Add Tree Circom Verifier Proofs

Circom Verifier Proofs allow to verify through a zkSNARK proof the
inclusion/exclusion of a leaf in a tree. This commit adds the needed
code in go to generate the circuit inputs for a CircomVerifierProof.

circomproofs_test.go

@@ -0,0 +1,63 @@
+package arbo
+
+import (
+	"encoding/json"
+	"math/big"
+	"testing"
+
+	qt "github.com/frankban/quicktest"
+	"go.vocdoni.io/dvote/db"
+)
+
+func TestCircomVerifierProof(t *testing.T) {
+	c := qt.New(t)
+	database, err := db.NewBadgerDB(c.TempDir())
+	c.Assert(err, qt.IsNil)
+	tree, err := NewTree(database, 4, HashFunctionPoseidon)
+	c.Assert(err, qt.IsNil)
+	defer tree.db.Close() //nolint:errcheck
+
+	bLen := tree.HashFunction().Len()
+
+	testVector := [][]int64{
+		{1, 11},
+		{2, 22},
+		{3, 33},
+		{4, 44},
+	}
+	for i := 0; i < len(testVector); i++ {
+		k := BigIntToBytes(bLen, big.NewInt(testVector[i][0]))
+		v := BigIntToBytes(bLen, big.NewInt(testVector[i][1]))
+		if err := tree.Add(k, v); err != nil {
+			t.Fatal(err)
+		}
+	}
+
+	// proof of existence
+	k := BigIntToBytes(bLen, big.NewInt(int64(2)))
+	cvp, err := tree.GenerateCircomVerifierProof(k)
+	c.Assert(err, qt.IsNil)
+	jCvp, err := json.Marshal(cvp)
+	c.Assert(err, qt.IsNil)
+	// test vector checked with a circom circuit (arbo/testvectors/circom)
+	c.Assert(string(jCvp), qt.Equals, `{"fnc":0,"isOld0":"0","key":"2","oldK`+
+		`ey":"0","oldValue":"0","root":"1355816845522055904274785395894906304622`+
+		`6645447188878859760119761585093422436","siblings":["1162013050763544193`+
+		`2056895853942898236773847390796721536119314875877874016518","5158240518`+
+		`874928563648144881543092238925265313977134167935552944620041388700","0"`+
+		`,"0"],"value":"22"}`)
+
+	// proof of non-existence
+	k = BigIntToBytes(bLen, big.NewInt(int64(5)))
+	cvp, err = tree.GenerateCircomVerifierProof(k)
+	c.Assert(err, qt.IsNil)
+	jCvp, err = json.Marshal(cvp)
+	c.Assert(err, qt.IsNil)
+	// test vector checked with a circom circuit (arbo/testvectors/circom)
+	c.Assert(string(jCvp), qt.Equals, `{"fnc":1,"isOld0":"0","key":"5","oldK`+
+		`ey":"1","oldValue":"11","root":"135581684552205590427478539589490630462`+
+		`26645447188878859760119761585093422436","siblings":["756056982086999933`+
+		`1905412009838015295115276841209205575174464206730109811365","1276103081`+
+		`3800436751877086580591648324911598798716611088294049841213649313596","0`+
+		`","0"],"value":"11"}`)
+}