src/crypto/elliptic/elliptic_test.go - go - Git at Google

 // Copyright 2010 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 package elliptic

 import (
 	"bytes"
 	"crypto/rand"
 	"encoding/hex"
 	"fmt"
 	"math/big"
 	"testing"
 )

 func TestOnCurve(t *testing.T) {
 	p224 := P224()
 	if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
 		t.Errorf("FAIL")
 	}
 }

 func TestOffCurve(t *testing.T) {
 	p224 := P224()
 	x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
 	if p224.IsOnCurve(x, y) {
 		t.Errorf("FAIL: point off curve is claimed to be on the curve")
 	}
 	b := Marshal(p224, x, y)
 	x1, y1 := Unmarshal(p224, b)
 	if x1 != nil || y1 != nil {
 		t.Errorf("FAIL: unmarshaling a point not on the curve succeeded")
 	}
 }

 type baseMultTest struct {
 	k    string
 	x, y string
 }

 var p224BaseMultTests = []baseMultTest{
 	{
 		"1",
 		"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
 		"bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
 	},
 	{
 		"2",
 		"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
 		"1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb",
 	},
 	{
 		"3",
 		"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
 		"a3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925",
 	},
 	{
 		"4",
 		"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
 		"482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9",
 	},
 	{
 		"5",
 		"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
 		"27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b",
 	},
 	{
 		"6",
 		"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
 		"89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e",
 	},
 	{
 		"7",
 		"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
 		"f3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963",
 	},
 	{
 		"8",
 		"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
 		"46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a",
 	},
 	{
 		"9",
 		"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
 		"371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463",
 	},
 	{
 		"10",
 		"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
 		"39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f",
 	},
 	{
 		"11",
 		"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
 		"20b510004092e96636cfb7e32efded8265c266dfb754fa6d6491a6da",
 	},
 	{
 		"12",
 		"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
 		"207dddf0385bfdeab6e9acda8da06b3bbef224a93ab1e9e036109d13",
 	},
 	{
 		"13",
 		"34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
 		"252819f71c7fb7fbcb159be337d37d3336d7feb963724fdfb0ecb767",
 	},
 	{
 		"14",
 		"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
 		"d5814cd724199c4a5b974a43685fbf5b8bac69459c9469bc8f23ccaf",
 	},
 	{
 		"15",
 		"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
 		"979a5f4759f80f4fb4ec2e34f5566d595680a11735e7b61046127989",
 	},
 	{
 		"16",
 		"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
 		"3399d464345906b11b00e363ef429221f2ec720d2f665d7dead5b482",
 	},
 	{
 		"17",
 		"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
 		"ff149efa6606a6bd20ef7d1b06bd92f6904639dce5174db6cc554a26",
 	},
 	{
 		"18",
 		"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
 		"ea98d60e5ffc9b8fcf999fab1df7e7ef7084f20ddb61bb045a6ce002",
 	},
 	{
 		"19",
 		"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
 		"dcf1f6c3db09c70acc25391d492fe25b4a180babd6cea356c04719cd",
 	},
 	{
 		"20",
 		"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
 		"d5d7110274cba7cdee90e1a8b0d394c376a5573db6be0bf2747f530",
 	},
 	{
 		"112233445566778899",
 		"61f077c6f62ed802dad7c2f38f5c67f2cc453601e61bd076bb46179e",
 		"2272f9e9f5933e70388ee652513443b5e289dd135dcc0d0299b225e4",
 	},
 	{
 		"112233445566778899112233445566778899",
 		"29895f0af496bfc62b6ef8d8a65c88c613949b03668aab4f0429e35",
 		"3ea6e53f9a841f2019ec24bde1a75677aa9b5902e61081c01064de93",
 	},
 	{
 		"6950511619965839450988900688150712778015737983940691968051900319680",
 		"ab689930bcae4a4aa5f5cb085e823e8ae30fd365eb1da4aba9cf0379",
 		"3345a121bbd233548af0d210654eb40bab788a03666419be6fbd34e7",
 	},
 	{
 		"13479972933410060327035789020509431695094902435494295338570602119423",
 		"bdb6a8817c1f89da1c2f3dd8e97feb4494f2ed302a4ce2bc7f5f4025",
 		"4c7020d57c00411889462d77a5438bb4e97d177700bf7243a07f1680",
 	},
 	{
 		"13479971751745682581351455311314208093898607229429740618390390702079",
 		"d58b61aa41c32dd5eba462647dba75c5d67c83606c0af2bd928446a9",
 		"d24ba6a837be0460dd107ae77725696d211446c5609b4595976b16bd",
 	},
 	{
 		"13479972931865328106486971546324465392952975980343228160962702868479",
 		"dc9fa77978a005510980e929a1485f63716df695d7a0c18bb518df03",
 		"ede2b016f2ddffc2a8c015b134928275ce09e5661b7ab14ce0d1d403",
 	},
 	{
 		"11795773708834916026404142434151065506931607341523388140225443265536",
 		"499d8b2829cfb879c901f7d85d357045edab55028824d0f05ba279ba",
 		"bf929537b06e4015919639d94f57838fa33fc3d952598dcdbb44d638",
 	},
 	{
 		"784254593043826236572847595991346435467177662189391577090",
 		"8246c999137186632c5f9eddf3b1b0e1764c5e8bd0e0d8a554b9cb77",
 		"e80ed8660bc1cb17ac7d845be40a7a022d3306f116ae9f81fea65947",
 	},
 	{
 		"13479767645505654746623887797783387853576174193480695826442858012671",
 		"6670c20afcceaea672c97f75e2e9dd5c8460e54bb38538ebb4bd30eb",
 		"f280d8008d07a4caf54271f993527d46ff3ff46fd1190a3f1faa4f74",
 	},
 	{
 		"205688069665150753842126177372015544874550518966168735589597183",
 		"eca934247425cfd949b795cb5ce1eff401550386e28d1a4c5a8eb",
 		"d4c01040dba19628931bc8855370317c722cbd9ca6156985f1c2e9ce",
 	},
 	{
 		"13479966930919337728895168462090683249159702977113823384618282123295",
 		"ef353bf5c73cd551b96d596fbc9a67f16d61dd9fe56af19de1fba9cd",
 		"21771b9cdce3e8430c09b3838be70b48c21e15bc09ee1f2d7945b91f",
 	},
 	{
 		"50210731791415612487756441341851895584393717453129007497216",
 		"4036052a3091eb481046ad3289c95d3ac905ca0023de2c03ecd451cf",
 		"d768165a38a2b96f812586a9d59d4136035d9c853a5bf2e1c86a4993",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368041",
 		"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
 		"f2a28eefd8b345832116f1e574f2c6b2c895aa8c24941f40d8b80ad1",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368042",
 		"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
 		"230e093c24f638f533dac6e2b6d01da3b5e7f45429315ca93fb8e634",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368043",
 		"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
 		"156729f1a003647030666054e208180f8f7b0df2249e44fba5931fff",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368044",
 		"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
 		"eb610599f95942df1082e4f9426d086fb9c6231ae8b24933aab5db",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368045",
 		"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
 		"cc662b9bcba6f94ee4ff1c9c10bd6ddd0d138df2d099a282152a4b7f",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368046",
 		"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
 		"6865a0b8a607f0b04b13d1cb0aa992a5a97f5ee8ca1849efb9ed8678",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368047",
 		"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
 		"2a7eb328dbe663b5a468b5bc97a040a3745396ba636b964370dc3352",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368048",
 		"34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
 		"dad7e608e380480434ea641cc82c82cbc92801469c8db0204f13489a",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368049",
 		"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
 		"df82220fc7a4021549165325725f94c3410ddb56c54e161fc9ef62ee",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368050",
 		"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
 		"df4aefffbf6d1699c930481cd102127c9a3d992048ab05929b6e5927",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368051",
 		"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
 		"c644cf154cc81f5ade49345e541b4d4b5c1adb3eb5c01c14ee949aa2",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368052",
 		"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
 		"c8e8cd1b0be40b0877cfca1958603122f1e6914f84b7e8e968ae8b9e",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368053",
 		"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
 		"fb9232c15a3bc7673a3a03b0253824c53d0fd1411b1cabe2e187fb87",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368054",
 		"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
 		"f0c5cff7ab680d09ee11dae84e9c1072ac48ea2e744b1b7f72fd469e",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368055",
 		"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
 		"76050f3348af2664aac3a8b05281304ebc7a7914c6ad50a4b4eac383",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368056",
 		"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
 		"d817400e8ba9ca13a45f360e3d121eaaeb39af82d6001c8186f5f866",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368057",
 		"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
 		"fb7da7f5f13a43b81774373c879cd32d6934c05fa758eeb14fcfab38",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368058",
 		"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
 		"5c080fc3522f41bbb3f55a97cfecf21f882ce8cbb1e50ca6e67e56dc",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368059",
 		"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
 		"e3d4895843da188fd58fb0567976d7b50359d6b78530c8f62d1b1746",
 	},
 	{
 		"26959946667150639794667015087019625940457807714424391721682722368060",
 		"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
 		"42c89c774a08dc04b3dd201932bc8a5ea5f8b89bbb2a7e667aff81cd",
 	},
 }

 type scalarMultTest struct {
 	k          string
 	xIn, yIn   string
 	xOut, yOut string
 }

 var p256MultTests = []scalarMultTest{
 	{
 		"2a265f8bcbdcaf94d58519141e578124cb40d64a501fba9c11847b28965bc737",
 		"023819813ac969847059028ea88a1f30dfbcde03fc791d3a252c6b41211882ea",
 		"f93e4ae433cc12cf2a43fc0ef26400c0e125508224cdb649380f25479148a4ad",
 		"4d4de80f1534850d261075997e3049321a0864082d24a917863366c0724f5ae3",
 		"a22d2b7f7818a3563e0f7a76c9bf0921ac55e06e2e4d11795b233824b1db8cc0",
 	},
 	{
 		"313f72ff9fe811bf573176231b286a3bdb6f1b14e05c40146590727a71c3bccd",
 		"cc11887b2d66cbae8f4d306627192522932146b42f01d3c6f92bd5c8ba739b06",
 		"a2f08a029cd06b46183085bae9248b0ed15b70280c7ef13a457f5af382426031",
 		"831c3f6b5f762d2f461901577af41354ac5f228c2591f84f8a6e51e2e3f17991",
 		"93f90934cd0ef2c698cc471c60a93524e87ab31ca2412252337f364513e43684",
 	},
 }

 func TestBaseMult(t *testing.T) {
 	p224 := P224()
 	for i, e := range p224BaseMultTests {
 		k, ok := new(big.Int).SetString(e.k, 10)
 		if !ok {
 			t.Errorf("%d: bad value for k: %s", i, e.k)
 		}
 		x, y := p224.ScalarBaseMult(k.Bytes())
 		if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
 			t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
 		}
 		if testing.Short() && i > 5 {
 			break
 		}
 	}
 }

 func TestGenericBaseMult(t *testing.T) {
 	// We use the P224 CurveParams directly in order to test the generic implementation.
 	p224 := P224().Params()
 	for i, e := range p224BaseMultTests {
 		k, ok := new(big.Int).SetString(e.k, 10)
 		if !ok {
 			t.Errorf("%d: bad value for k: %s", i, e.k)
 		}
 		x, y := p224.ScalarBaseMult(k.Bytes())
 		if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
 			t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
 		}
 		if testing.Short() && i > 5 {
 			break
 		}
 	}
 }

 func TestP256BaseMult(t *testing.T) {
 	p256 := P256()
 	p256Generic := p256.Params()

 	scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
 	for _, e := range p224BaseMultTests {
 		k, _ := new(big.Int).SetString(e.k, 10)
 		scalars = append(scalars, k)
 	}
 	k := new(big.Int).SetInt64(1)
 	k.Lsh(k, 500)
 	scalars = append(scalars, k)

 	for i, k := range scalars {
 		x, y := p256.ScalarBaseMult(k.Bytes())
 		x2, y2 := p256Generic.ScalarBaseMult(k.Bytes())
 		if x.Cmp(x2) != 0 || y.Cmp(y2) != 0 {
 			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, x, y, x2, y2)
 		}

 		if testing.Short() && i > 5 {
 			break
 		}
 	}
 }

 func TestP256Mult(t *testing.T) {
 	p256 := P256()
 	p256Generic := p256.Params()

 	for i, e := range p224BaseMultTests {
 		x, _ := new(big.Int).SetString(e.x, 16)
 		y, _ := new(big.Int).SetString(e.y, 16)
 		k, _ := new(big.Int).SetString(e.k, 10)

 		xx, yy := p256.ScalarMult(x, y, k.Bytes())
 		xx2, yy2 := p256Generic.ScalarMult(x, y, k.Bytes())
 		if xx.Cmp(xx2) != 0 || yy.Cmp(yy2) != 0 {
 			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, xx2, yy2)
 		}
 		if testing.Short() && i > 5 {
 			break
 		}
 	}

 	for i, e := range p256MultTests {
 		x, _ := new(big.Int).SetString(e.xIn, 16)
 		y, _ := new(big.Int).SetString(e.yIn, 16)
 		k, _ := new(big.Int).SetString(e.k, 16)
 		expectedX, _ := new(big.Int).SetString(e.xOut, 16)
 		expectedY, _ := new(big.Int).SetString(e.yOut, 16)

 		xx, yy := p256.ScalarMult(x, y, k.Bytes())
 		if xx.Cmp(expectedX) != 0 || yy.Cmp(expectedY) != 0 {
 			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, expectedX, expectedY)
 		}
 	}
 }

 func TestInfinity(t *testing.T) {
 	tests := []struct {
 		name  string
 		curve Curve
 	}{
 		{"p224", P224()},
 		{"p256", P256()},
 	}

 	for _, test := range tests {
 		curve := test.curve
 		x, y := curve.ScalarBaseMult(nil)
 		if x.Sign() != 0 || y.Sign() != 0 {
 			t.Errorf("%s: x^0 != ∞", test.name)
 		}
 		x.SetInt64(0)
 		y.SetInt64(0)

 		x2, y2 := curve.Double(x, y)
 		if x2.Sign() != 0 || y2.Sign() != 0 {
 			t.Errorf("%s: 2∞ != ∞", test.name)
 		}

 		baseX := curve.Params().Gx
 		baseY := curve.Params().Gy

 		x3, y3 := curve.Add(baseX, baseY, x, y)
 		if x3.Cmp(baseX) != 0 || y3.Cmp(baseY) != 0 {
 			t.Errorf("%s: x+∞ != x", test.name)
 		}

 		x4, y4 := curve.Add(x, y, baseX, baseY)
 		if x4.Cmp(baseX) != 0 || y4.Cmp(baseY) != 0 {
 			t.Errorf("%s: ∞+x != x", test.name)
 		}
 	}
 }

 type synthCombinedMult struct {
 	Curve
 }

 func (s synthCombinedMult) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
 	x1, y1 := s.ScalarBaseMult(baseScalar)
 	x2, y2 := s.ScalarMult(bigX, bigY, scalar)
 	return s.Add(x1, y1, x2, y2)
 }

 func TestCombinedMult(t *testing.T) {
 	type combinedMult interface {
 		Curve
 		CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
 	}

 	p256, ok := P256().(combinedMult)
 	if !ok {
 		p256 = &synthCombinedMult{P256()}
 	}

 	gx := p256.Params().Gx
 	gy := p256.Params().Gy

 	zero := make([]byte, 32)
 	one := make([]byte, 32)
 	one[31] = 1
 	two := make([]byte, 32)
 	two[31] = 2

 	// 0×G + 0×G = ∞
 	x, y := p256.CombinedMult(gx, gy, zero, zero)
 	if x.Sign() != 0 || y.Sign() != 0 {
 		t.Errorf("0×G + 0×G = (%d, %d), should be ∞", x, y)
 	}

 	// 1×G + 0×G = G
 	x, y = p256.CombinedMult(gx, gy, one, zero)
 	if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
 		t.Errorf("1×G + 0×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
 	}

 	// 0×G + 1×G = G
 	x, y = p256.CombinedMult(gx, gy, zero, one)
 	if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
 		t.Errorf("0×G + 1×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
 	}

 	// 1×G + 1×G = 2×G
 	x, y = p256.CombinedMult(gx, gy, one, one)
 	ggx, ggy := p256.ScalarBaseMult(two)
 	if x.Cmp(ggx) != 0 || y.Cmp(ggy) != 0 {
 		t.Errorf("1×G + 1×G = (%d, %d), should be (%d, %d)", x, y, ggx, ggy)
 	}

 	minusOne := new(big.Int).Sub(p256.Params().N, big.NewInt(1))
 	// 1×G + (-1)×G = ∞
 	x, y = p256.CombinedMult(gx, gy, one, minusOne.Bytes())
 	if x.Sign() != 0 || y.Sign() != 0 {
 		t.Errorf("1×G + (-1)×G = (%d, %d), should be ∞", x, y)
 	}
 }

 func BenchmarkBaseMult(b *testing.B) {
 	b.ResetTimer()
 	p224 := P224()
 	e := p224BaseMultTests[25]
 	k, _ := new(big.Int).SetString(e.k, 10)
 	b.ReportAllocs()
 	b.StartTimer()
 	b.RunParallel(func(pb *testing.PB) {
 		for pb.Next() {
 			p224.ScalarBaseMult(k.Bytes())
 		}
 	})
 }

 func BenchmarkBaseMultP256(b *testing.B) {
 	b.ResetTimer()
 	p256 := P256()
 	e := p224BaseMultTests[25]
 	k, _ := new(big.Int).SetString(e.k, 10)
 	b.ReportAllocs()
 	b.StartTimer()
 	b.RunParallel(func(pb *testing.PB) {
 		for pb.Next() {
 			p256.ScalarBaseMult(k.Bytes())
 		}
 	})
 }

 func BenchmarkScalarMultP256(b *testing.B) {
 	b.ResetTimer()
 	p256 := P256()
 	_, x, y, _ := GenerateKey(p256, rand.Reader)
 	priv, _, _, _ := GenerateKey(p256, rand.Reader)

 	b.ReportAllocs()
 	b.StartTimer()
 	b.RunParallel(func(pb *testing.PB) {
 		for pb.Next() {
 			p256.ScalarMult(x, y, priv)
 		}
 	})
 }

 func TestMarshal(t *testing.T) {
 	p224 := P224()
 	_, x, y, err := GenerateKey(p224, rand.Reader)
 	if err != nil {
 		t.Error(err)
 		return
 	}
 	serialized := Marshal(p224, x, y)
 	xx, yy := Unmarshal(p224, serialized)
 	if xx == nil {
 		t.Error("failed to unmarshal")
 		return
 	}
 	if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
 		t.Error("unmarshal returned different values")
 		return
 	}
 }

 func TestP224Overflow(t *testing.T) {
 	// This tests for a specific bug in the P224 implementation.
 	p224 := P224()
 	pointData, _ := hex.DecodeString("049B535B45FB0A2072398A6831834624C7E32CCFD5A4B933BCEAF77F1DD945E08BBE5178F5EDF5E733388F196D2A631D2E075BB16CBFEEA15B")
 	x, y := Unmarshal(p224, pointData)
 	if !p224.IsOnCurve(x, y) {
 		t.Error("P224 failed to validate a correct point")
 	}
 }

 // See https://golang.org/issues/20482
 func TestUnmarshalToLargeCoordinates(t *testing.T) {
 	curve := P256()
 	p := curve.Params().P

 	invalidX, invalidY := make([]byte, 65), make([]byte, 65)
 	invalidX[0], invalidY[0] = 4, 4 // uncompressed encoding

 	// Set x to be greater than curve's parameter P – specifically, to P+5.
 	// Set y to mod_sqrt(x^3 - 3x + B)) so that (x mod P = 5 , y) is on the
 	// curve.
 	x := new(big.Int).Add(p, big.NewInt(5))
 	y, _ := new(big.Int).SetString("31468013646237722594854082025316614106172411895747863909393730389177298123724", 10)

 	copy(invalidX[1:], x.Bytes())
 	copy(invalidX[33:], y.Bytes())

 	if X, Y := Unmarshal(curve, invalidX); X != nil || Y != nil {
 		t.Errorf("Unmarshal accepts invalid X coordinate")
 	}

 	// This is a point on the curve with a small y value, small enough that we can add p and still be within 32 bytes.
 	x, _ = new(big.Int).SetString("31931927535157963707678568152204072984517581467226068221761862915403492091210", 10)
 	y, _ = new(big.Int).SetString("5208467867388784005506817585327037698770365050895731383201516607147", 10)
 	y.Add(y, p)

 	if p.Cmp(y) > 0 || y.BitLen() != 256 {
 		t.Fatal("y not within expected range")
 	}

 	// marshal
 	copy(invalidY[1:], x.Bytes())
 	copy(invalidY[33:], y.Bytes())

 	if X, Y := Unmarshal(curve, invalidY); X != nil || Y != nil {
 		t.Errorf("Unmarshal accepts invalid Y coordinate")
 	}
 }

 func TestMarshalCompressed(t *testing.T) {
 	t.Run("P-256/03", func(t *testing.T) {
 		data, _ := hex.DecodeString("031e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
 		x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
 		y, _ := new(big.Int).SetString("66200849279091436748794323380043701364391950689352563629885086590854940586447", 10)
 		testMarshalCompressed(t, P256(), x, y, data)
 	})
 	t.Run("P-256/02", func(t *testing.T) {
 		data, _ := hex.DecodeString("021e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
 		x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
 		y, _ := new(big.Int).SetString("49591239931264812013903123569363872165694192725937750565648544718012157267504", 10)
 		testMarshalCompressed(t, P256(), x, y, data)
 	})

 	t.Run("Invalid", func(t *testing.T) {
 		data, _ := hex.DecodeString("02fd4bf61763b46581fd9174d623516cf3c81edd40e29ffa2777fb6cb0ae3ce535")
 		X, Y := UnmarshalCompressed(P256(), data)
 		if X != nil || Y != nil {
 			t.Error("expected an error for invalid encoding")
 		}
 	})

 	if testing.Short() {
 		t.Skip("skipping other curves on short test")
 	}

 	t.Run("P-224", func(t *testing.T) {
 		_, x, y, err := GenerateKey(P224(), rand.Reader)
 		if err != nil {
 			t.Fatal(err)
 		}
 		testMarshalCompressed(t, P224(), x, y, nil)
 	})
 	t.Run("P-384", func(t *testing.T) {
 		_, x, y, err := GenerateKey(P384(), rand.Reader)
 		if err != nil {
 			t.Fatal(err)
 		}
 		testMarshalCompressed(t, P384(), x, y, nil)
 	})
 	t.Run("P-521", func(t *testing.T) {
 		_, x, y, err := GenerateKey(P521(), rand.Reader)
 		if err != nil {
 			t.Fatal(err)
 		}
 		testMarshalCompressed(t, P521(), x, y, nil)
 	})
 }

 func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte) {
 	if !curve.IsOnCurve(x, y) {
 		t.Fatal("invalid test point")
 	}
 	got := MarshalCompressed(curve, x, y)
 	if want != nil && !bytes.Equal(got, want) {
 		t.Errorf("got unexpected MarshalCompressed result: got %x, want %x", got, want)
 	}

 	X, Y := UnmarshalCompressed(curve, got)
 	if X == nil || Y == nil {
 		t.Fatalf("UnmarshalCompressed failed unexpectedly")
 	}

 	if !curve.IsOnCurve(X, Y) {
 		t.Error("UnmarshalCompressed returned a point not on the curve")
 	}
 	if X.Cmp(x) != 0 || Y.Cmp(y) != 0 {
 		t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
 	}
 }
	// Copyright 2010 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	package elliptic

	import (
	"bytes"
	"crypto/rand"
	"encoding/hex"
	"fmt"
	"math/big"
	"testing"
	)

	func TestOnCurve(t *testing.T) {
	p224 := P224()
	if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
	t.Errorf("FAIL")
	}
	}

	func TestOffCurve(t *testing.T) {
	p224 := P224()
	x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
	if p224.IsOnCurve(x, y) {
	t.Errorf("FAIL: point off curve is claimed to be on the curve")
	}
	b := Marshal(p224, x, y)
	x1, y1 := Unmarshal(p224, b)
	if x1 != nil \|\| y1 != nil {
	t.Errorf("FAIL: unmarshaling a point not on the curve succeeded")
	}
	}

	type baseMultTest struct {
	k string
	x, y string
	}

	var p224BaseMultTests = []baseMultTest{
	{
	"1",
	"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
	"bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
	},
	{
	"2",
	"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
	"1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb",
	},
	{
	"3",
	"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
	"a3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925",
	},
	{
	"4",
	"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
	"482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9",
	},
	{
	"5",
	"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
	"27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b",
	},
	{
	"6",
	"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
	"89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e",
	},
	{
	"7",
	"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
	"f3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963",
	},
	{
	"8",
	"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
	"46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a",
	},
	{
	"9",
	"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
	"371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463",
	},
	{
	"10",
	"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
	"39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f",
	},
	{
	"11",
	"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
	"20b510004092e96636cfb7e32efded8265c266dfb754fa6d6491a6da",
	},
	{
	"12",
	"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
	"207dddf0385bfdeab6e9acda8da06b3bbef224a93ab1e9e036109d13",
	},
	{
	"13",
	"34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
	"252819f71c7fb7fbcb159be337d37d3336d7feb963724fdfb0ecb767",
	},
	{
	"14",
	"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
	"d5814cd724199c4a5b974a43685fbf5b8bac69459c9469bc8f23ccaf",
	},
	{
	"15",
	"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
	"979a5f4759f80f4fb4ec2e34f5566d595680a11735e7b61046127989",
	},
	{
	"16",
	"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
	"3399d464345906b11b00e363ef429221f2ec720d2f665d7dead5b482",
	},
	{
	"17",
	"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
	"ff149efa6606a6bd20ef7d1b06bd92f6904639dce5174db6cc554a26",
	},
	{
	"18",
	"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
	"ea98d60e5ffc9b8fcf999fab1df7e7ef7084f20ddb61bb045a6ce002",
	},
	{
	"19",
	"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
	"dcf1f6c3db09c70acc25391d492fe25b4a180babd6cea356c04719cd",
	},
	{
	"20",
	"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
	"d5d7110274cba7cdee90e1a8b0d394c376a5573db6be0bf2747f530",
	},
	{
	"112233445566778899",
	"61f077c6f62ed802dad7c2f38f5c67f2cc453601e61bd076bb46179e",
	"2272f9e9f5933e70388ee652513443b5e289dd135dcc0d0299b225e4",
	},
	{
	"112233445566778899112233445566778899",
	"29895f0af496bfc62b6ef8d8a65c88c613949b03668aab4f0429e35",
	"3ea6e53f9a841f2019ec24bde1a75677aa9b5902e61081c01064de93",
	},
	{
	"6950511619965839450988900688150712778015737983940691968051900319680",
	"ab689930bcae4a4aa5f5cb085e823e8ae30fd365eb1da4aba9cf0379",
	"3345a121bbd233548af0d210654eb40bab788a03666419be6fbd34e7",
	},
	{
	"13479972933410060327035789020509431695094902435494295338570602119423",
	"bdb6a8817c1f89da1c2f3dd8e97feb4494f2ed302a4ce2bc7f5f4025",
	"4c7020d57c00411889462d77a5438bb4e97d177700bf7243a07f1680",
	},
	{
	"13479971751745682581351455311314208093898607229429740618390390702079",
	"d58b61aa41c32dd5eba462647dba75c5d67c83606c0af2bd928446a9",
	"d24ba6a837be0460dd107ae77725696d211446c5609b4595976b16bd",
	},
	{
	"13479972931865328106486971546324465392952975980343228160962702868479",
	"dc9fa77978a005510980e929a1485f63716df695d7a0c18bb518df03",
	"ede2b016f2ddffc2a8c015b134928275ce09e5661b7ab14ce0d1d403",
	},
	{
	"11795773708834916026404142434151065506931607341523388140225443265536",
	"499d8b2829cfb879c901f7d85d357045edab55028824d0f05ba279ba",
	"bf929537b06e4015919639d94f57838fa33fc3d952598dcdbb44d638",
	},
	{
	"784254593043826236572847595991346435467177662189391577090",
	"8246c999137186632c5f9eddf3b1b0e1764c5e8bd0e0d8a554b9cb77",
	"e80ed8660bc1cb17ac7d845be40a7a022d3306f116ae9f81fea65947",
	},
	{
	"13479767645505654746623887797783387853576174193480695826442858012671",
	"6670c20afcceaea672c97f75e2e9dd5c8460e54bb38538ebb4bd30eb",
	"f280d8008d07a4caf54271f993527d46ff3ff46fd1190a3f1faa4f74",
	},
	{
	"205688069665150753842126177372015544874550518966168735589597183",
	"eca934247425cfd949b795cb5ce1eff401550386e28d1a4c5a8eb",
	"d4c01040dba19628931bc8855370317c722cbd9ca6156985f1c2e9ce",
	},
	{
	"13479966930919337728895168462090683249159702977113823384618282123295",
	"ef353bf5c73cd551b96d596fbc9a67f16d61dd9fe56af19de1fba9cd",
	"21771b9cdce3e8430c09b3838be70b48c21e15bc09ee1f2d7945b91f",
	},
	{
	"50210731791415612487756441341851895584393717453129007497216",
	"4036052a3091eb481046ad3289c95d3ac905ca0023de2c03ecd451cf",
	"d768165a38a2b96f812586a9d59d4136035d9c853a5bf2e1c86a4993",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368041",
	"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
	"f2a28eefd8b345832116f1e574f2c6b2c895aa8c24941f40d8b80ad1",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368042",
	"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
	"230e093c24f638f533dac6e2b6d01da3b5e7f45429315ca93fb8e634",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368043",
	"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
	"156729f1a003647030666054e208180f8f7b0df2249e44fba5931fff",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368044",
	"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
	"eb610599f95942df1082e4f9426d086fb9c6231ae8b24933aab5db",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368045",
	"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
	"cc662b9bcba6f94ee4ff1c9c10bd6ddd0d138df2d099a282152a4b7f",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368046",
	"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
	"6865a0b8a607f0b04b13d1cb0aa992a5a97f5ee8ca1849efb9ed8678",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368047",
	"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
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	"dad7e608e380480434ea641cc82c82cbc92801469c8db0204f13489a",
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	"26959946667150639794667015087019625940457807714424391721682722368049",
	"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
	"df82220fc7a4021549165325725f94c3410ddb56c54e161fc9ef62ee",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368050",
	"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
	"df4aefffbf6d1699c930481cd102127c9a3d992048ab05929b6e5927",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368051",
	"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
	"c644cf154cc81f5ade49345e541b4d4b5c1adb3eb5c01c14ee949aa2",
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	"26959946667150639794667015087019625940457807714424391721682722368052",
	"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
	"c8e8cd1b0be40b0877cfca1958603122f1e6914f84b7e8e968ae8b9e",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368053",
	"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
	"fb9232c15a3bc7673a3a03b0253824c53d0fd1411b1cabe2e187fb87",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368054",
	"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
	"f0c5cff7ab680d09ee11dae84e9c1072ac48ea2e744b1b7f72fd469e",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368055",
	"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
	"76050f3348af2664aac3a8b05281304ebc7a7914c6ad50a4b4eac383",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368056",
	"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
	"d817400e8ba9ca13a45f360e3d121eaaeb39af82d6001c8186f5f866",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368057",
	"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
	"fb7da7f5f13a43b81774373c879cd32d6934c05fa758eeb14fcfab38",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368058",
	"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
	"5c080fc3522f41bbb3f55a97cfecf21f882ce8cbb1e50ca6e67e56dc",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368059",
	"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
	"e3d4895843da188fd58fb0567976d7b50359d6b78530c8f62d1b1746",
	},
	{
	"26959946667150639794667015087019625940457807714424391721682722368060",
	"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
	"42c89c774a08dc04b3dd201932bc8a5ea5f8b89bbb2a7e667aff81cd",
	},
	}

	type scalarMultTest struct {
	k string
	xIn, yIn string
	xOut, yOut string
	}

	var p256MultTests = []scalarMultTest{
	{
	"2a265f8bcbdcaf94d58519141e578124cb40d64a501fba9c11847b28965bc737",
	"023819813ac969847059028ea88a1f30dfbcde03fc791d3a252c6b41211882ea",
	"f93e4ae433cc12cf2a43fc0ef26400c0e125508224cdb649380f25479148a4ad",
	"4d4de80f1534850d261075997e3049321a0864082d24a917863366c0724f5ae3",
	"a22d2b7f7818a3563e0f7a76c9bf0921ac55e06e2e4d11795b233824b1db8cc0",
	},
	{
	"313f72ff9fe811bf573176231b286a3bdb6f1b14e05c40146590727a71c3bccd",
	"cc11887b2d66cbae8f4d306627192522932146b42f01d3c6f92bd5c8ba739b06",
	"a2f08a029cd06b46183085bae9248b0ed15b70280c7ef13a457f5af382426031",
	"831c3f6b5f762d2f461901577af41354ac5f228c2591f84f8a6e51e2e3f17991",
	"93f90934cd0ef2c698cc471c60a93524e87ab31ca2412252337f364513e43684",
	},
	}

	func TestBaseMult(t *testing.T) {
	p224 := P224()
	for i, e := range p224BaseMultTests {
	k, ok := new(big.Int).SetString(e.k, 10)
	if !ok {
	t.Errorf("%d: bad value for k: %s", i, e.k)
	}
	x, y := p224.ScalarBaseMult(k.Bytes())
	if fmt.Sprintf("%x", x) != e.x \|\| fmt.Sprintf("%x", y) != e.y {
	t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
	}
	if testing.Short() && i > 5 {
	break
	}
	}
	}

	func TestGenericBaseMult(t *testing.T) {
	// We use the P224 CurveParams directly in order to test the generic implementation.
	p224 := P224().Params()
	for i, e := range p224BaseMultTests {
	k, ok := new(big.Int).SetString(e.k, 10)
	if !ok {
	t.Errorf("%d: bad value for k: %s", i, e.k)
	}
	x, y := p224.ScalarBaseMult(k.Bytes())
	if fmt.Sprintf("%x", x) != e.x \|\| fmt.Sprintf("%x", y) != e.y {
	t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
	}
	if testing.Short() && i > 5 {
	break
	}
	}
	}

	func TestP256BaseMult(t *testing.T) {
	p256 := P256()
	p256Generic := p256.Params()

	scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
	for _, e := range p224BaseMultTests {
	k, _ := new(big.Int).SetString(e.k, 10)
	scalars = append(scalars, k)
	}
	k := new(big.Int).SetInt64(1)
	k.Lsh(k, 500)
	scalars = append(scalars, k)

	for i, k := range scalars {
	x, y := p256.ScalarBaseMult(k.Bytes())
	x2, y2 := p256Generic.ScalarBaseMult(k.Bytes())
	if x.Cmp(x2) != 0 \|\| y.Cmp(y2) != 0 {
	t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, x, y, x2, y2)
	}

	if testing.Short() && i > 5 {
	break
	}
	}
	}

	func TestP256Mult(t *testing.T) {
	p256 := P256()
	p256Generic := p256.Params()

	for i, e := range p224BaseMultTests {
	x, _ := new(big.Int).SetString(e.x, 16)
	y, _ := new(big.Int).SetString(e.y, 16)
	k, _ := new(big.Int).SetString(e.k, 10)

	xx, yy := p256.ScalarMult(x, y, k.Bytes())
	xx2, yy2 := p256Generic.ScalarMult(x, y, k.Bytes())
	if xx.Cmp(xx2) != 0 \|\| yy.Cmp(yy2) != 0 {
	t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, xx2, yy2)
	}
	if testing.Short() && i > 5 {
	break
	}
	}

	for i, e := range p256MultTests {
	x, _ := new(big.Int).SetString(e.xIn, 16)
	y, _ := new(big.Int).SetString(e.yIn, 16)
	k, _ := new(big.Int).SetString(e.k, 16)
	expectedX, _ := new(big.Int).SetString(e.xOut, 16)
	expectedY, _ := new(big.Int).SetString(e.yOut, 16)

	xx, yy := p256.ScalarMult(x, y, k.Bytes())
	if xx.Cmp(expectedX) != 0 \|\| yy.Cmp(expectedY) != 0 {
	t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, expectedX, expectedY)
	}
	}
	}

	func TestInfinity(t *testing.T) {
	tests := []struct {
	name string
	curve Curve
	}{
	{"p224", P224()},
	{"p256", P256()},
	}

	for _, test := range tests {
	curve := test.curve
	x, y := curve.ScalarBaseMult(nil)
	if x.Sign() != 0 \|\| y.Sign() != 0 {
	t.Errorf("%s: x^0 != ∞", test.name)
	}
	x.SetInt64(0)
	y.SetInt64(0)

	x2, y2 := curve.Double(x, y)
	if x2.Sign() != 0 \|\| y2.Sign() != 0 {
	t.Errorf("%s: 2∞ != ∞", test.name)
	}

	baseX := curve.Params().Gx
	baseY := curve.Params().Gy

	x3, y3 := curve.Add(baseX, baseY, x, y)
	if x3.Cmp(baseX) != 0 \|\| y3.Cmp(baseY) != 0 {
	t.Errorf("%s: x+∞ != x", test.name)
	}

	x4, y4 := curve.Add(x, y, baseX, baseY)
	if x4.Cmp(baseX) != 0 \|\| y4.Cmp(baseY) != 0 {
	t.Errorf("%s: ∞+x != x", test.name)
	}
	}
	}

	type synthCombinedMult struct {
	Curve
	}

	func (s synthCombinedMult) CombinedMult(bigX, bigY big.Int, baseScalar, scalar []byte) (x, y big.Int) {
	x1, y1 := s.ScalarBaseMult(baseScalar)
	x2, y2 := s.ScalarMult(bigX, bigY, scalar)
	return s.Add(x1, y1, x2, y2)
	}

	func TestCombinedMult(t *testing.T) {
	type combinedMult interface {
	Curve
	CombinedMult(bigX, bigY big.Int, baseScalar, scalar []byte) (x, y big.Int)
	}

	p256, ok := P256().(combinedMult)
	if !ok {
	p256 = &synthCombinedMult{P256()}
	}

	gx := p256.Params().Gx
	gy := p256.Params().Gy

	zero := make([]byte, 32)
	one := make([]byte, 32)
	one[31] = 1
	two := make([]byte, 32)
	two[31] = 2

	// 0×G + 0×G = ∞
	x, y := p256.CombinedMult(gx, gy, zero, zero)
	if x.Sign() != 0 \|\| y.Sign() != 0 {
	t.Errorf("0×G + 0×G = (%d, %d), should be ∞", x, y)
	}

	// 1×G + 0×G = G
	x, y = p256.CombinedMult(gx, gy, one, zero)
	if x.Cmp(gx) != 0 \|\| y.Cmp(gy) != 0 {
	t.Errorf("1×G + 0×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
	}

	// 0×G + 1×G = G
	x, y = p256.CombinedMult(gx, gy, zero, one)
	if x.Cmp(gx) != 0 \|\| y.Cmp(gy) != 0 {
	t.Errorf("0×G + 1×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
	}

	// 1×G + 1×G = 2×G
	x, y = p256.CombinedMult(gx, gy, one, one)
	ggx, ggy := p256.ScalarBaseMult(two)
	if x.Cmp(ggx) != 0 \|\| y.Cmp(ggy) != 0 {
	t.Errorf("1×G + 1×G = (%d, %d), should be (%d, %d)", x, y, ggx, ggy)
	}

	minusOne := new(big.Int).Sub(p256.Params().N, big.NewInt(1))
	// 1×G + (-1)×G = ∞
	x, y = p256.CombinedMult(gx, gy, one, minusOne.Bytes())
	if x.Sign() != 0 \|\| y.Sign() != 0 {
	t.Errorf("1×G + (-1)×G = (%d, %d), should be ∞", x, y)
	}
	}

	func BenchmarkBaseMult(b *testing.B) {
	b.ResetTimer()
	p224 := P224()
	e := p224BaseMultTests[25]
	k, _ := new(big.Int).SetString(e.k, 10)
	b.ReportAllocs()
	b.StartTimer()
	b.RunParallel(func(pb *testing.PB) {
	for pb.Next() {
	p224.ScalarBaseMult(k.Bytes())
	}
	})
	}

	func BenchmarkBaseMultP256(b *testing.B) {
	b.ResetTimer()
	p256 := P256()
	e := p224BaseMultTests[25]
	k, _ := new(big.Int).SetString(e.k, 10)
	b.ReportAllocs()
	b.StartTimer()
	b.RunParallel(func(pb *testing.PB) {
	for pb.Next() {
	p256.ScalarBaseMult(k.Bytes())
	}
	})
	}

	func BenchmarkScalarMultP256(b *testing.B) {
	b.ResetTimer()
	p256 := P256()
	_, x, y, _ := GenerateKey(p256, rand.Reader)
	priv, _, _, _ := GenerateKey(p256, rand.Reader)

	b.ReportAllocs()
	b.StartTimer()
	b.RunParallel(func(pb *testing.PB) {
	for pb.Next() {
	p256.ScalarMult(x, y, priv)
	}
	})
	}

	func TestMarshal(t *testing.T) {
	p224 := P224()
	_, x, y, err := GenerateKey(p224, rand.Reader)
	if err != nil {
	t.Error(err)
	return
	}
	serialized := Marshal(p224, x, y)
	xx, yy := Unmarshal(p224, serialized)
	if xx == nil {
	t.Error("failed to unmarshal")
	return
	}
	if xx.Cmp(x) != 0 \|\| yy.Cmp(y) != 0 {
	t.Error("unmarshal returned different values")
	return
	}
	}

	func TestP224Overflow(t *testing.T) {
	// This tests for a specific bug in the P224 implementation.
	p224 := P224()
	pointData, _ := hex.DecodeString("049B535B45FB0A2072398A6831834624C7E32CCFD5A4B933BCEAF77F1DD945E08BBE5178F5EDF5E733388F196D2A631D2E075BB16CBFEEA15B")
	x, y := Unmarshal(p224, pointData)
	if !p224.IsOnCurve(x, y) {
	t.Error("P224 failed to validate a correct point")
	}
	}

	// See https://golang.org/issues/20482
	func TestUnmarshalToLargeCoordinates(t *testing.T) {
	curve := P256()
	p := curve.Params().P

	invalidX, invalidY := make([]byte, 65), make([]byte, 65)
	invalidX[0], invalidY[0] = 4, 4 // uncompressed encoding

	// Set x to be greater than curve's parameter P – specifically, to P+5.
	// Set y to mod_sqrt(x^3 - 3x + B)) so that (x mod P = 5 , y) is on the
	// curve.
	x := new(big.Int).Add(p, big.NewInt(5))
	y, _ := new(big.Int).SetString("31468013646237722594854082025316614106172411895747863909393730389177298123724", 10)

	copy(invalidX[1:], x.Bytes())
	copy(invalidX[33:], y.Bytes())

	if X, Y := Unmarshal(curve, invalidX); X != nil \|\| Y != nil {
	t.Errorf("Unmarshal accepts invalid X coordinate")
	}

	// This is a point on the curve with a small y value, small enough that we can add p and still be within 32 bytes.
	x, _ = new(big.Int).SetString("31931927535157963707678568152204072984517581467226068221761862915403492091210", 10)
	y, _ = new(big.Int).SetString("5208467867388784005506817585327037698770365050895731383201516607147", 10)
	y.Add(y, p)

	if p.Cmp(y) > 0 \|\| y.BitLen() != 256 {
	t.Fatal("y not within expected range")
	}

	// marshal
	copy(invalidY[1:], x.Bytes())
	copy(invalidY[33:], y.Bytes())

	if X, Y := Unmarshal(curve, invalidY); X != nil \|\| Y != nil {
	t.Errorf("Unmarshal accepts invalid Y coordinate")
	}
	}

	func TestMarshalCompressed(t *testing.T) {
	t.Run("P-256/03", func(t *testing.T) {
	data, _ := hex.DecodeString("031e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
	x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
	y, _ := new(big.Int).SetString("66200849279091436748794323380043701364391950689352563629885086590854940586447", 10)
	testMarshalCompressed(t, P256(), x, y, data)
	})
	t.Run("P-256/02", func(t *testing.T) {
	data, _ := hex.DecodeString("021e3987d9f9ea9d7dd7155a56a86b2009e1e0ab332f962d10d8beb6406ab1ad79")
	x, _ := new(big.Int).SetString("13671033352574878777044637384712060483119675368076128232297328793087057702265", 10)
	y, _ := new(big.Int).SetString("49591239931264812013903123569363872165694192725937750565648544718012157267504", 10)
	testMarshalCompressed(t, P256(), x, y, data)
	})

	t.Run("Invalid", func(t *testing.T) {
	data, _ := hex.DecodeString("02fd4bf61763b46581fd9174d623516cf3c81edd40e29ffa2777fb6cb0ae3ce535")
	X, Y := UnmarshalCompressed(P256(), data)
	if X != nil \|\| Y != nil {
	t.Error("expected an error for invalid encoding")
	}
	})

	if testing.Short() {
	t.Skip("skipping other curves on short test")
	}

	t.Run("P-224", func(t *testing.T) {
	_, x, y, err := GenerateKey(P224(), rand.Reader)
	if err != nil {
	t.Fatal(err)
	}
	testMarshalCompressed(t, P224(), x, y, nil)
	})
	t.Run("P-384", func(t *testing.T) {
	_, x, y, err := GenerateKey(P384(), rand.Reader)
	if err != nil {
	t.Fatal(err)
	}
	testMarshalCompressed(t, P384(), x, y, nil)
	})
	t.Run("P-521", func(t *testing.T) {
	_, x, y, err := GenerateKey(P521(), rand.Reader)
	if err != nil {
	t.Fatal(err)
	}
	testMarshalCompressed(t, P521(), x, y, nil)
	})
	}

	func testMarshalCompressed(t testing.T, curve Curve, x, y big.Int, want []byte) {
	if !curve.IsOnCurve(x, y) {
	t.Fatal("invalid test point")
	}
	got := MarshalCompressed(curve, x, y)
	if want != nil && !bytes.Equal(got, want) {
	t.Errorf("got unexpected MarshalCompressed result: got %x, want %x", got, want)
	}

	X, Y := UnmarshalCompressed(curve, got)
	if X == nil \|\| Y == nil {
	t.Fatalf("UnmarshalCompressed failed unexpectedly")
	}

	if !curve.IsOnCurve(X, Y) {
	t.Error("UnmarshalCompressed returned a point not on the curve")
	}
	if X.Cmp(x) != 0 \|\| Y.Cmp(y) != 0 {
	t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
	}
	}