github.com/incognitochain/go-incognito-sdk@v1.0.1/privacy/curve25519/edwards25519_test.go

// Copyright 2017-2018 DERO Project. All rights reserved.
// Use of this source code in any form is governed by RESEARCH license.
// license can be found in the LICENSE file.
// GPG: 0F39 E425 8C65 3947 702A  8234 08B2 0360 A03A 9DE8
//
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

package curve25519

import (
	"crypto/subtle"
	"os"
)
import "runtime/pprof"
import "crypto/rand"
import "testing"

func TestScMulSub(t *testing.T) {
	tests := []struct {
		name    string
		aHex    string
		bHex    string
		cHex    string
		wantHex string
	}{
		{
			name:    "simple",
			aHex:    "0100000000000000000000000000000000000000000000000000000000000000",
			bHex:    "0100000000000000000000000000000000000000000000000000000000000000",
			cHex:    "0200000000000000000000000000000000000000000000000000000000000000",
			wantHex: "0100000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:    "more complex",
			aHex:    "1000000000000000000000000000000000000000000000000000000000000000",
			bHex:    "1000000000000000000000000000000000000000000000000000000000000000",
			cHex:    "0002000000000000000000000000000000000000000000000000000000000000",
			wantHex: "0001000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:    "more complex",
			aHex:    "0000000000000000000000000000000000000000000000000000000000000010",
			bHex:    "0000000000000000000000000000000000000000000000000000000000000010",
			cHex:    "0000000000000000000000000000000000000000000000000000000000000000",
			wantHex: "844ae3b1946c2475b8f95e806867dbac410ae82d8c1331c265cf83e4be664c0e",
		},
	}
	for _, test := range tests {
		a := HexToKey(test.aHex)
		b := HexToKey(test.bHex)
		c := HexToKey(test.cHex)
		want := HexToKey(test.wantHex)
		var got Key
		ScMulSub(&got, &a, &b, &c)
		if want != got {
			t.Errorf("%s: want %x, got %x", test.name, want, got)
		}
	}
}

func TestScalarMult(t *testing.T) {
	tests := []struct {
		name      string
		scalarHex string
		pointHex  string
		wantHex   string
	}{
		{
			name:      "zero",
			scalarHex: "0000000000000000000000000000000000000000000000000000000000000000",
			pointHex:  "0100000000000000000000000000000000000000000000000000000000000000",
			wantHex:   "0100000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:      "basepoint * 1",
			scalarHex: "0100000000000000000000000000000000000000000000000000000000000000",
			pointHex:  "5866666666666666666666666666666666666666666666666666666666666666",
			wantHex:   "5866666666666666666666666666666666666666666666666666666666666666",
		},
		{
			name:      "basepoint * 8",
			scalarHex: "0800000000000000000000000000000000000000000000000000000000000000",
			pointHex:  "5866666666666666666666666666666666666666666666666666666666666666",
			wantHex:   "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
		{
			name:      "basepoint * 2",
			scalarHex: "0200000000000000000000000000000000000000000000000000000000000000",
			pointHex:  "2f1132ca61ab38dff00f2fea3228f24c6c71d58085b80e47e19515cb27e8d047",
			wantHex:   "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
	}
	for _, test := range tests {
		scalarBytes := HexToKey(test.scalarHex)
		pointBytes := HexToKey(test.pointHex)
		want := HexToKey(test.wantHex)
		point := new(ExtendedGroupElement)
		point.FromBytes(&pointBytes)
		result := new(ProjectiveGroupElement)
		GeScalarMult(result, &scalarBytes, point)
		var got Key
		point.ToBytes(&got)

		if got != pointBytes {
			t.Fatalf("%s: want %s, got %s point testing failed", test.name, pointBytes, got)
		}

		result.ToBytes(&got)

		if want != got {
			t.Fatalf("%s: want %s, got %s", test.name, want, got)
		}
	}
}

func TestMultiScalarMultKey(t *testing.T) {
	for i := 0; i < 100; i++ {
		len := 64
		scalarLs := make([]*Key, len)
		pointLs := make([]*Key, len)

		for j:=0; j <len; j++ {
			scalarLs[j] = RandomScalar()
			pointLs[j] = RandomPubKey()

		}

		res := ScalarMultKey(pointLs[0],scalarLs[0])

		for j:= 1; j < len; j++ {
			tmp := ScalarMultKey(pointLs[j],scalarLs[j])
			AddKeys(res, res, tmp)
		}

		resultPrime := MultiScalarMultKey(pointLs, scalarLs)
		ok := subtle.ConstantTimeCompare(res.MarshalText(), resultPrime.MarshalText()) == 1
		if !ok {
			t.Fatalf("expected Multi Scalar Mul correct !")
		}
	}
}

func BenchmarkMultiScalarMultKey(b *testing.B) {
	len := 64
	scalarLs := make([]*Key, len)
	pointLs := make([]*Key, len)

	for j:=0; j <len; j++ {
		scalarLs[j] = RandomScalar()
		pointLs[j] = RandomPubKey()

	}

	b.ResetTimer()

	for i:=0; i< b.N; i++ {

		MultiScalarMultKey(pointLs, scalarLs)
	}
}
//
//func TestMultiScalarMultKey(t *testing.T) {
//	len := 64
//	scalarLs := make([]*Key, len)
//	pointLs := make([]*ExtendedGroupElement, len)
//	resultProjLs := make([]*ProjectiveGroupElement, len)
//	resultKeyLs := make([]*Key, len)
//	result := new(Key)
//
//	scalarLs[0] = RandomScalar()
//	pointLs[0] = new(ExtendedGroupElement)
//	GeScalarMultBase(pointLs[0],scalarLs[0])
//	resultProjLs[0] = new(ProjectiveGroupElement)
//	GeScalarMult(resultProjLs[0],scalarLs[0], pointLs[0])
//	resultProjLs[0].ToBytes(result)
//
//	for i := 1; i< len; i ++ {
//		scalarLs[i] = RandomScalar()
//		pointLs[i] = new(ExtendedGroupElement)
//		GeScalarMultBase(pointLs[i],scalarLs[i])
//		resultProjLs[i] = new(ProjectiveGroupElement)
//		GeScalarMult(resultProjLs[i],scalarLs[i], pointLs[i])
//		resultKeyLs[i] = new(Key)
//		resultProjLs[i].ToBytes(resultKeyLs[i])
//		AddKeys(result, result, resultKeyLs[i])
//	}
//
//	fmt.Println(result)
//
//	resultPrime := new(ProjectiveGroupElement)
//	GeMultiScalarMult(resultPrime, scalarLs, pointLs)
//
//	resultPrimeKey := new(Key)
//	resultPrime.ToBytes(resultPrimeKey)
//	fmt.Println(resultPrimeKey)
//}

func TestGeMul8(t *testing.T) {
	tests := []struct {
		name     string
		pointHex string
		wantHex  string
	}{
		{
			name:     "zero",
			pointHex: "0100000000000000000000000000000000000000000000000000000000000000",
			wantHex:  "0100000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:     "basepoint",
			pointHex: "5866666666666666666666666666666666666666666666666666666666666666",
			wantHex:  "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
	}
	for _, test := range tests {
		pointBytes := HexToKey(test.pointHex)
		want := HexToKey(test.wantHex)
		tmp := new(ExtendedGroupElement)
		tmp.FromBytes(&pointBytes)
		point := new(ProjectiveGroupElement)
		tmp.ToProjective(point)
		tmp2 := new(CompletedGroupElement)
		result := new(ExtendedGroupElement)
		var got Key
		GeMul8(tmp2, point)
		tmp2.ToExtended(result)
		result.ToBytes(&got)
		if want != got {
			t.Errorf("%s: want %x, got %x", test.name, want, got)
		}
	}
}

func TestGeDoubleScalarMultVartime(t *testing.T) {
	tests := []struct {
		name       string
		pointHex   string
		scalar1Hex string
		scalar2Hex string
		wantHex    string
	}{
		{
			name:       "zero",
			pointHex:   "0100000000000000000000000000000000000000000000000000000000000000",
			scalar1Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "0100000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:       "8 times base point only",
			pointHex:   "0100000000000000000000000000000000000000000000000000000000000000",
			scalar1Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0800000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
		{
			name:       "2 times non-base-point",
			pointHex:   "2f1132ca61ab38dff00f2fea3228f24c6c71d58085b80e47e19515cb27e8d047",
			scalar1Hex: "0200000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
		{
			name:       "Combination",
			pointHex:   "2f1132ca61ab38dff00f2fea3228f24c6c71d58085b80e47e19515cb27e8d047",
			scalar1Hex: "0100000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0400000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
	}
	for _, test := range tests {
		pointBytes := HexToKey(test.pointHex)
		a := HexToKey(test.scalar1Hex)
		b := HexToKey(test.scalar2Hex)
		want := HexToKey(test.wantHex)
		point := new(ExtendedGroupElement)
		point.FromBytes(&pointBytes)
		result := new(ProjectiveGroupElement)
		GeDoubleScalarMultVartime(result, &a, point, &b)
		var got Key
		result.ToBytes(&got)
		if want != got {
			t.Errorf("%s: want %x, got %x", test.name, want, got)
		}
	}
}

func TestGeDoubleScalarMultPrecompVartime(t *testing.T) {
	tests := []struct {
		name       string
		point1Hex  string
		point2Hex  string
		scalar1Hex string
		scalar2Hex string
		wantHex    string
	}{
		{
			name:       "zero",
			point1Hex:  "0100000000000000000000000000000000000000000000000000000000000000",
			point2Hex:  "0100000000000000000000000000000000000000000000000000000000000000",
			scalar1Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "0100000000000000000000000000000000000000000000000000000000000000",
		},
		{
			name:       "scalar 1 only",
			point1Hex:  "5866666666666666666666666666666666666666666666666666666666666666",
			point2Hex:  "0100000000000000000000000000000000000000000000000000000000000000",
			scalar1Hex: "0800000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
		{
			name:       "scalar 2 only",
			point1Hex:  "0100000000000000000000000000000000000000000000000000000000000000",
			point2Hex:  "5866666666666666666666666666666666666666666666666666666666666666",
			scalar1Hex: "0000000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0800000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
		{
			name:       "Combination",
			point1Hex:  "2f1132ca61ab38dff00f2fea3228f24c6c71d58085b80e47e19515cb27e8d047",
			point2Hex:  "5866666666666666666666666666666666666666666666666666666666666666",
			scalar1Hex: "0100000000000000000000000000000000000000000000000000000000000000",
			scalar2Hex: "0400000000000000000000000000000000000000000000000000000000000000",
			wantHex:    "b4b937fca95b2f1e93e41e62fc3c78818ff38a66096fad6e7973e5c90006d321",
		},
	}
	for _, test := range tests {
		point1Bytes := HexToKey(test.point1Hex)
		point2Bytes := HexToKey(test.point2Hex)
		a := HexToKey(test.scalar1Hex)
		b := HexToKey(test.scalar2Hex)
		want := HexToKey(test.wantHex)
		point1 := new(ExtendedGroupElement)
		point1.FromBytes(&point1Bytes)
		point2 := new(ExtendedGroupElement)
		point2.FromBytes(&point2Bytes)
		var point2Precomp [8]CachedGroupElement
		GePrecompute(&point2Precomp, point2)
		result := new(ProjectiveGroupElement)
		GeDoubleScalarMultPrecompVartime(result, &a, point1, &b, &point2Precomp)
		var got Key
		result.ToBytes(&got)
		if want != got {
			t.Errorf("%s: want %x, got %x", test.name, want, got)
		}
	}
}

func TestScValid(t *testing.T) {
	// All tests from github.com/monero-project/monero/tests/crypto/tests.txt
	tests := []struct {
		scalarHex string
		valid     bool
	}{
		{
			scalarHex: "ac10e070c8574ef374bdd1c5dbe9bacfd927f9ae0705cf08018ff865f6092d0f",
			valid:     true,
		},
		{
			scalarHex: "fa939388e8cb0ffc5c776cc517edc2a9457c11a89820a7bee91654ce2e2fb300",
			valid:     true,
		},
		{
			scalarHex: "6d728f89e567522dffe81cf641c2e483e2cee7051c1b3cd9cd38cba09d2dc900",
			valid:     true,
		},
		{
			scalarHex: "18fd66f7a0874de792f12a1b2add7d294100ea454537ae5794d0abc91dbf098a",
			valid:     false,
		},
		{
			scalarHex: "fdb4cee00230c448aeaa4790dd12e855eca6223d81dab6bfe3fe99ce5e702325",
			valid:     false,
		},
		{
			scalarHex: "f3ab5c4a64f9afbd48c75ad25700996a69504d31c75a6aa8beb24d178cfc32ba",
			valid:     false,
		},
		{
			scalarHex: "167e88e9298926ecd66d32a890148a9adcfb80a7ecc69396edc5f5ee8848ce91",
			valid:     false,
		},
		{
			scalarHex: "a9172ced17605ab2ba82caec382f1176fe6a1e0b92a9c95679978b3999d22605",
			valid:     true,
		},
		{
			scalarHex: "44f65ce00e64cf29e07bf3843e8e43e83b8b26d3dfcd83160d9a3fedda3fc908",
			valid:     true,
		},
		{
			scalarHex: "69951c807647f4dea33f8a40b0ddef999a9e8efd1b1b176f45fb92aae6287000",
			valid:     true,
		},
		{
			scalarHex: "dcb6f94312b4b815101af10775d189301d063816b0aa9b9ac028c0eb9b17dd0e",
			valid:     true,
		},
		{
			scalarHex: "a1a9574a90bed7f58bfd4c3295e181e152a4a39f9ad56520947e94fea40dfe2e",
			valid:     false,
		},
		{
			scalarHex: "757ebb27b14433f3ed696cd291825eba555af0863862216a98cf3080432bda01",
			valid:     true,
		},
		{
			scalarHex: "a7401d68c7956d41a05d8c6c1a3cc692cc269ad8a5837f93ac2c7654abaebf0e",
			valid:     true,
		},
		{
			scalarHex: "7c84ef4d9627529723f5e171a88bba91118192e6e19929204a6d23f5a541850b",
			valid:     true,
		},
		{
			scalarHex: "ebe4b2f9eadd52271e1115aa3b89b7bb3f68d58bf74d75486b77e6ae8216f609",
			valid:     true,
		},
		{
			scalarHex: "6221caf5dfd623587ca7aac45f5312faf1c2847d7bfbc5c46f88fd933970c866",
			valid:     false,
		},
		{
			scalarHex: "b38334b41f0b829bf3a2ea73b58c16afb56ccba5144668e78257ed4aa9a33a5e",
			valid:     false,
		},
		{
			scalarHex: "92e5df37f5412d9e9910cd28d27138ba46bdd4dee5dab1125f200f0a4e66f01c",
			valid:     false,
		},
		{
			scalarHex: "2d1717fe2965133009bdcf0c13b02ca85df4dc23d969d7b16fdab94341c2b90e",
			valid:     true,
		},
		{
			scalarHex: "82d771565024cf4b5c9add6d10a4114a2fbdbf7626f03749c8bddcf6c6feee03",
			valid:     true,
		},
		{
			scalarHex: "2db0f3d9bf47666bb40ae25ef7508296af2ef665a5333efff92c9daee5ecd986",
			valid:     false,
		},
		{
			scalarHex: "47883a3f0b0e624512887f3dae6f401b2f02eb8950eb8e741f07347108fbea14",
			valid:     false,
		},
		{
			scalarHex: "dae25f27f2756b8270f78015b1beafbd03a8d67a4dd940ee9550cecae9f3560f",
			valid:     true,
		},
		{
			scalarHex: "bab79d355572361259484ca77308943b7c71f5831be5dde11b3c7a26ac6e9a01",
			valid:     true,
		},
		{
			scalarHex: "f0bf30a9862d51fd8d1ca3a4e5a0e4330a5beab751af075b2e46f3e2d0297101",
			valid:     true,
		},
		{
			scalarHex: "a94270659333c985ab1461e9820f219416ad76f551a34f4c983ca967aa6b618c",
			valid:     false,
		},
		{
			scalarHex: "98e582e9d0e485e6b756e44b1cb187e9f2d4e16c02d2713a41dcee6d7fac0205",
			valid:     true,
		},
		{
			scalarHex: "62b57869238e72f05992e01f07c7a26c71ef9e3078ee7390cd4fc6406d3b37e3",
			valid:     false,
		},
		{
			scalarHex: "c751566f5420232cd626d2bd8073debedf219a0a28a7390200a2df9df8981647",
			valid:     false,
		},
		{
			scalarHex: "cfafede7d76def164bf15047a388365d712a600f1369bf692cb2dcb249f66508",
			valid:     true,
		},
		{
			scalarHex: "c0eb03c2c46a77b0cf67bea7d547b9b4d02116f70702790398bdabbfa775100a",
			valid:     true,
		},
		{
			scalarHex: "58c5afbb7b334e921bb46eeee1dfebadfbbc3a77c420b0b325b9470eff94cc0e",
			valid:     true,
		},
		{
			scalarHex: "b31b178b4dc8f7a7c24f6eb0987e32b8a9446ce8207186259074cc3d925c530d",
			valid:     true,
		},
		{
			scalarHex: "467b2c5f63120744b5aee7ec255d170aba83babdec9e76c2690300540eb17483",
			valid:     false,
		},
		{
			scalarHex: "9bc3be487bea81da020af0353660878e7deca693ac81278fac343b8b1809bd9c",
			valid:     false,
		},
		{
			scalarHex: "162cdb42f9d9147118537cc4d5eadb8f589f6de3929188f6c41428bdab2c650e",
			valid:     true,
		},
		{
			scalarHex: "6eeb88f685d1b5c99f8c27dcadf95f5bea9082e2735a4f8aafc3c3a35f749002",
			valid:     true,
		},
		{
			scalarHex: "e03bb5c9bedc41d324ca6d988e50b7e7c6cd6d2b1e471b752a00a10a19c9a604",
			valid:     true,
		},
		{
			scalarHex: "4fa064dcef2f14fc453c30865583468ad35af81c460a643b11285c15f2babb04",
			valid:     true,
		},
		{
			scalarHex: "bf067a7b53dab7fcd6a1f5a2c8b9b54c262e9be5ea5892dba5e4ad25585be702",
			valid:     true,
		},
		{
			scalarHex: "14d8d255c2156bb12133d5ee792061a21d3fbda2f14310753f3a90c2ad4ccbc8",
			valid:     false,
		},
		{
			scalarHex: "81e78a37b7e2dfed35ad8228a6c4a6f0aa34cc1de43da23895c5c86790804e01",
			valid:     true,
		},
		{
			scalarHex: "62366805970fb07b877bf1705d9c10517c6667ab7586d9afa82c30236a72f50f",
			valid:     true,
		},
		{
			scalarHex: "bb3b0e27b7c57052e5ac20bc6390229f57c6dbc8213dbc4ee1cbb9e174e389f9",
			valid:     false,
		},
		{
			scalarHex: "5c4039f162531ce9129667ed424446ef375a18da246a72c0dab00321fa04e929",
			valid:     false,
		},
		{
			scalarHex: "8d41a450d98a6f354266e36510921649e5229412976f8f318a3090d390a46807",
			valid:     true,
		},
		{
			scalarHex: "2fbce4441723379b8b6ef417803eb9220c8fee42f72da7e36e2c64b51628a10c",
			valid:     true,
		},
		{
			scalarHex: "5bbf0e5b58e3df89a5f4c607e3033fff8b9643fc900813f4ea50b889260bb004",
			valid:     true,
		},
		{
			scalarHex: "e5acfcb2ecb7175f90aa24db107cea1be7a45bc471c4c65b9f46535768545de5",
			valid:     false,
		},
		{
			scalarHex: "fae6e8d7226e6dc25faafdd8b5c63b68587980f6e76ea59b8595f18f64a96bd5",
			valid:     false,
		},
		{
			scalarHex: "6736f7939157ccee066a40056c13d96230ca5ffd014b0ebb0a454e3d8ea6830f",
			valid:     true,
		},
		{
			scalarHex: "b2b490d52f6e4d9ef14fc1ab3e1e97160693ba5d1220e4d63956eca316693504",
			valid:     true,
		},
		{
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		{
			scalarHex: "ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "eeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "efffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f0ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f2ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f3ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f4ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f5ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f6ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f8ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "f9ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "faffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "fbffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "fcffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "fdffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
		{
			scalarHex: "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
			valid:     false,
		},
	}
	for _, test := range tests {
		scalar := HexToKey(test.scalarHex)
		got := ScValid(&scalar)
		if test.valid != got {
			t.Errorf("%x: want %t, got %t", scalar, test.valid, got)
		}
	}
}

func TestAddKeys3_3(t *testing.T) {

	for i := 0; i < 1000; i++ {
		s1 := *(RandomScalar())
		s2 := *(RandomScalar()) //*(identity()) // *(RandomScalar())

		p1 := s1.PublicKey()
		p2 := s2.PublicKey()

		first_part := ScalarMultKey(p1, &s1)
		second_part := ScalarMultKey(p2, &s2)

		// do it traditional way
		var sum_result Key
		AddKeys(&sum_result, first_part, second_part)

		// lets do it optimal way, pre compute
		var p1_extended, p2_extended ExtendedGroupElement
		var p1_precomputed, p2_precomputed [8]CachedGroupElement

		p1_extended.FromBytes(p1)
		p2_extended.FromBytes(p2)

		GePrecompute(&p1_precomputed, &p1_extended)
		GePrecompute(&p2_precomputed, &p2_extended)

		var fast_result Key
		AddKeys3_3(&fast_result, &s1, &p1_precomputed, &s2, &p2_precomputed)

		if sum_result != fast_result {
			t.Fatalf("AddKeys3_3 Failed Expected %s Actual %s", sum_result, fast_result)
		}
	}

}

func TestElements(t *testing.T) {

	for i := 0; i < 100; i++ {
		p1 := *(RandomScalar()).PublicKey()
		p2 := *(RandomScalar()).PublicKey()

		var exp1, exp2 ExtendedGroupElement
		var cached CachedGroupElement
		var precomputed PreComputedGroupElement
		var actual, naive, fast Key
		var tmpe ExtendedGroupElement

		exp1.FromBytes(&p1)
		exp2.FromBytes(&p2)

		//original
		AddKeys(&actual, &p1, &p2)

		// naive
		var r CompletedGroupElement
		exp2.ToCached(&cached)
		geAdd(&r, &exp1, &cached)
		r.ToExtended(&tmpe)
		tmpe.ToBytes(&naive)

		if actual != naive {
			t.Fatalf("Naive addition failed")
		}

		exp2.ToPreComputed(&precomputed)
		geMixedAdd(&r, &exp1, &precomputed)
		r.ToExtended(&tmpe)
		tmpe.ToBytes(&fast)

		if actual != fast {
			t.Fatalf("Fast addition failed")
		}
	}
}

func TestPrecompute(t *testing.T) {

	var table PRECOMPUTE_TABLE

	s1 := *(RandomScalar())
	//p1 := &GBASE //identity() // s1.PublicKey()
	p1 := s1.PublicKey()

	GenPrecompute(&table, *p1)

	//s1[1]=29

	expected := ScalarMultKey(p1, &s1)

	var actual Key

	var result_extended ExtendedGroupElement
	ScalarMultPrecompute(&result_extended, &s1, &table)

	result_extended.ToBytes(&actual)

	//t.Logf("Super compute Expected %s actual %s", expected,actual)

	if actual != *expected {
		t.Logf("Super compute failed Expected %s actual %s", expected, actual)
	}

}

func TestSuperPrecompute(t *testing.T) {
	var table PRECOMPUTE_TABLE
	var stable SUPER_PRECOMPUTE_TABLE

	s1 := *(RandomScalar())
	p1 := s1.PublicKey()

	GenPrecompute(&table, *p1)
	GenSuperPrecompute(&stable, &table)

	//s1[1]=29

	expected := ScalarMultKey(p1, &s1)

	var actual Key

	var result_extended ExtendedGroupElement
	ScalarMultSuperPrecompute(&result_extended, &s1, &stable)

	result_extended.ToBytes(&actual)

	//t.Logf("Super compute Expected %s actual %s", expected,actual)

	if actual != *expected {
		t.Logf("Super compute failed Expected %s actual %s", expected, actual)
	}

}

func Test_DoubleScalarDoubleBaseMulPrecomputed(t *testing.T) {

	var ex ExtendedGroupElement

	s1 := *(RandomScalar())
	s2 := *(RandomScalar()) //*(RandomScalar()) //*(identity()) // *(RandomScalar())

	p1 := s1.PublicKey()
	p2 := s2.PublicKey()

	first_part := ScalarMultKey(p1, &s1)
	second_part := ScalarMultKey(p2, &s2)

	// do it traditional way
	var sum_result Key
	var actual Key
	AddKeys(&sum_result, first_part, second_part)

	// lets do it using precomputed tables
	var table PRECOMPUTE_TABLE

	GenDoublePrecompute(&table, *p1, *p2)

	/*
	   multprecompscalar(&ex,&s1)


	   ex.ToBytes(&actual)

	   if *first_part != actual{

	   	//t.Logf("%+v table ", table)
	   	t.Fatalf("simple scalar precompyed failed  expected %s  actual %s", sum_result,actual)
	   }
	*/

	DoubleScalarDoubleBaseMulPrecomputed(&ex, &s1, &s2, &table)
	ex.ToBytes(&actual)

	//  t.Logf("first part %s", first_part)
	//  t.Logf("second_part part %s", second_part)
	//  t.Logf("actual %s expected %s", actual,sum_result)

	if sum_result != actual {

		//t.Logf("%+v table ", table)
		t.Fatalf("Double scalar precompyed failed %s %s", sum_result, actual)
	}

}

func BenchmarkDoublePrecompute(b *testing.B) {
	var table PRECOMPUTE_TABLE

	s1 := *(identity()) //  *(RandomScalar())
	s2 := *(identity()) //*(RandomScalar()) //*(identity()) // *(RandomScalar())

	p1 := identity() //s1.PublicKey()
	p2 := s2.PublicKey()

	GenDoublePrecompute(&table, *p1, *p2)

	cpufile, err := os.Create("/tmp/dprecompute_cpuprofile.prof")
	if err != nil {

	}
	if err := pprof.StartCPUProfile(cpufile); err != nil {
	}
	defer pprof.StopCPUProfile()

	var result_extended ExtendedGroupElement
	result_extended.Zero() // make it identity

	b.ResetTimer()

	for i := 0; i < b.N; i++ {
		DoubleScalarDoubleBaseMulPrecomputed(&result_extended, &s1, &s2, &table)

	}
}

// test 64 bit version used for bulletproofs
func Test_DoubleScalarDoubleBaseMulPrecomputed64(t *testing.T) {

	var s1, s2 [64]Key
	var p1, p2 [64]Key

	for i := 0; i < 64; i++ {
		s1[i] = *(RandomScalar())
		s2[i] = *(RandomScalar()) //*(RandomScalar()) //*(identity()) // *(RandomScalar())

		p1[i] = *(s1[i].PublicKey())
		p2[i] = *(s2[i].PublicKey())

	}

	// compute actual result using naive method
	naive_result := Identity
	for i := 0; i < 64; i++ {

		first_part := ScalarMultKey(&p1[i], &s1[i])
		second_part := ScalarMultKey(&p2[i], &s2[i])

		// do it traditional way
		var sum_result Key
		AddKeys(&sum_result, first_part, second_part)
		AddKeys(&naive_result, &naive_result, &sum_result)

	}

	// lets do it using precomputed tables
	var table [64]PRECOMPUTE_TABLE
	for i := 0; i < 64; i++ {
		GenDoublePrecompute(&table[i], p1[i], p2[i])
	}

	var ex ExtendedGroupElement
	var actual Key
	DoubleScalarDoubleBaseMulPrecomputed64(&ex, s1[:], s2[:], table[:])

	ex.ToBytes(&actual)

	//  t.Logf("first part %s", first_part)
	//  t.Logf("second_part part %s", second_part)
	//  t.Logf("actual %s expected %s", actual,sum_result)

	if naive_result != actual {

		//t.Logf("%+v table ", table)
		t.Fatalf("Double scalar precomputed 64 failed  expected %s actual %s", naive_result, actual)
	}

}

// test 64 bit version used for bulletproofs
func Benchmark_DoubleScalarDoubleBaseMulPrecomputed64(b *testing.B) {

	var s1, s2 [64]Key
	var p1, p2 [64]Key

	for i := 0; i < 64; i++ {
		s1[i] = *(RandomScalar())
		s2[i] = *(RandomScalar()) //*(RandomScalar()) //*(identity()) // *(RandomScalar())

		p1[i] = *(s1[i].PublicKey())
		p2[i] = *(s2[i].PublicKey())

	}

	// compute actual result using naive method
	naive_result := Identity
	for i := 0; i < 64; i++ {

		first_part := ScalarMultKey(&p1[i], &s1[i])
		second_part := ScalarMultKey(&p2[i], &s2[i])

		// do it traditional way
		var sum_result Key
		AddKeys(&sum_result, first_part, second_part)
		AddKeys(&naive_result, &naive_result, &sum_result)

	}

	// lets do it using precomputed tables
	var table [64]PRECOMPUTE_TABLE
	for i := 0; i < 64; i++ {
		GenDoublePrecompute(&table[i], p1[i], p2[i])
	}

	var ex ExtendedGroupElement
	var actual Key

	b.ResetTimer()

	for i := 0; i < b.N; i++ {
		DoubleScalarDoubleBaseMulPrecomputed64(&ex, s1[:], s2[:], table[:])

		ex.ToBytes(&actual)

		//  t.Logf("first part %s", first_part)
		//  t.Logf("second_part part %s", second_part)
		//  t.Logf("actual %s expected %s", actual,sum_result)

		if naive_result != actual {

			//t.Logf("%+v table ", table)
			b.Fatalf("Double scalar precomputed 64 failed  expected %s actual %s", naive_result, actual)
		}
	}

}

func BenchmarkPrecompute(b *testing.B) {
	var table PRECOMPUTE_TABLE

	GenPrecompute(&table, GBASE)

	s1 := *(RandomScalar())
	//s1[1]=29

	/*
	   	cpufile,err := os.Create("/tmp/precompute_cpuprofile.prof")
	   			if err != nil{

	   			}
	   			if err := pprof.StartCPUProfile(cpufile); err != nil {
	               }
	           	defer pprof.StopCPUProfile()

	*/

	var result_extended ExtendedGroupElement
	result_extended.Zero() // make it identity

	b.ResetTimer()

	for i := 0; i < b.N; i++ {
		result_extended.Zero() // make it identity

		ScalarMultPrecompute(&result_extended, &s1, &table)

	}
}

func BenchmarkSuperPrecompute(b *testing.B) {
	var table PRECOMPUTE_TABLE
	var stable SUPER_PRECOMPUTE_TABLE

	GenPrecompute(&table, GBASE)
	GenSuperPrecompute(&stable, &table)

	s1 := *(RandomScalar())
	//s1[1]=29

	/*
	   	cpufile,err := os.Create("/tmp/superprecompute_cpuprofile.prof")
	   			if err != nil{

	   			}
	   			if err := pprof.StartCPUProfile(cpufile); err != nil {
	               }
	           	defer pprof.StopCPUProfile()

	*/

	var result_extended ExtendedGroupElement
	result_extended.Zero() // make it identity

	b.ResetTimer()

	for i := 0; i < b.N; i++ {
		result_extended.Zero() // make it identity

		ScalarMultSuperPrecompute(&result_extended, &s1, &stable)

	}
}

func BenchmarkGeScalarMultBase(b *testing.B) {
	var s Key
	rand.Reader.Read(s[:])
	var P ExtendedGroupElement

	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		GeScalarMultBase(&P, &s)
	}
}

func BenchmarkGeScalarMult(b *testing.B) {
	var s Key
	rand.Reader.Read(s[:])

	var P ExtendedGroupElement
	var E ProjectiveGroupElement
	s[31] &= 127
	GeScalarMultBase(&P, &s)

	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		GeScalarMult(&E, &s, &P)
	}
}

func BenchmarkGeDoubleScalarMultVartime(b *testing.B) {
	var s Key
	rand.Reader.Read(s[:])

	var P, Pout ExtendedGroupElement
	s[31] &= 127
	GeScalarMultBase(&P, &s)
	_ = Pout

	var out ProjectiveGroupElement

	b.ResetTimer()
	var x Key
	for i := 0; i < b.N; i++ {
		GeDoubleScalarMultVartime(&out, &s, &P, &x)
		//out.ToExtended(&Pout)
	}
}

/*
func BenchmarkGeAdd(b *testing.B) {
	var s Key
	rand.Reader.Read(s[:])

	var R, P ExtendedGroupElement
	s[31] &= 127
	GeScalarMultBase(&P, &s)
	R = P

	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		GeAdd(&R, &R, &P)
	}
}
*/

/*
func BenchmarkGeDouble(b *testing.B) {
	var s [32]byte
	rand.Reader.Read(s[:])

	var R, P ExtendedGroupElement
	s[31] &= 127
	GeScalarMultBase(&P, &s)
	R = P

	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		GeDouble(&R, &P)
	}
}
*/