diff --git a/README.md b/README.md index 58a98b2..ad8a7e5 100644 --- a/README.md +++ b/README.md @@ -4,7 +4,10 @@ Doing this to study and learn [KZG commitments](http://cacr.uwaterloo.ca/techrep Thanks to [Dankrad Feist](https://dankradfeist.de/ethereum/2020/06/16/kate-polynomial-commitments.html), [Alin Tomescu](https://alinush.github.io/2020/05/06/kzg-polynomial-commitments.html), [Tom Walton-Pocock](https://hackmd.io/@tompocock/Hk2A7BD6U) for their articles, which helped me understand a bit the KZG Commitments. +It uses the [ethereum bn256](https://github.com/ethereum/go-ethereum/tree/master/crypto/bn256/cloudflare). + ### Usage + ```go // p(x) = x^3 + x + 5 p := []*big.Int{ @@ -34,3 +37,18 @@ assert.Nil(t, err) v := Verify(ts, c, proof, z, y) assert.True(t, v) ``` + +Batch Proofs: +```go +// zs & ys contain the f(z_i)=y_i values that will be proved inside a batch proof +zs := []*big.Int{z0, z1, z2} +ys := []*big.Int{y0, y1, y2} + +// prove an evaluation of the multiple z_i & y_i +proof, err := EvaluationBatchProof(ts, p, zs, ys) +assert.Nil(t, err) + +// batch proof verification +v := VerifyBatchProof(ts, c, proof, zs, ys) +assert.True(t, v) +``` diff --git a/arithmetic.go b/arithmetic.go index 7dead6c..9696166 100644 --- a/arithmetic.go +++ b/arithmetic.go @@ -223,9 +223,9 @@ func newPolZeroAt(pointPos, totalPoints int, height *big.Int) []*big.Int { // zeroPolynomial returns the zero polynomial: // z(x) = (x - z_0) (x - z_1) ... (x - z_{k-1}) func zeroPolynomial(zs []*big.Int) []*big.Int { - z := []*big.Int{fNeg(zs[0]), big.NewInt(1)} + z := []*big.Int{fNeg(zs[0]), big.NewInt(1)} // (x - z0) for i := 1; i < len(zs); i++ { - z = polynomialMul(z, []*big.Int{fNeg(zs[i]), big.NewInt(1)}) + z = polynomialMul(z, []*big.Int{fNeg(zs[i]), big.NewInt(1)}) // (x - zi) } return z } @@ -257,7 +257,9 @@ func intToSNum(n int) string { func PolynomialToString(p []*big.Int) string { s := "" for i := len(p) - 1; i >= 1; i-- { - if !bytes.Equal(p[i].Bytes(), big.NewInt(0).Bytes()) { + if bytes.Equal(p[i].Bytes(), big.NewInt(1).Bytes()) { + s += fmt.Sprintf("x%s + ", intToSNum(i)) + } else if !bytes.Equal(p[i].Bytes(), big.NewInt(0).Bytes()) { s += fmt.Sprintf("%sx%s + ", p[i], intToSNum(i)) } } diff --git a/arithmetic_test.go b/arithmetic_test.go index 2d21080..494ee42 100644 --- a/arithmetic_test.go +++ b/arithmetic_test.go @@ -6,7 +6,6 @@ import ( "math/big" "testing" - cryptoConstants "github.com/iden3/go-iden3-crypto/constants" "github.com/stretchr/testify/assert" ) @@ -18,7 +17,7 @@ func randBI() *big.Int { panic(err) } r := new(big.Int).SetBytes(b) - return new(big.Int).Mod(r, cryptoConstants.Q) + return new(big.Int).Mod(r, Q) } func neg(a *big.Int) *big.Int { @@ -89,7 +88,7 @@ func TestPolynomial(t *testing.T) { big.NewInt(0), // x^2 big.NewInt(1), // x^3 } - assert.Equal(t, "1x³ + 1x¹ + 5", PolynomialToString(p)) + assert.Equal(t, "x³ + x¹ + 5", PolynomialToString(p)) assert.Equal(t, "35", polynomialEval(p, big.NewInt(3)).String()) assert.Equal(t, "1015", polynomialEval(p, big.NewInt(10)).String()) assert.Equal(t, "16777477", polynomialEval(p, big.NewInt(256)).String()) @@ -140,7 +139,7 @@ func TestLagrangeInterpolation(t *testing.T) { p, err := LagrangeInterpolation(xs, ys) assert.Nil(t, err) - assert.Equal(t, "1x³ + 1x¹ + 5", PolynomialToString(p)) + assert.Equal(t, "x³ + x¹ + 5", PolynomialToString(p)) assert.Equal(t, y0, polynomialEval(p, x0)) assert.Equal(t, y1, polynomialEval(p, x1)) @@ -154,7 +153,7 @@ func TestZeroPolynomial(t *testing.T) { xs := []*big.Int{x0, x1, x2} z := zeroPolynomial(xs) - assert.Equal(t, "1x³ "+ + assert.Equal(t, "x³ "+ "+ 21888242871839275222246405745257275088548364400416034343698204186575808495064x² "+ "+ 21032x¹ + 21888242871839275222246405745257275088548364400416034343698204186575808475137", PolynomialToString(z)) diff --git a/go.mod b/go.mod index 491d160..35864c5 100644 --- a/go.mod +++ b/go.mod @@ -4,6 +4,5 @@ go 1.16 require ( github.com/ethereum/go-ethereum v1.10.4 - github.com/iden3/go-iden3-crypto v0.0.5 github.com/stretchr/testify v1.7.0 ) diff --git a/go.sum b/go.sum index 7616479..7bcdfdd 100644 --- a/go.sum +++ b/go.sum @@ -35,9 +35,7 @@ github.com/BurntSushi/toml v0.3.1/go.mod h1:xHWCNGjB5oqiDr8zfno3MHue2Ht5sIBksp03 github.com/BurntSushi/xgb v0.0.0-20160522181843-27f122750802/go.mod h1:IVnqGOEym/WlBOVXweHU+Q+/VP0lqqI8lqeDx9IjBqo= github.com/DATA-DOG/go-sqlmock v1.3.3/go.mod h1:f/Ixk793poVmq4qj/V1dPUg2JEAKC73Q5eFN3EC/SaM= github.com/OneOfOne/xxhash v1.2.2/go.mod h1:HSdplMjZKSmBqAxg5vPj2TmRDmfkzw+cTzAElWljhcU= -github.com/OneOfOne/xxhash v1.2.5/go.mod h1:eZbhyaAYD41SGSSsnmcpxVoRiQ/MPUTjUdIIOT9Um7Q= github.com/StackExchange/wmi v0.0.0-20180116203802-5d049714c4a6/go.mod h1:3eOhrUMpNV+6aFIbp5/iudMxNCF27Vw2OZgy4xEx0Fg= -github.com/VictoriaMetrics/fastcache v1.5.3/go.mod h1:+jv9Ckb+za/P1ZRg/sulP5Ni1v49daAVERr0H3CuscE= github.com/VictoriaMetrics/fastcache v1.6.0/go.mod h1:0qHz5QP0GMX4pfmMA/zt5RgfNuXJrTP0zS7DqpHGGTw= github.com/aead/siphash v1.0.1/go.mod h1:Nywa3cDsYNNK3gaciGTWPwHt0wlpNV15vwmswBAUSII= github.com/ajstarks/svgo v0.0.0-20180226025133-644b8db467af/go.mod h1:K08gAheRH3/J6wwsYMMT4xOr94bZjxIelGM0+d/wbFw= @@ -46,8 +44,6 @@ github.com/alecthomas/units v0.0.0-20151022065526-2efee857e7cf/go.mod h1:ybxpYRF github.com/allegro/bigcache v1.2.1-0.20190218064605-e24eb225f156/go.mod h1:Cb/ax3seSYIx7SuZdm2G2xzfwmv3TPSk2ucNfQESPXM= github.com/andreyvit/diff v0.0.0-20170406064948-c7f18ee00883/go.mod h1:rCTlJbsFo29Kk6CurOXKm700vrz8f0KW0JNfpkRJY/8= github.com/apache/arrow/go/arrow v0.0.0-20191024131854-af6fa24be0db/go.mod h1:VTxUBvSJ3s3eHAg65PNgrsn5BtqCRPdmyXh6rAfdxN0= -github.com/aristanetworks/goarista v0.0.0-20170210015632-ea17b1a17847/go.mod h1:D/tb0zPVXnP7fmsLZjtdUhSsumbK/ij54UXjjVgMGxQ= -github.com/aws/aws-sdk-go v1.25.48/go.mod h1:KmX6BPdI08NWTb3/sm4ZGu5ShLoqVDhKgpiN924inxo= github.com/aws/aws-sdk-go-v2 v1.2.0/go.mod h1:zEQs02YRBw1DjK0PoJv3ygDYOFTre1ejlJWl8FwAuQo= github.com/aws/aws-sdk-go-v2/config v1.1.1/go.mod h1:0XsVy9lBI/BCXm+2Tuvt39YmdHwS5unDQmxZOYe8F5Y= github.com/aws/aws-sdk-go-v2/credentials v1.1.1/go.mod h1:mM2iIjwl7LULWtS6JCACyInboHirisUUdkBPoTHMOUo= @@ -61,7 +57,6 @@ github.com/beorn7/perks v0.0.0-20180321164747-3a771d992973/go.mod h1:Dwedo/Wpr24 github.com/beorn7/perks v1.0.0/go.mod h1:KWe93zE9D1o94FZ5RNwFwVgaQK1VOXiVxmqh+CedLV8= github.com/bmizerany/pat v0.0.0-20170815010413-6226ea591a40/go.mod h1:8rLXio+WjiTceGBHIoTvn60HIbs7Hm7bcHjyrSqYB9c= github.com/boltdb/bolt v1.3.1/go.mod h1:clJnj/oiGkjum5o1McbSZDSLxVThjynRyGBgiAx27Ps= -github.com/btcsuite/btcd v0.0.0-20171128150713-2e60448ffcc6/go.mod h1:Dmm/EzmjnCiweXmzRIAiUWCInVmPgjkzgv5k4tVyXiQ= github.com/btcsuite/btcd v0.20.1-beta/go.mod h1:wVuoA8VJLEcwgqHBwHmzLRazpKxTv13Px/pDuV7OomQ= github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f/go.mod h1:TdznJufoqS23FtqVCzL0ZqgP5MqXbb4fg/WgDys70nA= github.com/btcsuite/btcutil v0.0.0-20190425235716-9e5f4b9a998d/go.mod h1:+5NJ2+qvTyV9exUAL/rxXi3DcLg2Ts+ymUAY5y4NvMg= @@ -74,13 +69,11 @@ github.com/c-bata/go-prompt v0.2.2/go.mod h1:VzqtzE2ksDBcdln8G7mk2RX9QyGjH+OVqOC github.com/census-instrumentation/opencensus-proto v0.2.1/go.mod h1:f6KPmirojxKA12rnyqOA5BBL4O983OfeGPqjHWSTneU= github.com/cespare/cp v0.1.0/go.mod h1:SOGHArjBr4JWaSDEVpWpo/hNg6RoKrls6Oh40hiwW+s= github.com/cespare/xxhash v1.1.0/go.mod h1:XrSqR1VqqWfGrhpAt58auRo0WTKS1nRRg3ghfAqPWnc= -github.com/cespare/xxhash/v2 v2.0.1-0.20190104013014-3767db7a7e18/go.mod h1:HD5P3vAIAh+Y2GAxg0PrPN1P8WkepXGpjbUPDHJqqKM= github.com/cespare/xxhash/v2 v2.1.1/go.mod h1:VGX0DQ3Q6kWi7AoAeZDth3/j3BFtOZR5XLFGgcrjCOs= github.com/chzyer/logex v1.1.10/go.mod h1:+Ywpsq7O8HXn0nuIou7OrIPyXbp3wmkHB+jjWRnGsAI= github.com/chzyer/readline v0.0.0-20180603132655-2972be24d48e/go.mod h1:nSuG5e5PlCu98SY8svDHJxuZscDgtXS6KTTbou5AhLI= github.com/chzyer/test v0.0.0-20180213035817-a1ea475d72b1/go.mod h1:Q3SI9o4m/ZMnBNeIyt5eFwwo7qiLfzFZmjNmxjkiQlU= github.com/client9/misspell v0.3.4/go.mod h1:qj6jICC3Q7zFZvVWo7KLAzC3yx5G7kyvSDkc90ppPyw= -github.com/cloudflare/cloudflare-go v0.10.2-0.20190916151808-a80f83b9add9/go.mod h1:1MxXX1Ux4x6mqPmjkUgTP1CdXIBXKX7T+Jk9Gxrmx+U= github.com/cloudflare/cloudflare-go v0.14.0/go.mod h1:EnwdgGMaFOruiPZRFSgn+TsQ3hQ7C/YWzIGLeu5c304= github.com/consensys/bavard v0.1.8-0.20210406032232-f3452dc9b572/go.mod h1:Bpd0/3mZuaj6Sj+PqrmIquiOKy397AKGThQPaGzNXAQ= github.com/consensys/gnark-crypto v0.4.1-0.20210426202927-39ac3d4b3f1f/go.mod h1:815PAHg3wvysy0SyIqanF8gZ0Y1wjk/hrDHD/iT88+Q= @@ -90,27 +83,20 @@ github.com/davecgh/go-spew v0.0.0-20171005155431-ecdeabc65495/go.mod h1:J7Y8YcW2 github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38= github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c= github.com/davecgh/go-spew v1.1.1/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38= -github.com/dchest/blake512 v1.0.0/go.mod h1:FV1x7xPPLWukZlpDpWQ88rF/SFwZ5qbskrzhLMB92JI= github.com/deckarep/golang-set v0.0.0-20180603214616-504e848d77ea/go.mod h1:93vsz/8Wt4joVM7c2AVqh+YRMiUSc14yDtF28KmMOgQ= github.com/dgrijalva/jwt-go v3.2.0+incompatible/go.mod h1:E3ru+11k8xSBh+hMPgOLZmtrrCbhqsmaPHjLKYnJCaQ= github.com/dgryski/go-bitstream v0.0.0-20180413035011-3522498ce2c8/go.mod h1:VMaSuZ+SZcx/wljOQKvp5srsbCiKDEb6K2wC4+PiBmQ= github.com/dgryski/go-sip13 v0.0.0-20181026042036-e10d5fee7954/go.mod h1:vAd38F8PWV+bWy6jNmig1y/TA+kYO4g3RSRF0IAv0no= github.com/dlclark/regexp2 v1.2.0/go.mod h1:2pZnwuY/m+8K6iRw6wQdMtk+rH5tNGR1i55kozfMjCc= github.com/docker/docker v1.4.2-0.20180625184442-8e610b2b55bf/go.mod h1:eEKB0N0r5NX/I1kEveEz05bcu8tLC/8azJZsviup8Sk= -github.com/dop251/goja v0.0.0-20200219165308-d1232e640a87/go.mod h1:Mw6PkjjMXWbTj+nnj4s3QPXq1jaT0s5pC0iFD4+BOAA= github.com/dop251/goja v0.0.0-20200721192441-a695b0cdd498/go.mod h1:Mw6PkjjMXWbTj+nnj4s3QPXq1jaT0s5pC0iFD4+BOAA= github.com/eclipse/paho.mqtt.golang v1.2.0/go.mod h1:H9keYFcgq3Qr5OUJm/JZI/i6U7joQ8SYLhZwfeOo6Ts= -github.com/edsrzf/mmap-go v0.0.0-20160512033002-935e0e8a636c/go.mod h1:YO35OhQPt3KJa3ryjFM5Bs14WD66h8eGKpfaBNrHW5M= github.com/edsrzf/mmap-go v1.0.0/go.mod h1:YO35OhQPt3KJa3ryjFM5Bs14WD66h8eGKpfaBNrHW5M= -github.com/elastic/gosigar v0.8.1-0.20180330100440-37f05ff46ffa/go.mod h1:cdorVVzy1fhmEqmtgqkoE3bYtCfSCkVyjTyCIo22xvs= github.com/envoyproxy/go-control-plane v0.9.1-0.20191026205805-5f8ba28d4473/go.mod h1:YTl/9mNaCwkRvm6d1a2C3ymFceY/DCBVvsKhRF0iEA4= github.com/envoyproxy/protoc-gen-validate v0.1.0/go.mod h1:iSmxcyjqTsJpI2R4NaDN7+kN2VEUnK/pcBlmesArF7c= -github.com/ethereum/go-ethereum v1.9.12/go.mod h1:PvsVkQmhZFx92Y+h2ylythYlheEDt/uBgFbl61Js/jo= github.com/ethereum/go-ethereum v1.10.4 h1:JPZPL2MHbegfFStcaOrrggMVIcf57OQHQ0J3UhjQ+xQ= github.com/ethereum/go-ethereum v1.10.4/go.mod h1:nEE0TP5MtxGzOMd7egIrbPJMQBnhVU3ELNxhBglIzhg= -github.com/fatih/color v1.3.0/go.mod h1:Zm6kSWBoL9eyXnKyktHP6abPY2pDugNf5KwzbycvMj4= github.com/fatih/color v1.7.0/go.mod h1:Zm6kSWBoL9eyXnKyktHP6abPY2pDugNf5KwzbycvMj4= -github.com/fjl/memsize v0.0.0-20180418122429-ca190fb6ffbc/go.mod h1:VvhXpOYNQvB+uIk2RvXzuaQtkQJzzIx6lSBe1xv7hi0= github.com/fjl/memsize v0.0.0-20190710130421-bcb5799ab5e5/go.mod h1:VvhXpOYNQvB+uIk2RvXzuaQtkQJzzIx6lSBe1xv7hi0= github.com/fogleman/gg v1.2.1-0.20190220221249-0403632d5b90/go.mod h1:R/bRT+9gY/C5z7JzPU0zXsXHKM4/ayA+zqcVNZzPa1k= github.com/fsnotify/fsnotify v1.4.7/go.mod h1:jwhsz4b93w/PPRr/qN1Yymfu8t87LnFCMoQvtojpjFo= @@ -140,7 +126,6 @@ github.com/golang/mock v1.2.0/go.mod h1:oTYuIxOrZwtPieC+H1uAHpcLFnEyAGVDL/k47Jfb github.com/golang/mock v1.3.1/go.mod h1:sBzyDLLjw3U8JLTeZvSv8jJB+tU5PVekmnlKIyFUx0Y= github.com/golang/protobuf v1.2.0/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U= github.com/golang/protobuf v1.3.1/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U= -github.com/golang/protobuf v1.3.2-0.20190517061210-b285ee9cfc6c/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U= github.com/golang/protobuf v1.3.2/go.mod h1:6lQm79b+lXiMfvg/cZm0SGofjICqVBUtrP5yJMmIC1U= github.com/golang/protobuf v1.4.0-rc.1/go.mod h1:ceaxUfeHdC40wWswd/P6IGgMaK3YpKi5j83Wpe3EHw8= github.com/golang/protobuf v1.4.0-rc.1.0.20200221234624-67d41d38c208/go.mod h1:xKAWHe0F5eneWXFV3EuXVDTCmh+JuBKY0li0aMyXATA= @@ -171,26 +156,19 @@ github.com/google/uuid v1.1.5/go.mod h1:TIyPZe4MgqvfeYDBFedMoGGpEw/LqOeaOT+nhxU+ github.com/googleapis/gax-go/v2 v2.0.4/go.mod 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github.com/philhofer/fwd v1.0.0/go.mod h1:gk3iGcWd9+svBvR0sR+KPcfE+RNWozjowpeBVG3ZVNU= @@ -287,14 +259,11 @@ github.com/prometheus/common v0.4.1/go.mod h1:TNfzLD0ON7rHzMJeJkieUDPYmFC7Snx/y8 github.com/prometheus/common v0.6.0/go.mod h1:eBmuwkDJBwy6iBfxCBob6t6dR6ENT/y+J+Zk0j9GMYc= github.com/prometheus/procfs v0.0.0-20181005140218-185b4288413d/go.mod h1:c3At6R/oaqEKCNdg8wHV1ftS6bRYblBhIjjI8uT2IGk= github.com/prometheus/procfs v0.0.2/go.mod h1:TjEm7ze935MbeOT/UhFTIMYKhuLP4wbCsTZCD3I8kEA= -github.com/prometheus/tsdb v0.6.2-0.20190402121629-4f204dcbc150/go.mod h1:qhTCs0VvXwvX/y3TZrWD7rabWM+ijKTux40TwIPHuXU= github.com/prometheus/tsdb v0.7.1/go.mod h1:qhTCs0VvXwvX/y3TZrWD7rabWM+ijKTux40TwIPHuXU= github.com/retailnext/hllpp v1.0.1-0.20180308014038-101a6d2f8b52/go.mod h1:RDpi1RftBQPUCDRw6SmxeaREsAaRKnOclghuzp/WRzc= github.com/rjeczalik/notify v0.9.1/go.mod h1:rKwnCoCGeuQnwBtTSPL9Dad03Vh2n40ePRrjvIXnJho= github.com/rogpeppe/go-internal v1.3.0/go.mod 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h1:x3qojaO3uyYt0i56EW/VUYs7uBvdl2fkfZFu0T9wgjM= github.com/tyler-smith/go-bip39 v1.0.1-0.20181017060643-dbb3b84ba2ef/go.mod h1:sJ5fKU0s6JVwZjjcUEX2zFOnvq0ASQ2K9Zr6cf67kNs= -github.com/urfave/cli v1.22.1/go.mod h1:Gos4lmkARVdJ6EkW0WaNv/tZAAMe9V7XWyB60NtXRu0= github.com/urfave/cli/v2 v2.3.0/go.mod h1:LJmUH05zAU44vOAcrfzZQKsZbVcdbOG8rtL3/XcUArI= github.com/willf/bitset v1.1.3/go.mod h1:RjeCKbqT1RxIR/KWY6phxZiaY1IyutSBfGjNPySAYV4= -github.com/wsddn/go-ecdh v0.0.0-20161211032359-48726bab9208/go.mod h1:IotVbo4F+mw0EzQ08zFqg7pK3FebNXpaMsRy2RT+Ees= github.com/xlab/treeprint v0.0.0-20180616005107-d6fb6747feb6/go.mod h1:ce1O1j6UtZfjr22oyGxGLbauSBp2YVXpARAosm7dHBg= github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74= go.opencensus.io v0.21.0/go.mod h1:mSImk1erAIZhrmZN+AvHh14ztQfjbGwt4TtuofqLduU= @@ -345,7 +308,6 @@ golang.org/x/crypto v0.0.0-20190510104115-cbcb75029529/go.mod h1:yigFU9vqHzYiE8U golang.org/x/crypto v0.0.0-20190605123033-f99c8df09eb5/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI= golang.org/x/crypto v0.0.0-20190909091759-094676da4a83/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI= golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI= -golang.org/x/crypto v0.0.0-20200311171314-f7b00557c8c4/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto= golang.org/x/crypto v0.0.0-20210322153248-0c34fe9e7dc2/go.mod h1:T9bdIzuCu7OtxOm1hfPfRQxPLYneinmdGuTeoZ9dtd4= golang.org/x/exp v0.0.0-20180321215751-8460e604b9de/go.mod h1:CJ0aWSM057203Lf6IL+f9T1iT9GByDxfZKAQTCR3kQA= @@ -392,7 +354,6 @@ golang.org/x/net v0.0.0-20190613194153-d28f0bde5980/go.mod h1:z5CRVTTTmAJ677TzLL golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20190724013045-ca1201d0de80/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20191209160850-c0dbc17a3553/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= -golang.org/x/net v0.0.0-20200301022130-244492dfa37a/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s= golang.org/x/net v0.0.0-20200520004742-59133d7f0dd7/go.mod h1:qpuaurCH72eLCgpAm/N6yyVIVM9cpaDIP3A8BGJEC5A= golang.org/x/net v0.0.0-20200813134508-3edf25e44fcc/go.mod h1:/O7V0waA8r7cgGh81Ro3o1hOxt32SMVPicZroKQ2sZA= golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU= @@ -431,7 +392,6 @@ golang.org/x/sys v0.0.0-20191120155948-bd437916bb0e/go.mod h1:h1NjWce9XRLGQEsW7w golang.org/x/sys v0.0.0-20191204072324-ce4227a45e2e/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20191228213918-04cbcbbfeed8/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200107162124-548cf772de50/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= -golang.org/x/sys v0.0.0-20200302150141-5c8b2ff67527/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200323222414-85ca7c5b95cd/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200519105757-fe76b779f299/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= golang.org/x/sys v0.0.0-20200814200057-3d37ad5750ed/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs= @@ -532,7 +492,6 @@ gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127/go.mod h1:Co6ibVJAznAaIkqp8 gopkg.in/errgo.v2 v2.1.0/go.mod h1:hNsd1EY+bozCKY1Ytp96fpM3vjJbqLJn88ws8XvfDNI= gopkg.in/fsnotify.v1 v1.4.7/go.mod h1:Tz8NjZHkW78fSQdbUxIjBTcgA1z1m8ZHf0WmKUhAMys= gopkg.in/natefinch/npipe.v2 v2.0.0-20160621034901-c1b8fa8bdcce/go.mod h1:5AcXVHNjg+BDxry382+8OKon8SEWiKktQR07RKPsv1c= -gopkg.in/olebedev/go-duktape.v3 v3.0.0-20190213234257-ec84240a7772/go.mod h1:uAJfkITjFhyEEuUfm7bsmCZRbW5WRq8s9EY8HZ6hCns= gopkg.in/olebedev/go-duktape.v3 v3.0.0-20200619000410-60c24ae608a6/go.mod h1:uAJfkITjFhyEEuUfm7bsmCZRbW5WRq8s9EY8HZ6hCns= gopkg.in/tomb.v1 v1.0.0-20141024135613-dd632973f1e7/go.mod h1:dt/ZhP58zS4L8KSrWDmTeBkI65Dw0HsyUHuEVlX15mw= gopkg.in/urfave/cli.v1 v1.20.0/go.mod h1:vuBzUtMdQeixQj8LVd+/98pzhxNGQoyuPBlsXHOQNO0= diff --git a/kzg.go b/kzg.go index 1c2bbca..f182e7d 100644 --- a/kzg.go +++ b/kzg.go @@ -15,7 +15,7 @@ type TrustedSetup struct { // NewTrustedSetup returns a new trusted setup. This step should be done in a // secure & distributed way -func NewTrustedSetup(p []*big.Int) (*TrustedSetup, error) { +func NewTrustedSetup(l int) (*TrustedSetup, error) { // compute random s s, err := randBigInt() if err != nil { @@ -26,10 +26,10 @@ func NewTrustedSetup(p []*big.Int) (*TrustedSetup, error) { // τ₁: [x₀]₁, [x₁]₁, [x₂]₁, ..., [x n₋₁]₁ // τ₂: [x₀]₂, [x₁]₂, [x₂]₂, ..., [x n₋₁]₂ - // sPow := make([]*big.Int, len(p)) - tauG1 := make([]*bn256.G1, len(p)) - tauG2 := make([]*bn256.G2, len(p)) - for i := 0; i < len(p); i++ { + // sPow := make([]*big.Int, l) + tauG1 := make([]*bn256.G1, l) + tauG2 := make([]*bn256.G2, l) + for i := 0; i < l; i++ { sPow := fExp(s, big.NewInt(int64(i))) tauG1[i] = new(bn256.G1).ScalarBaseMult(sPow) tauG2[i] = new(bn256.G2).ScalarBaseMult(sPow) @@ -73,19 +73,18 @@ func EvaluationProof(ts *TrustedSetup, p []*big.Int, z, y *big.Int) (*bn256.G1, return nil, fmt.Errorf("remainder should be 0, instead is %d", rem) } - fmt.Println("q(x):", PolynomialToString(q)) // TMP DBG - // proof: e = [q(s)]₁ + // proof: e = [q(t)]₁ e := evaluateG1(ts, q) return e, nil } // Verify computes the KZG commitment verification func Verify(ts *TrustedSetup, c, proof *bn256.G1, z, y *big.Int) bool { - s2 := ts.Tau2[1] // [s]₂ = sG ∈ 𝔾₂ = Tau2[1] + s2 := ts.Tau2[1] // [t]₂ = sG ∈ 𝔾₂ = Tau2[1] zG2Neg := new(bn256.G2).Neg( new(bn256.G2).ScalarBaseMult(z)) // [z]₂ = zG ∈ 𝔾₂ - // [s]₂ - [z]₂ + // [t]₂ - [z]₂ sz := new(bn256.G2).Add(s2, zG2Neg) yG1Neg := new(bn256.G1).Neg( @@ -95,8 +94,72 @@ func Verify(ts *TrustedSetup, c, proof *bn256.G1, z, y *big.Int) bool { h := new(bn256.G2).ScalarBaseMult(big.NewInt(1)) // H ∈ 𝔾₂ - // e(proof, [s]₂ - [z]₂) == e(c - [y]₁, H) + // e(proof, [t]₂ - [z]₂) == e(c - [y]₁, H) e1 := bn256.Pair(proof, sz) e2 := bn256.Pair(cy, h) return e1.String() == e2.String() } + +// +// Batch proofs +// + +// EvaluationBatchProof generates the evalutation proof for the given list of points +func EvaluationBatchProof(ts *TrustedSetup, p []*big.Int, zs, ys []*big.Int) (*bn256.G1, error) { + if len(zs) != len(ys) { + return nil, fmt.Errorf("len(zs)!=len(ys), %d!=%d", len(zs), len(ys)) + } + if len(p) <= len(zs)+1 { + return nil, fmt.Errorf("polynomial p(x) can not be of degree"+ + " equal or smaller than the number of given points+1."+ + " Polynomial p(x) degree: %d, number of points: %d", + len(p), len(zs)) + } + + // z(x) = (x-z0)(x-z1)...(x-zn) + z := zeroPolynomial(zs) + + // I(x) = Lagrange interpolation through (z0, y0), (z1, y1), ... + i, err := LagrangeInterpolation(zs, ys) + if err != nil { + return nil, err + } + + // q(x) = ( p(x) - I(x) ) / z(x) + pMinusI := polynomialSub(p, i) + q, rem := polynomialDiv(pMinusI, z) + if compareBigIntArray(rem, arrayOfZeroes(len(rem))) { + return nil, + fmt.Errorf("remainder should be 0, instead is %d", rem) + } + + // proof: e = [q(t)]₁ + e := evaluateG1(ts, q) + return e, nil +} + +// VerifyBatchProof computes the KZG batch proof commitment verification +func VerifyBatchProof(ts *TrustedSetup, c, proof *bn256.G1, zs, ys []*big.Int) bool { + // [z(s)]₂ + z := zeroPolynomial(zs) + zG2 := evaluateG2(ts, z) // [z(t)]₂ = z(t) G ∈ 𝔾₂ + + // I(x) = Lagrange interpolation through (z0, y0), (z1, y1), ... + i, err := LagrangeInterpolation(zs, ys) + if err != nil { + return false + } + // [i(t)]₁ + iG1 := evaluateG1(ts, i) // [i(t)]₁ = i(t) G ∈ 𝔾₁ + + // c - [i(t)]₁ + iG1Neg := new(bn256.G1).Neg(iG1) + ciG1 := new(bn256.G1).Add(c, iG1Neg) + + h := new(bn256.G2).ScalarBaseMult(big.NewInt(1)) // H ∈ 𝔾₂ + + // e(proof, [z(t)]₂) == e(c - [I(t)]₁, H) + e1 := bn256.Pair(proof, zG2) + e2 := bn256.Pair(ciG1, h) + return e1.String() == e2.String() +} diff --git a/kzg_test.go b/kzg_test.go index e865e9f..694aa0c 100644 --- a/kzg_test.go +++ b/kzg_test.go @@ -15,10 +15,10 @@ func TestSimpleFlow(t *testing.T) { big.NewInt(0), // x^2 big.NewInt(1), // x^3 } - assert.Equal(t, "1x³ + 1x¹ + 5", PolynomialToString(p)) + assert.Equal(t, "x³ + x¹ + 5", PolynomialToString(p)) // TrustedSetup - ts, err := NewTrustedSetup(p) + ts, err := NewTrustedSetup(len(p)) assert.Nil(t, err) // Commit @@ -38,3 +38,67 @@ func TestSimpleFlow(t *testing.T) { v = Verify(ts, c, proof, big.NewInt(4), y) assert.False(t, v) } + +func TestBatchProof(t *testing.T) { + // p(x) = x^3 + x + 5 + p := []*big.Int{ + big.NewInt(5), + big.NewInt(1), // x^1 + big.NewInt(0), // x^2 + big.NewInt(1), // x^3 + big.NewInt(10), // x^4 + } + assert.Equal(t, "10x⁴ + x³ + x¹ + 5", PolynomialToString(p)) + + // TrustedSetup + ts, err := NewTrustedSetup(len(p)) + assert.Nil(t, err) + + // Commit + c := Commit(ts, p) + + // 1st point: p(z)=y --> p(3)=35 + z0 := big.NewInt(3) + y0 := polynomialEval(p, z0) + + // 2nd point: p(10)=1015 + z1 := big.NewInt(10) + y1 := polynomialEval(p, z1) + + // 3nd point: p(256)=16777477 + z2 := big.NewInt(256) + y2 := polynomialEval(p, z2) + + zs := []*big.Int{z0, z1, z2} + ys := []*big.Int{y0, y1, y2} + + // prove an evaluation of the multiple z_i & y_i + proof, err := EvaluationBatchProof(ts, p, zs, ys) + assert.Nil(t, err) + + // batch proof verification + v := VerifyBatchProof(ts, c, proof, zs, ys) + assert.True(t, v) + + // changing order of the points to be verified + zs[0], zs[1], zs[2] = zs[1], zs[2], zs[0] + ys[0], ys[1], ys[2] = ys[1], ys[2], ys[0] + v = VerifyBatchProof(ts, c, proof, zs, ys) + assert.True(t, v) + + // change a value of zs and check that verification fails + zs[0] = big.NewInt(2) + v = VerifyBatchProof(ts, c, proof, zs, ys) + assert.False(t, v) + + // using a value that is not in the evaluation proof should generate a + // proof that will not correctly be verified + zs = []*big.Int{z0, z1, z2} + ys = []*big.Int{y0, y1, y2} + proof, err = EvaluationBatchProof(ts, p, zs, ys) + assert.Nil(t, err) + zs[2] = big.NewInt(2500) + ys[2] = polynomialEval(p, zs[2]) + v = VerifyBatchProof(ts, c, proof, zs, ys) + assert.False(t, v) +}