx), len(px)-len(setup.Pk.Z)+1)
 
-	proof, err := groth16.GenerateProofs(*circuit, setup, w, px)
+	proof, err := groth16.GenerateProofs(*circuit, setup.Pk, w, px)
 	assert.Nil(t, err)
 
 	// fmt.Println("\n proofs:")
@@ -98,13 +98,13 @@ func TestGroth16MinimalFlow(t *testing.T) {
 	b35Verif := big.NewInt(int64(35))
 	publicSignalsVerif := []*big.Int{b35Verif}
 	before := time.Now()
-	assert.True(t, groth16.VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
+	assert.True(t, groth16.VerifyProof(setup.Vk, proof, publicSignalsVerif, true))
 	fmt.Println("verify proof time elapsed:", time.Since(before))
 
 	// check that with another public input the verification returns false
 	bOtherWrongPublic := big.NewInt(int64(34))
 	wrongPublicSignalsVerif := []*big.Int{bOtherWrongPublic}
-	assert.True(t, !groth16.VerifyProof(*circuit, setup, proof, wrongPublicSignalsVerif, false))
+	assert.True(t, !groth16.VerifyProof(setup.Vk, proof, wrongPublicSignalsVerif, false))
 }
 
 func TestZkFromFlatCircuitCode(t *testing.T) {
@@ -221,7 +221,7 @@ func TestZkFromFlatCircuitCode(t *testing.T) {
 	assert.Equal(t, len(hx), len(px)-len(setup.Pk.Z)+1)
 	assert.Equal(t, len(hxQAP), len(px)-len(zxQAP)+1)
 
-	proof, err := GenerateProofs(*circuit, setup, w, px)
+	proof, err := GenerateProofs(*circuit, setup.Pk, w, px)
 	assert.Nil(t, err)
 
 	// fmt.Println("\n proofs:")
@@ -233,13 +233,13 @@ func TestZkFromFlatCircuitCode(t *testing.T) {
 	b35Verif := big.NewInt(int64(35))
 	publicSignalsVerif := []*big.Int{b35Verif}
 	before := time.Now()
-	assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
+	assert.True(t, VerifyProof(setup.Vk, proof, publicSignalsVerif, true))
 	fmt.Println("verify proof time elapsed:", time.Since(before))
 
 	// check that with another public input the verification returns false
 	bOtherWrongPublic := big.NewInt(int64(34))
 	wrongPublicSignalsVerif := []*big.Int{bOtherWrongPublic}
-	assert.True(t, !VerifyProof(*circuit, setup, proof, wrongPublicSignalsVerif, false))
+	assert.True(t, !VerifyProof(setup.Vk, proof, wrongPublicSignalsVerif, false))
 }
 
 func TestZkMultiplication(t *testing.T) {
@@ -329,7 +329,7 @@ func TestZkMultiplication(t *testing.T) {
 	assert.Equal(t, len(hx), len(px)-len(setup.Pk.Z)+1)
 	assert.Equal(t, len(hxQAP), len(px)-len(zxQAP)+1)
 
-	proof, err := GenerateProofs(*circuit, setup, w, px)
+	proof, err := GenerateProofs(*circuit, setup.Pk, w, px)
 	assert.Nil(t, err)
 
 	// fmt.Println("\n proofs:")
@@ -341,13 +341,13 @@ func TestZkMultiplication(t *testing.T) {
 	b12Verif := big.NewInt(int64(12))
 	publicSignalsVerif := []*big.Int{b12Verif}
 	before := time.Now()
-	assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
+	assert.True(t, VerifyProof(setup.Vk, proof, publicSignalsVerif, true))
 	fmt.Println("verify proof time elapsed:", time.Since(before))
 
 	// check that with another public input the verification returns false
 	bOtherWrongPublic := big.NewInt(int64(11))
 	wrongPublicSignalsVerif := []*big.Int{bOtherWrongPublic}
-	assert.True(t, !VerifyProof(*circuit, setup, proof, wrongPublicSignalsVerif, false))
+	assert.True(t, !VerifyProof(setup.Vk, proof, wrongPublicSignalsVerif, false))
 }
 
 func TestMinimalFlow(t *testing.T) {
@@ -418,7 +418,7 @@ func TestMinimalFlow(t *testing.T) {
 	// check length of polynomials H(x) and Z(x)
 	assert.Equal(t, len(hx), len(px)-len(setup.Pk.Z)+1)
 
-	proof, err := GenerateProofs(*circuit, setup, w, px)
+	proof, err := GenerateProofs(*circuit, setup.Pk, w, px)
 	assert.Nil(t, err)
 
 	// fmt.Println("\n proofs:")
@@ -430,11 +430,11 @@ func TestMinimalFlow(t *testing.T) {
 	b35Verif := big.NewInt(int64(35))
 	publicSignalsVerif := []*big.Int{b35Verif}
 	before := time.Now()
-	assert.True(t, VerifyProof(*circuit, setup, proof, publicSignalsVerif, true))
+	assert.True(t, VerifyProof(setup.Vk, proof, publicSignalsVerif, true))
 	fmt.Println("verify proof time elapsed:", time.Since(before))
 
 	// check that with another public input the verification returns false
 	bOtherWrongPublic := big.NewInt(int64(34))
 	wrongPublicSignalsVerif := []*big.Int{bOtherWrongPublic}
-	assert.True(t, !VerifyProof(*circuit, setup, proof, wrongPublicSignalsVerif, false))
+	assert.True(t, !VerifyProof(setup.Vk, proof, wrongPublicSignalsVerif, false))
 }

utils/base10parsers.go

@@ -0,0 +1,585 @@
+package utils
+
+import (
+	"errors"
+	"math/big"
+
+	snark "github.com/arnaucube/go-snark-study"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/groth16"
+)
+
+// []*big.Int
+func ArrayBigIntToString(b []*big.Int) []string {
+	var o []string
+	for i := 0; i < len(b); i++ {
+		o = append(o, b[i].String())
+	}
+	return o
+}
+func ArrayStringToBigInt(s []string) ([]*big.Int, error) {
+	var px []*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 10)
+		if !ok {
+			return nil, errors.New("error parsing px from pxString")
+		}
+		px = append(px, param)
+	}
+	return px, nil
+}
+
+// [3]*big.Int
+func String3ToBigInt(s [3]string) ([3]*big.Int, error) {
+	var o [3]*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 10)
+		if !ok {
+			return o, errors.New("error parsing [3]*big.Int from [3]string")
+		}
+		o[i] = param
+	}
+	return o, nil
+}
+func BigInt3ToString(b [3]*big.Int) [3]string {
+	var o [3]string
+	o[0] = b[0].String()
+	o[1] = b[1].String()
+	o[2] = b[2].String()
+	return o
+}
+
+// [][3]*big.Int
+func Array3StringToBigInt(s [][3]string) ([][3]*big.Int, error) {
+	var o [][3]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := String3ToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func Array3BigIntToString(b [][3]*big.Int) [][3]string {
+	var o [][3]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, BigInt3ToString(b[i]))
+	}
+	return o
+}
+
+func String2ToBigInt(s [2]string) ([2]*big.Int, error) {
+	var o [2]*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 10)
+		if !ok {
+			return o, errors.New("error parsing [2]*big.Int from [2]string")
+		}
+		o[i] = param
+	}
+	return o, nil
+}
+
+// [3][2]*big.Int
+func String32ToBigInt(s [3][2]string) ([3][2]*big.Int, error) {
+	var o [3][2]*big.Int
+	var err error
+
+	o[0], err = String2ToBigInt(s[0])
+	if err != nil {
+		return o, err
+	}
+	o[1], err = String2ToBigInt(s[1])
+	if err != nil {
+		return o, err
+	}
+	o[2], err = String2ToBigInt(s[2])
+	if err != nil {
+		return o, err
+	}
+	return o, nil
+}
+func BigInt32ToString(b [3][2]*big.Int) [3][2]string {
+	var o [3][2]string
+	o[0][0] = b[0][0].String()
+	o[0][1] = b[0][1].String()
+	o[1][0] = b[1][0].String()
+	o[1][1] = b[1][1].String()
+	o[2][0] = b[2][0].String()
+	o[2][1] = b[2][1].String()
+	return o
+}
+
+// [][3][2]*big.Int
+func Array32StringToBigInt(s [][3][2]string) ([][3][2]*big.Int, error) {
+	var o [][3][2]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := String32ToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func Array32BigIntToString(b [][3][2]*big.Int) [][3][2]string {
+	var o [][3][2]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, BigInt32ToString(b[i]))
+	}
+	return o
+}
+
+// Setup
+type SetupString struct {
+	// public
+	Pk struct {
+		G1T [][3]string
+		A   [][3]string
+		B   [][3][2]string
+		C   [][3]string
+		Kp  [][3]string
+		Ap  [][3]string
+		Bp  [][3]string
+		Cp  [][3]string
+		Z   []string
+	}
+	Vk struct {
+		Vka   [3][2]string
+		Vkb   [3]string
+		Vkc   [3][2]string
+		IC    [][3]string
+		G1Kbg [3]string
+		G2Kbg [3][2]string
+		G2Kg  [3][2]string
+		Vkz   [3][2]string
+	}
+}
+
+func SetupToString(setup snark.Setup) SetupString {
+	var s SetupString
+	s.Pk.G1T = Array3BigIntToString(setup.Pk.G1T)
+	s.Pk.A = Array3BigIntToString(setup.Pk.A)
+	s.Pk.B = Array32BigIntToString(setup.Pk.B)
+	s.Pk.C = Array3BigIntToString(setup.Pk.C)
+	s.Pk.Kp = Array3BigIntToString(setup.Pk.Kp)
+	s.Pk.Ap = Array3BigIntToString(setup.Pk.Ap)
+	s.Pk.Bp = Array3BigIntToString(setup.Pk.Bp)
+	s.Pk.Cp = Array3BigIntToString(setup.Pk.Cp)
+	s.Pk.Z = ArrayBigIntToString(setup.Pk.Z)
+	s.Vk.Vka = BigInt32ToString(setup.Vk.Vka)
+	s.Vk.Vkb = BigInt3ToString(setup.Vk.Vkb)
+	s.Vk.Vkc = BigInt32ToString(setup.Vk.Vkc)
+	s.Vk.IC = Array3BigIntToString(setup.Vk.IC)
+	s.Vk.G1Kbg = BigInt3ToString(setup.Vk.G1Kbg)
+	s.Vk.G2Kbg = BigInt32ToString(setup.Vk.G2Kbg)
+	s.Vk.G2Kg = BigInt32ToString(setup.Vk.G2Kg)
+	s.Vk.Vkz = BigInt32ToString(setup.Vk.Vkz)
+	return s
+}
+func SetupFromString(s SetupString) (snark.Setup, error) {
+	var o snark.Setup
+	var err error
+	o.Pk.G1T, err = Array3StringToBigInt(s.Pk.G1T)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.A, err = Array3StringToBigInt(s.Pk.A)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.B, err = Array32StringToBigInt(s.Pk.B)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.C, err = Array3StringToBigInt(s.Pk.C)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Kp, err = Array3StringToBigInt(s.Pk.Kp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Ap, err = Array3StringToBigInt(s.Pk.Ap)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Bp, err = Array3StringToBigInt(s.Pk.Bp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Cp, err = Array3StringToBigInt(s.Pk.Cp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Z, err = ArrayStringToBigInt(s.Pk.Z)
+	if err != nil {
+		return o, err
+	}
+
+	o.Vk.Vka, err = String32ToBigInt(s.Vk.Vka)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkb, err = String3ToBigInt(s.Vk.Vkb)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkc, err = String32ToBigInt(s.Vk.Vkc)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.IC, err = Array3StringToBigInt(s.Vk.IC)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G1Kbg, err = String3ToBigInt(s.Vk.G1Kbg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2Kbg, err = String32ToBigInt(s.Vk.G2Kbg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2Kg, err = String32ToBigInt(s.Vk.G2Kg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkz, err = String32ToBigInt(s.Vk.Vkz)
+	if err != nil {
+		return o, err
+	}
+
+	return o, nil
+
+}
+
+// circuit
+type CircuitString struct {
+	NVars         int
+	NPublic       int
+	NSignals      int
+	PrivateInputs []string
+	PublicInputs  []string
+	Signals       []string
+	Witness       []string
+	Constraints   []circuitcompiler.Constraint
+	R1CS          struct {
+		A [][]string
+		B [][]string
+		C [][]string
+	}
+}
+
+func ArrayArrayBigIntToString(b [][]*big.Int) [][]string {
+	var o [][]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, ArrayBigIntToString(b[i]))
+	}
+	return o
+}
+func ArrayArrayStringToBigInt(s [][]string) ([][]*big.Int, error) {
+	var o [][]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := ArrayStringToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func CircuitToString(c circuitcompiler.Circuit) CircuitString {
+	var cs CircuitString
+	cs.NVars = c.NVars
+	cs.NPublic = c.NPublic
+	cs.NSignals = c.NSignals
+	cs.PrivateInputs = c.PrivateInputs
+	cs.PublicInputs = c.PublicInputs
+	cs.Signals = c.Signals
+	cs.Witness = ArrayBigIntToString(c.Witness)
+	cs.Constraints = c.Constraints
+	cs.R1CS.A = ArrayArrayBigIntToString(c.R1CS.A)
+	cs.R1CS.B = ArrayArrayBigIntToString(c.R1CS.B)
+	cs.R1CS.C = ArrayArrayBigIntToString(c.R1CS.C)
+	return cs
+}
+func CircuitFromString(cs CircuitString) (circuitcompiler.Circuit, error) {
+	var c circuitcompiler.Circuit
+	var err error
+	c.NVars = cs.NVars
+	c.NPublic = cs.NPublic
+	c.NSignals = cs.NSignals
+	c.PrivateInputs = cs.PrivateInputs
+	c.PublicInputs = cs.PublicInputs
+	c.Signals = cs.Signals
+	c.Witness, err = ArrayStringToBigInt(cs.Witness)
+	if err != nil {
+		return c, err
+	}
+	c.Constraints = cs.Constraints
+	c.R1CS.A, err = ArrayArrayStringToBigInt(cs.R1CS.A)
+	if err != nil {
+		return c, err
+	}
+	c.R1CS.B, err = ArrayArrayStringToBigInt(cs.R1CS.B)
+	if err != nil {
+		return c, err
+	}
+	c.R1CS.C, err = ArrayArrayStringToBigInt(cs.R1CS.C)
+	if err != nil {
+		return c, err
+	}
+	return c, nil
+}
+
+// Proof
+type ProofString struct {
+	PiA  [3]string
+	PiAp [3]string
+	PiB  [3][2]string
+	PiBp [3]string
+	PiC  [3]string
+	PiCp [3]string
+	PiH  [3]string
+	PiKp [3]string
+}
+
+func ProofToString(p snark.Proof) ProofString {
+	var s ProofString
+	s.PiA = BigInt3ToString(p.PiA)
+	s.PiAp = BigInt3ToString(p.PiAp)
+	s.PiB = BigInt32ToString(p.PiB)
+	s.PiBp = BigInt3ToString(p.PiBp)
+	s.PiC = BigInt3ToString(p.PiC)
+	s.PiCp = BigInt3ToString(p.PiCp)
+	s.PiH = BigInt3ToString(p.PiH)
+	s.PiKp = BigInt3ToString(p.PiKp)
+	return s
+}
+func ProofFromString(s ProofString) (snark.Proof, error) {
+	var p snark.Proof
+	var err error
+
+	p.PiA, err = String3ToBigInt(s.PiA)
+	if err != nil {
+		return p, err
+	}
+	p.PiAp, err = String3ToBigInt(s.PiAp)
+	if err != nil {
+		return p, err
+	}
+	p.PiB, err = String32ToBigInt(s.PiB)
+	if err != nil {
+		return p, err
+	}
+	p.PiBp, err = String3ToBigInt(s.PiBp)
+	if err != nil {
+		return p, err
+	}
+	p.PiC, err = String3ToBigInt(s.PiC)
+	if err != nil {
+		return p, err
+	}
+	p.PiCp, err = String3ToBigInt(s.PiCp)
+	if err != nil {
+		return p, err
+	}
+	p.PiH, err = String3ToBigInt(s.PiH)
+	if err != nil {
+		return p, err
+	}
+	p.PiKp, err = String3ToBigInt(s.PiKp)
+	if err != nil {
+		return p, err
+	}
+	return p, nil
+}
+
+// groth
+type GrothPkString struct { // Proving Key
+	BACDelta [][3]string
+	Z        []string
+	G1       struct {
+		Alpha    [3]string
+		Beta     [3]string
+		Delta    [3]string
+		At       [][3]string
+		BACGamma [][3]string
+	}
+	G2 struct {
+		Beta     [3][2]string
+		Gamma    [3][2]string
+		Delta    [3][2]string
+		BACGamma [][3][2]string
+	}
+	PowersTauDelta [][3]string
+}
+type GrothVkString struct {
+	IC [][3]string
+	G1 struct {
+		Alpha [3]string
+	}
+	G2 struct {
+		Beta  [3][2]string
+		Gamma [3][2]string
+		Delta [3][2]string
+	}
+}
+type GrothSetupString struct {
+	Pk GrothPkString
+	Vk GrothVkString
+}
+
+func GrothSetupToString(setup groth16.Setup) GrothSetupString {
+	var s GrothSetupString
+	s.Pk.BACDelta = Array3BigIntToString(setup.Pk.BACDelta)
+	s.Pk.Z = ArrayBigIntToString(setup.Pk.Z)
+	s.Pk.G1.Alpha = BigInt3ToString(setup.Pk.G1.Alpha)
+	s.Pk.G1.Beta = BigInt3ToString(setup.Pk.G1.Beta)
+	s.Pk.G1.Delta = BigInt3ToString(setup.Pk.G1.Delta)
+	s.Pk.G1.At = Array3BigIntToString(setup.Pk.G1.At)
+	s.Pk.G1.BACGamma = Array3BigIntToString(setup.Pk.G1.BACGamma)
+	s.Pk.G2.Beta = BigInt32ToString(setup.Pk.G2.Beta)
+	s.Pk.G2.Gamma = BigInt32ToString(setup.Pk.G2.Gamma)
+	s.Pk.G2.Delta = BigInt32ToString(setup.Pk.G2.Delta)
+	s.Pk.G2.BACGamma = Array32BigIntToString(setup.Pk.G2.BACGamma)
+	s.Pk.PowersTauDelta = Array3BigIntToString(setup.Pk.PowersTauDelta)
+	s.Vk.IC = Array3BigIntToString(setup.Vk.IC)
+	s.Vk.G1.Alpha = BigInt3ToString(setup.Vk.G1.Alpha)
+	s.Vk.G2.Beta = BigInt32ToString(setup.Vk.G2.Beta)
+	s.Vk.G2.Gamma = BigInt32ToString(setup.Vk.G2.Gamma)
+	s.Vk.G2.Delta = BigInt32ToString(setup.Vk.G2.Delta)
+	return s
+}
+func GrothVkFromString(s GrothVkString) (groth16.Vk, error) {
+	var vk groth16.Vk
+	var err error
+	vk.IC, err = Array3StringToBigInt(s.IC)
+	if err != nil {
+		return vk, err
+	}
+	vk.G1.Alpha, err = String3ToBigInt(s.G1.Alpha)
+	if err != nil {
+		return vk, err
+	}
+	vk.G2.Beta, err = String32ToBigInt(s.G2.Beta)
+	if err != nil {
+		return vk, err
+	}
+	vk.G2.Gamma, err = String32ToBigInt(s.G2.Gamma)
+	if err != nil {
+		return vk, err
+	}
+	vk.G2.Delta, err = String32ToBigInt(s.G2.Delta)
+	if err != nil {
+		return vk, err
+	}
+	return vk, nil
+}
+func GrothSetupFromString(s GrothSetupString) (groth16.Setup, error) {
+	var o groth16.Setup
+	var err error
+	o.Pk.BACDelta, err = Array3StringToBigInt(s.Pk.BACDelta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Z, err = ArrayStringToBigInt(s.Pk.Z)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Alpha, err = String3ToBigInt(s.Pk.G1.Alpha)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Beta, err = String3ToBigInt(s.Pk.G1.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Delta, err = String3ToBigInt(s.Pk.G1.Delta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.At, err = Array3StringToBigInt(s.Pk.G1.At)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.BACGamma, err = Array3StringToBigInt(s.Pk.G1.BACGamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Beta, err = String32ToBigInt(s.Pk.G2.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Gamma, err = String32ToBigInt(s.Pk.G2.Gamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Delta, err = String32ToBigInt(s.Pk.G2.Delta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.BACGamma, err = Array32StringToBigInt(s.Pk.G2.BACGamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.PowersTauDelta, err = Array3StringToBigInt(s.Pk.PowersTauDelta)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.IC, err = Array3StringToBigInt(s.Vk.IC)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G1.Alpha, err = String3ToBigInt(s.Vk.G1.Alpha)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Beta, err = String32ToBigInt(s.Vk.G2.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Gamma, err = String32ToBigInt(s.Vk.G2.Gamma)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Delta, err = String32ToBigInt(s.Vk.G2.Delta)
+	if err != nil {
+		return o, err
+	}
+	return o, nil
+}
+
+type GrothProofString struct {
+	PiA [3]string
+	PiB [3][2]string
+	PiC [3]string
+}
+
+func GrothProofToString(p groth16.Proof) GrothProofString {
+	var s GrothProofString
+	s.PiA = BigInt3ToString(p.PiA)
+	s.PiB = BigInt32ToString(p.PiB)
+	s.PiC = BigInt3ToString(p.PiC)
+	return s
+}
+func GrothProofFromString(s GrothProofString) (groth16.Proof, error) {
+	var p groth16.Proof
+	var err error
+
+	p.PiA, err = String3ToBigInt(s.PiA)
+	if err != nil {
+		return p, err
+	}
+	p.PiB, err = String32ToBigInt(s.PiB)
+	if err != nil {
+		return p, err
+	}
+	p.PiC, err = String3ToBigInt(s.PiC)
+	if err != nil {
+		return p, err
+	}
+	return p, nil
+}

utils/hexparsers.go

@@ -0,0 +1,562 @@
+package utils
+
+import (
+	"errors"
+	"fmt"
+	"math/big"
+
+	snark "github.com/arnaucube/go-snark-study"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/groth16"
+)
+
+// []*big.Int
+func ArrayBigIntToHex(b []*big.Int) []string {
+	var o []string
+	for i := 0; i < len(b); i++ {
+		o = append(o, fmt.Sprintf("%x", b[i]))
+	}
+	return o
+}
+func ArrayHexToBigInt(s []string) ([]*big.Int, error) {
+	var px []*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 16)
+		if !ok {
+			return nil, errors.New("error parsing px from pxHex")
+		}
+		px = append(px, param)
+	}
+	return px, nil
+}
+
+// [3]*big.Int
+func Hex3ToBigInt(s [3]string) ([3]*big.Int, error) {
+	var o [3]*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 16)
+		if !ok {
+			return o, errors.New("error parsing [3]*big.Int from [3]string")
+		}
+		o[i] = param
+	}
+	return o, nil
+}
+func BigInt3ToHex(b [3]*big.Int) [3]string {
+	var o [3]string
+	o[0] = fmt.Sprintf("%x", b[0])
+	o[1] = fmt.Sprintf("%x", b[1])
+	o[2] = fmt.Sprintf("%x", b[2])
+	return o
+}
+
+// [][3]*big.Int
+func Array3HexToBigInt(s [][3]string) ([][3]*big.Int, error) {
+	var o [][3]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := Hex3ToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func Array3BigIntToHex(b [][3]*big.Int) [][3]string {
+	var o [][3]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, BigInt3ToHex(b[i]))
+	}
+	return o
+}
+
+func Hex2ToBigInt(s [2]string) ([2]*big.Int, error) {
+	var o [2]*big.Int
+	for i := 0; i < len(s); i++ {
+		param, ok := new(big.Int).SetString(s[i], 16)
+		if !ok {
+			return o, errors.New("error parsing [2]*big.Int from [2]string")
+		}
+		o[i] = param
+	}
+	return o, nil
+}
+
+// [3][2]*big.Int
+func Hex32ToBigInt(s [3][2]string) ([3][2]*big.Int, error) {
+	var o [3][2]*big.Int
+	var err error
+
+	o[0], err = Hex2ToBigInt(s[0])
+	if err != nil {
+		return o, err
+	}
+	o[1], err = Hex2ToBigInt(s[1])
+	if err != nil {
+		return o, err
+	}
+	o[2], err = Hex2ToBigInt(s[2])
+	if err != nil {
+		return o, err
+	}
+	return o, nil
+}
+func BigInt32ToHex(b [3][2]*big.Int) [3][2]string {
+	var o [3][2]string
+	o[0][0] = fmt.Sprintf("%x", b[0][0])
+	o[0][1] = fmt.Sprintf("%x", b[0][1])
+	o[1][0] = fmt.Sprintf("%x", b[1][0])
+	o[1][1] = fmt.Sprintf("%x", b[1][1])
+	o[2][0] = fmt.Sprintf("%x", b[2][0])
+	o[2][1] = fmt.Sprintf("%x", b[2][1])
+	return o
+}
+
+// [][3][2]*big.Int
+func Array32HexToBigInt(s [][3][2]string) ([][3][2]*big.Int, error) {
+	var o [][3][2]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := Hex32ToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func Array32BigIntToHex(b [][3][2]*big.Int) [][3][2]string {
+	var o [][3][2]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, BigInt32ToHex(b[i]))
+	}
+	return o
+}
+
+// Setup
+type PkHex struct {
+	G1T [][3]string
+	A   [][3]string
+	B   [][3][2]string
+	C   [][3]string
+	Kp  [][3]string
+	Ap  [][3]string
+	Bp  [][3]string
+	Cp  [][3]string
+	Z   []string
+}
+type VkHex struct {
+	Vka   [3][2]string
+	Vkb   [3]string
+	Vkc   [3][2]string
+	IC    [][3]string
+	G1Kbg [3]string
+	G2Kbg [3][2]string
+	G2Kg  [3][2]string
+	Vkz   [3][2]string
+}
+type SetupHex struct {
+	Pk PkHex
+	Vk VkHex
+}
+
+func SetupToHex(setup snark.Setup) SetupHex {
+	var s SetupHex
+	s.Pk.G1T = Array3BigIntToHex(setup.Pk.G1T)
+	s.Pk.A = Array3BigIntToHex(setup.Pk.A)
+	s.Pk.B = Array32BigIntToHex(setup.Pk.B)
+	s.Pk.C = Array3BigIntToHex(setup.Pk.C)
+	s.Pk.Kp = Array3BigIntToHex(setup.Pk.Kp)
+	s.Pk.Ap = Array3BigIntToHex(setup.Pk.Ap)
+	s.Pk.Bp = Array3BigIntToHex(setup.Pk.Bp)
+	s.Pk.Cp = Array3BigIntToHex(setup.Pk.Cp)
+	s.Pk.Z = ArrayBigIntToHex(setup.Pk.Z)
+	s.Vk.Vka = BigInt32ToHex(setup.Vk.Vka)
+	s.Vk.Vkb = BigInt3ToHex(setup.Vk.Vkb)
+	s.Vk.Vkc = BigInt32ToHex(setup.Vk.Vkc)
+	s.Vk.IC = Array3BigIntToHex(setup.Vk.IC)
+	s.Vk.G1Kbg = BigInt3ToHex(setup.Vk.G1Kbg)
+	s.Vk.G2Kbg = BigInt32ToHex(setup.Vk.G2Kbg)
+	s.Vk.G2Kg = BigInt32ToHex(setup.Vk.G2Kg)
+	s.Vk.Vkz = BigInt32ToHex(setup.Vk.Vkz)
+	return s
+}
+func SetupFromHex(s SetupHex) (snark.Setup, error) {
+	var o snark.Setup
+	var err error
+	o.Pk.G1T, err = Array3HexToBigInt(s.Pk.G1T)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.A, err = Array3HexToBigInt(s.Pk.A)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.B, err = Array32HexToBigInt(s.Pk.B)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.C, err = Array3HexToBigInt(s.Pk.C)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Kp, err = Array3HexToBigInt(s.Pk.Kp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Ap, err = Array3HexToBigInt(s.Pk.Ap)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Bp, err = Array3HexToBigInt(s.Pk.Bp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Cp, err = Array3HexToBigInt(s.Pk.Cp)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Z, err = ArrayHexToBigInt(s.Pk.Z)
+	if err != nil {
+		return o, err
+	}
+
+	o.Vk.Vka, err = Hex32ToBigInt(s.Vk.Vka)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkb, err = Hex3ToBigInt(s.Vk.Vkb)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkc, err = Hex32ToBigInt(s.Vk.Vkc)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.IC, err = Array3HexToBigInt(s.Vk.IC)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G1Kbg, err = Hex3ToBigInt(s.Vk.G1Kbg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2Kbg, err = Hex32ToBigInt(s.Vk.G2Kbg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2Kg, err = Hex32ToBigInt(s.Vk.G2Kg)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.Vkz, err = Hex32ToBigInt(s.Vk.Vkz)
+	if err != nil {
+		return o, err
+	}
+
+	return o, nil
+
+}
+
+// circuit
+type CircuitHex struct {
+	NVars         int
+	NPublic       int
+	NSignals      int
+	PrivateInputs []string
+	PublicInputs  []string
+	Signals       []string
+	Witness       []string
+	Constraints   []circuitcompiler.Constraint
+	R1CS          struct {
+		A [][]string
+		B [][]string
+		C [][]string
+	}
+}
+
+func ArrayArrayBigIntToHex(b [][]*big.Int) [][]string {
+	var o [][]string
+	for i := 0; i < len(b); i++ {
+		o = append(o, ArrayBigIntToHex(b[i]))
+	}
+	return o
+}
+func ArrayArrayHexToBigInt(s [][]string) ([][]*big.Int, error) {
+	var o [][]*big.Int
+	for i := 0; i < len(s); i++ {
+		parsed, err := ArrayHexToBigInt(s[i])
+		if err != nil {
+			return o, err
+		}
+		o = append(o, parsed)
+	}
+	return o, nil
+}
+func CircuitToHex(c circuitcompiler.Circuit) CircuitHex {
+	var cs CircuitHex
+	cs.NVars = c.NVars
+	cs.NPublic = c.NPublic
+	cs.NSignals = c.NSignals
+	cs.PrivateInputs = c.PrivateInputs
+	cs.PublicInputs = c.PublicInputs
+	cs.Signals = c.Signals
+	cs.Witness = ArrayBigIntToHex(c.Witness)
+	cs.Constraints = c.Constraints
+	cs.R1CS.A = ArrayArrayBigIntToHex(c.R1CS.A)
+	cs.R1CS.B = ArrayArrayBigIntToHex(c.R1CS.B)
+	cs.R1CS.C = ArrayArrayBigIntToHex(c.R1CS.C)
+	return cs
+}
+func CircuitFromHex(cs CircuitHex) (circuitcompiler.Circuit, error) {
+	var c circuitcompiler.Circuit
+	var err error
+	c.NVars = cs.NVars
+	c.NPublic = cs.NPublic
+	c.NSignals = cs.NSignals
+	c.PrivateInputs = cs.PrivateInputs
+	c.PublicInputs = cs.PublicInputs
+	c.Signals = cs.Signals
+	c.Witness, err = ArrayHexToBigInt(cs.Witness)
+	if err != nil {
+		return c, err
+	}
+	c.Constraints = cs.Constraints
+	c.R1CS.A, err = ArrayArrayHexToBigInt(cs.R1CS.A)
+	if err != nil {
+		return c, err
+	}
+	c.R1CS.B, err = ArrayArrayHexToBigInt(cs.R1CS.B)
+	if err != nil {
+		return c, err
+	}
+	c.R1CS.C, err = ArrayArrayHexToBigInt(cs.R1CS.C)
+	if err != nil {
+		return c, err
+	}
+	return c, nil
+}
+
+// Proof
+type ProofHex struct {
+	PiA  [3]string
+	PiAp [3]string
+	PiB  [3][2]string
+	PiBp [3]string
+	PiC  [3]string
+	PiCp [3]string
+	PiH  [3]string
+	PiKp [3]string
+}
+
+func ProofToHex(p snark.Proof) ProofHex {
+	var s ProofHex
+	s.PiA = BigInt3ToHex(p.PiA)
+	s.PiAp = BigInt3ToHex(p.PiAp)
+	s.PiB = BigInt32ToHex(p.PiB)
+	s.PiBp = BigInt3ToHex(p.PiBp)
+	s.PiC = BigInt3ToHex(p.PiC)
+	s.PiCp = BigInt3ToHex(p.PiCp)
+	s.PiH = BigInt3ToHex(p.PiH)
+	s.PiKp = BigInt3ToHex(p.PiKp)
+	return s
+}
+func ProofFromHex(s ProofHex) (snark.Proof, error) {
+	var p snark.Proof
+	var err error
+
+	p.PiA, err = Hex3ToBigInt(s.PiA)
+	if err != nil {
+		return p, err
+	}
+	p.PiAp, err = Hex3ToBigInt(s.PiAp)
+	if err != nil {
+		return p, err
+	}
+	p.PiB, err = Hex32ToBigInt(s.PiB)
+	if err != nil {
+		return p, err
+	}
+	p.PiBp, err = Hex3ToBigInt(s.PiBp)
+	if err != nil {
+		return p, err
+	}
+	p.PiC, err = Hex3ToBigInt(s.PiC)
+	if err != nil {
+		return p, err
+	}
+	p.PiCp, err = Hex3ToBigInt(s.PiCp)
+	if err != nil {
+		return p, err
+	}
+	p.PiH, err = Hex3ToBigInt(s.PiH)
+	if err != nil {
+		return p, err
+	}
+	p.PiKp, err = Hex3ToBigInt(s.PiKp)
+	if err != nil {
+		return p, err
+	}
+	return p, nil
+}
+
+// groth
+type GrothPkHex struct { // Proving Key
+	BACDelta [][3]string
+	Z        []string
+	G1       struct {
+		Alpha    [3]string
+		Beta     [3]string
+		Delta    [3]string
+		At       [][3]string
+		BACGamma [][3]string
+	}
+	G2 struct {
+		Beta     [3][2]string
+		Gamma    [3][2]string
+		Delta    [3][2]string
+		BACGamma [][3][2]string
+	}
+	PowersTauDelta [][3]string
+}
+type GrothVkHex struct {
+	IC [][3]string
+	G1 struct {
+		Alpha [3]string
+	}
+	G2 struct {
+		Beta  [3][2]string
+		Gamma [3][2]string
+		Delta [3][2]string
+	}
+}
+type GrothSetupHex struct {
+	Pk GrothPkHex
+	Vk GrothVkHex
+}
+
+func GrothSetupToHex(setup groth16.Setup) GrothSetupHex {
+	var s GrothSetupHex
+	s.Pk.BACDelta = Array3BigIntToHex(setup.Pk.BACDelta)
+	s.Pk.Z = ArrayBigIntToHex(setup.Pk.Z)
+	s.Pk.G1.Alpha = BigInt3ToHex(setup.Pk.G1.Alpha)
+	s.Pk.G1.Beta = BigInt3ToHex(setup.Pk.G1.Beta)
+	s.Pk.G1.Delta = BigInt3ToHex(setup.Pk.G1.Delta)
+	s.Pk.G1.At = Array3BigIntToHex(setup.Pk.G1.At)
+	s.Pk.G1.BACGamma = Array3BigIntToHex(setup.Pk.G1.BACGamma)
+	s.Pk.G2.Beta = BigInt32ToHex(setup.Pk.G2.Beta)
+	s.Pk.G2.Gamma = BigInt32ToHex(setup.Pk.G2.Gamma)
+	s.Pk.G2.Delta = BigInt32ToHex(setup.Pk.G2.Delta)
+	s.Pk.G2.BACGamma = Array32BigIntToHex(setup.Pk.G2.BACGamma)
+	s.Pk.PowersTauDelta = Array3BigIntToHex(setup.Pk.PowersTauDelta)
+	s.Vk.IC = Array3BigIntToHex(setup.Vk.IC)
+	s.Vk.G1.Alpha = BigInt3ToHex(setup.Vk.G1.Alpha)
+	s.Vk.G2.Beta = BigInt32ToHex(setup.Vk.G2.Beta)
+	s.Vk.G2.Gamma = BigInt32ToHex(setup.Vk.G2.Gamma)
+	s.Vk.G2.Delta = BigInt32ToHex(setup.Vk.G2.Delta)
+	return s
+}
+func GrothSetupFromHex(s GrothSetupHex) (groth16.Setup, error) {
+	var o groth16.Setup
+	var err error
+	o.Pk.BACDelta, err = Array3HexToBigInt(s.Pk.BACDelta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.Z, err = ArrayHexToBigInt(s.Pk.Z)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Alpha, err = Hex3ToBigInt(s.Pk.G1.Alpha)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Beta, err = Hex3ToBigInt(s.Pk.G1.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.Delta, err = Hex3ToBigInt(s.Pk.G1.Delta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.At, err = Array3HexToBigInt(s.Pk.G1.At)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G1.BACGamma, err = Array3HexToBigInt(s.Pk.G1.BACGamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Beta, err = Hex32ToBigInt(s.Pk.G2.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Gamma, err = Hex32ToBigInt(s.Pk.G2.Gamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.Delta, err = Hex32ToBigInt(s.Pk.G2.Delta)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.G2.BACGamma, err = Array32HexToBigInt(s.Pk.G2.BACGamma)
+	if err != nil {
+		return o, err
+	}
+	o.Pk.PowersTauDelta, err = Array3HexToBigInt(s.Pk.PowersTauDelta)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.IC, err = Array3HexToBigInt(s.Vk.IC)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G1.Alpha, err = Hex3ToBigInt(s.Vk.G1.Alpha)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Beta, err = Hex32ToBigInt(s.Vk.G2.Beta)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Gamma, err = Hex32ToBigInt(s.Vk.G2.Gamma)
+	if err != nil {
+		return o, err
+	}
+	o.Vk.G2.Delta, err = Hex32ToBigInt(s.Vk.G2.Delta)
+	if err != nil {
+		return o, err
+	}
+	return o, nil
+}
+
+type GrothProofHex struct {
+	PiA [3]string
+	PiB [3][2]string
+	PiC [3]string
+}
+
+func GrothProofToHex(p groth16.Proof) GrothProofHex {
+	var s GrothProofHex
+	s.PiA = BigInt3ToHex(p.PiA)
+	s.PiB = BigInt32ToHex(p.PiB)
+	s.PiC = BigInt3ToHex(p.PiC)
+	return s
+}
+func GrothProofFromHex(s GrothProofHex) (groth16.Proof, error) {
+	var p groth16.Proof
+	var err error
+
+	p.PiA, err = Hex3ToBigInt(s.PiA)
+	if err != nil {
+		return p, err
+	}
+	p.PiB, err = Hex32ToBigInt(s.PiB)
+	if err != nil {
+		return p, err
+	}
+	p.PiC, err = Hex3ToBigInt(s.PiC)
+	if err != nil {
+		return p, err
+	}
+	return p, nil
+}

vim-syntax/README.md

@@ -3,8 +3,8 @@
 ## Installation in vim/nvim using plug
 Using [Plug](https://github.com/junegunn/vim-plug), add this lines into the `.vimrc`/`init.vim`:
 ```
-Plug 'arnaucube/go-snark'
+Plug 'arnaucube/go-snark-study'
-Plug 'arnaucube/go-snark', {'rtp': 'vim-syntax'}
+Plug 'arnaucube/go-snark-study', {'rtp': 'vim-syntax'}
 ```
 
-![screenshot-vim](https://raw.githubusercontent.com/arnaucube/go-snark/master/vim-syntax/screenshot.png "screenshot-vim")
+![screenshot-vim](https://raw.githubusercontent.com/arnaucube/go-snark-study/master/vim-syntax/screenshot.png "screenshot-vim")

vim-syntax/syntax/go-snark-circuit.vim

@@ -24,6 +24,7 @@ syn keyword goSnarkCircuitPrivatePublic		private public
 syn keyword goSnarkCircuitOut	out
 syn keyword goSnarkCircuitEquals	equals
 syn keyword goSnarkCircuitFunction	func
+syn keyword goSnarkCircuitStatement	return
 syn keyword goSnarkCircuitImport	import
 syn match goSnarkCircuitFuncCall /\<\K\k*\ze\s*(/
 syn keyword goSnarkCircuitPrivate private nextgroup=goSnarkCircuitInputName skipwhite
@@ -46,6 +47,7 @@ hi def link goSnarkCircuitOpSymbols		Operator
 hi def link goSnarkCircuitFuncCall		Function
 hi def link goSnarkCircuitEquals		Identifier
 hi def link goSnarkCircuitFunction		Keyword
+hi def link goSnarkCircuitStatement		Statement
 hi def link goSnarkCircuitImport		Keyword
 hi def link goSnarkCircuitBraces		Function
 hi def link goSnarkCircuitPrivate 		Keyword

wasm/.gitignore

@@ -0,0 +1,3 @@
+node_modules
+package-lock.json
+wasm_exec.js

wasm/README.md

@@ -0,0 +1,22 @@
+# go-snark-study wasm
+*Warning: this is an ongoing experimentation*
+
+WASM wrappers for zkSNARK Pinocchio & Groth16 protocols.
+
+## Wasm usage
+To compile to wasm, inside the `wasm` directory, execute:
+```
+GOARCH=wasm GOOS=js go build -o go-snark.wasm go-snark-wasm-wrapper.go
+```
+
+Add the file `wasm_exec.js` in the directory:
+```
+cp "$(go env GOROOT)/misc/wasm/wasm_exec.js" .
+```
+
+To see the usage from javascript, check `index.js` file.
+
+Run the http server that allows to load the `.wasm` file:
+```
+node server.js
+```

wasm/go-snark-wasm-wrapper.go

@@ -0,0 +1,246 @@
+package main
+
+import (
+	"encoding/json"
+	"math/big"
+	"syscall/js"
+
+	"github.com/arnaucube/go-snark-study"
+	"github.com/arnaucube/go-snark-study/circuitcompiler"
+	"github.com/arnaucube/go-snark-study/groth16"
+	"github.com/arnaucube/go-snark-study/utils"
+)
+
+func main() {
+	c := make(chan struct{}, 0)
+	println("WASM Go Initialized")
+	registerCallbacks()
+	<-c
+}
+
+func registerCallbacks() {
+	js.Global().Set("generateProofs", js.FuncOf(generateProofs))
+	js.Global().Set("verifyProofs", js.FuncOf(verifyProofs))
+	js.Global().Set("grothGenerateProofs", js.FuncOf(grothGenerateProofs))
+	js.Global().Set("grothVerifyProofs", js.FuncOf(grothVerifyProofs))
+}
+
+func generateProofs(this js.Value, i []js.Value) interface{} {
+	var circuitStr utils.CircuitString
+	err := json.Unmarshal([]byte(i[0].String()), &circuitStr)
+	if err != nil {
+		println(i[0].String())
+		println("error parsing circuit from stringified json")
+	}
+	circuit, err := utils.CircuitFromString(circuitStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	sj, err := json.Marshal(circuit)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("circuit", string(sj))
+
+	var setupStr utils.SetupString
+	println(i[1].String())
+	err = json.Unmarshal([]byte(i[1].String()), &setupStr)
+	if err != nil {
+		println("error parsing setup from stringified json")
+	}
+	setup, err := utils.SetupFromString(setupStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	sj, err = json.Marshal(setup)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("set", string(sj))
+
+	var pxStr []string
+	err = json.Unmarshal([]byte(i[2].String()), &pxStr)
+	if err != nil {
+		println("error parsing pxStr from stringified json")
+	}
+	px, err := utils.ArrayStringToBigInt(pxStr)
+	if err != nil {
+		println(err.Error())
+	}
+	sj, err = json.Marshal(px)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("px", string(sj))
+
+	var inputs circuitcompiler.Inputs
+	err = json.Unmarshal([]byte(i[3].String()), &inputs)
+	if err != nil {
+		println("error parsing inputs from stringified json")
+	}
+	w, err := circuit.CalculateWitness(inputs.Private, inputs.Public)
+
+	proof, err := snark.GenerateProofs(circuit, setup.Pk, w, px)
+	if err != nil {
+		println("error generating proof", err)
+	}
+	proofString := utils.ProofToString(proof)
+	proofJson, err := json.Marshal(proofString)
+	if err != nil {
+		println("error marshal proof to json", err)
+	}
+	println("proofJson", string(proofJson))
+	return js.ValueOf(string(proofJson))
+}
+
+func verifyProofs(this js.Value, i []js.Value) interface{} {
+	var setupStr utils.SetupString
+	println(i[0].String())
+	err := json.Unmarshal([]byte(i[0].String()), &setupStr)
+	if err != nil {
+		println("error parsing setup from stringified json")
+	}
+	setup, err := utils.SetupFromString(setupStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+
+	var proofStr utils.ProofString
+	err = json.Unmarshal([]byte(i[1].String()), &proofStr)
+	if err != nil {
+		println(i[1].String())
+		println("error parsing proof from stringified json")
+	}
+	proof, err := utils.ProofFromString(proofStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+
+	var publicInputs []*big.Int
+	err = json.Unmarshal([]byte(i[2].String()), &publicInputs)
+	if err != nil {
+		println(i[2].String())
+		println("error parsing publicInputs from stringified json")
+	}
+
+	verified := snark.VerifyProof(setup.Vk, proof, publicInputs, false)
+	if err != nil {
+		println("error verifiyng proof", err)
+	}
+	verifiedJson, err := json.Marshal(verified)
+	if err != nil {
+		println("error marshal verified to json", err)
+	}
+	println("verifiedJson", string(verifiedJson))
+	return js.ValueOf(string(verifiedJson))
+}
+
+func grothGenerateProofs(this js.Value, i []js.Value) interface{} {
+	var circuitStr utils.CircuitString
+	err := json.Unmarshal([]byte(i[0].String()), &circuitStr)
+	if err != nil {
+		println(i[0].String())
+		println("error parsing circuit from stringified json")
+	}
+	circuit, err := utils.CircuitFromString(circuitStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	sj, err := json.Marshal(circuit)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("circuit", string(sj))
+
+	var setupStr utils.GrothSetupString
+	println(i[1].String())
+	err = json.Unmarshal([]byte(i[1].String()), &setupStr)
+	if err != nil {
+		println("error parsing setup from stringified json")
+	}
+	setup, err := utils.GrothSetupFromString(setupStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	sj, err = json.Marshal(setup)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("set", string(sj))
+
+	var pxStr []string
+	err = json.Unmarshal([]byte(i[2].String()), &pxStr)
+	if err != nil {
+		println("error parsing pxStr from stringified json")
+	}
+	px, err := utils.ArrayStringToBigInt(pxStr)
+	if err != nil {
+		println(err.Error())
+	}
+	sj, err = json.Marshal(px)
+	if err != nil {
+		println("error " + err.Error())
+	}
+	println("px", string(sj))
+
+	var inputs circuitcompiler.Inputs
+	err = json.Unmarshal([]byte(i[3].String()), &inputs)
+	if err != nil {
+		println("error parsing inputs from stringified json")
+	}
+	w, err := circuit.CalculateWitness(inputs.Private, inputs.Public)
+
+	proof, err := groth16.GenerateProofs(circuit, setup.Pk, w, px)
+	if err != nil {
+		println("error generating proof", err)
+	}
+	proofString := utils.GrothProofToString(proof)
+	proofJson, err := json.Marshal(proofString)
+	if err != nil {
+		println("error marshal proof to json", err)
+	}
+	println("proofJson", string(proofJson))
+	return js.ValueOf(string(proofJson))
+}
+
+func grothVerifyProofs(this js.Value, i []js.Value) interface{} {
+	var setupStr utils.GrothSetupString
+	println(i[0].String())
+	err := json.Unmarshal([]byte(i[0].String()), &setupStr)
+	if err != nil {
+		println("error parsing setup from stringified json")
+	}
+	setup, err := utils.GrothSetupFromString(setupStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+
+	var proofStr utils.GrothProofString
+	err = json.Unmarshal([]byte(i[1].String()), &proofStr)
+	if err != nil {
+		println(i[1].String())
+		println("error parsing proof from stringified json")
+	}
+	proof, err := utils.GrothProofFromString(proofStr)
+	if err != nil {
+		println("error " + err.Error())
+	}
+
+	var publicInputs []*big.Int
+	err = json.Unmarshal([]byte(i[2].String()), &publicInputs)
+	if err != nil {
+		println(i[2].String())
+		println("error parsing publicInputs from stringified json")
+	}
+
+	verified := groth16.VerifyProof(setup.Vk, proof, publicInputs, false)
+	if err != nil {
+		println("error verifiyng proof", err)
+	}
+	verifiedJson, err := json.Marshal(verified)
+	if err != nil {
+		println("error marshal verified to json", err)
+	}
+	println("verifiedJson", string(verifiedJson))
+	return js.ValueOf(string(verifiedJson))
+}

wasm/index.html

@@ -0,0 +1,20 @@
+<html>
+<head>
+	<meta charset="utf-8">
+	<title>go-snark wasm experiments</title>
+</head>
+<body>
+	<script src="wasm_exec.js"></script>
+	<script>
+		const go = new Go();
+		WebAssembly.instantiateStreaming(fetch('go-snark.wasm'), go.importObject).then(function(dat) {
+		    go.run(dat.instance);
+		});
+	</script>
+	<button onClick="callGenerateProof();">Generate Proof</button>
+	<textarea id="proofResult" rows="15" style="width: 80%;">
+	</textarea>
+	<button onClick="callVerifyProof();">Verify Proof</button>
+	<script src="index.js"></script>
+</body>
+</html>

wasm/package.json

@@ -0,0 +1,15 @@
+{
+  "name": "server",
+  "version": "1.0.0",
+  "description": "",
+  "main": "server.js",
+  "scripts": {
+    "test": "echo \"Error: no test specified\" && exit 1",
+    "start": "node server.js"
+  },
+  "author": "",
+  "license": "ISC",
+  "dependencies": {
+    "express": "^4.16.4"
+  }
+}

wasm/server.js

@@ -0,0 +1,7 @@
+var express = require('express');
+var app = express();
+express.static.mime.types['wasm'] = 'application/wasm';
+app.use(express.static(__dirname + '/'));
+port=8080
+app.listen(8080);
+console.log("server running at :8080")