// 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 (
"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 accpets 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 accpets invalid Y coordinate")
}
}