...
Run Format

Source file src/crypto/elliptic/elliptic_test.go

Documentation: crypto/elliptic

     1  // Copyright 2010 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package elliptic
     6  
     7  import (
     8  	"crypto/rand"
     9  	"encoding/hex"
    10  	"fmt"
    11  	"math/big"
    12  	"testing"
    13  )
    14  
    15  func TestOnCurve(t *testing.T) {
    16  	p224 := P224()
    17  	if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
    18  		t.Errorf("FAIL")
    19  	}
    20  }
    21  
    22  func TestOffCurve(t *testing.T) {
    23  	p224 := P224()
    24  	x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
    25  	if p224.IsOnCurve(x, y) {
    26  		t.Errorf("FAIL: point off curve is claimed to be on the curve")
    27  	}
    28  	b := Marshal(p224, x, y)
    29  	x1, y1 := Unmarshal(p224, b)
    30  	if x1 != nil || y1 != nil {
    31  		t.Errorf("FAIL: unmarshaling a point not on the curve succeeded")
    32  	}
    33  }
    34  
    35  type baseMultTest struct {
    36  	k    string
    37  	x, y string
    38  }
    39  
    40  var p224BaseMultTests = []baseMultTest{
    41  	{
    42  		"1",
    43  		"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
    44  		"bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34",
    45  	},
    46  	{
    47  		"2",
    48  		"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
    49  		"1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb",
    50  	},
    51  	{
    52  		"3",
    53  		"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
    54  		"a3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925",
    55  	},
    56  	{
    57  		"4",
    58  		"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
    59  		"482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9",
    60  	},
    61  	{
    62  		"5",
    63  		"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
    64  		"27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b",
    65  	},
    66  	{
    67  		"6",
    68  		"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
    69  		"89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e",
    70  	},
    71  	{
    72  		"7",
    73  		"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
    74  		"f3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963",
    75  	},
    76  	{
    77  		"8",
    78  		"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
    79  		"46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a",
    80  	},
    81  	{
    82  		"9",
    83  		"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
    84  		"371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463",
    85  	},
    86  	{
    87  		"10",
    88  		"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
    89  		"39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f",
    90  	},
    91  	{
    92  		"11",
    93  		"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
    94  		"20b510004092e96636cfb7e32efded8265c266dfb754fa6d6491a6da",
    95  	},
    96  	{
    97  		"12",
    98  		"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
    99  		"207dddf0385bfdeab6e9acda8da06b3bbef224a93ab1e9e036109d13",
   100  	},
   101  	{
   102  		"13",
   103  		"34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
   104  		"252819f71c7fb7fbcb159be337d37d3336d7feb963724fdfb0ecb767",
   105  	},
   106  	{
   107  		"14",
   108  		"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
   109  		"d5814cd724199c4a5b974a43685fbf5b8bac69459c9469bc8f23ccaf",
   110  	},
   111  	{
   112  		"15",
   113  		"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
   114  		"979a5f4759f80f4fb4ec2e34f5566d595680a11735e7b61046127989",
   115  	},
   116  	{
   117  		"16",
   118  		"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
   119  		"3399d464345906b11b00e363ef429221f2ec720d2f665d7dead5b482",
   120  	},
   121  	{
   122  		"17",
   123  		"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
   124  		"ff149efa6606a6bd20ef7d1b06bd92f6904639dce5174db6cc554a26",
   125  	},
   126  	{
   127  		"18",
   128  		"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
   129  		"ea98d60e5ffc9b8fcf999fab1df7e7ef7084f20ddb61bb045a6ce002",
   130  	},
   131  	{
   132  		"19",
   133  		"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
   134  		"dcf1f6c3db09c70acc25391d492fe25b4a180babd6cea356c04719cd",
   135  	},
   136  	{
   137  		"20",
   138  		"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
   139  		"d5d7110274cba7cdee90e1a8b0d394c376a5573db6be0bf2747f530",
   140  	},
   141  	{
   142  		"112233445566778899",
   143  		"61f077c6f62ed802dad7c2f38f5c67f2cc453601e61bd076bb46179e",
   144  		"2272f9e9f5933e70388ee652513443b5e289dd135dcc0d0299b225e4",
   145  	},
   146  	{
   147  		"112233445566778899112233445566778899",
   148  		"29895f0af496bfc62b6ef8d8a65c88c613949b03668aab4f0429e35",
   149  		"3ea6e53f9a841f2019ec24bde1a75677aa9b5902e61081c01064de93",
   150  	},
   151  	{
   152  		"6950511619965839450988900688150712778015737983940691968051900319680",
   153  		"ab689930bcae4a4aa5f5cb085e823e8ae30fd365eb1da4aba9cf0379",
   154  		"3345a121bbd233548af0d210654eb40bab788a03666419be6fbd34e7",
   155  	},
   156  	{
   157  		"13479972933410060327035789020509431695094902435494295338570602119423",
   158  		"bdb6a8817c1f89da1c2f3dd8e97feb4494f2ed302a4ce2bc7f5f4025",
   159  		"4c7020d57c00411889462d77a5438bb4e97d177700bf7243a07f1680",
   160  	},
   161  	{
   162  		"13479971751745682581351455311314208093898607229429740618390390702079",
   163  		"d58b61aa41c32dd5eba462647dba75c5d67c83606c0af2bd928446a9",
   164  		"d24ba6a837be0460dd107ae77725696d211446c5609b4595976b16bd",
   165  	},
   166  	{
   167  		"13479972931865328106486971546324465392952975980343228160962702868479",
   168  		"dc9fa77978a005510980e929a1485f63716df695d7a0c18bb518df03",
   169  		"ede2b016f2ddffc2a8c015b134928275ce09e5661b7ab14ce0d1d403",
   170  	},
   171  	{
   172  		"11795773708834916026404142434151065506931607341523388140225443265536",
   173  		"499d8b2829cfb879c901f7d85d357045edab55028824d0f05ba279ba",
   174  		"bf929537b06e4015919639d94f57838fa33fc3d952598dcdbb44d638",
   175  	},
   176  	{
   177  		"784254593043826236572847595991346435467177662189391577090",
   178  		"8246c999137186632c5f9eddf3b1b0e1764c5e8bd0e0d8a554b9cb77",
   179  		"e80ed8660bc1cb17ac7d845be40a7a022d3306f116ae9f81fea65947",
   180  	},
   181  	{
   182  		"13479767645505654746623887797783387853576174193480695826442858012671",
   183  		"6670c20afcceaea672c97f75e2e9dd5c8460e54bb38538ebb4bd30eb",
   184  		"f280d8008d07a4caf54271f993527d46ff3ff46fd1190a3f1faa4f74",
   185  	},
   186  	{
   187  		"205688069665150753842126177372015544874550518966168735589597183",
   188  		"eca934247425cfd949b795cb5ce1eff401550386e28d1a4c5a8eb",
   189  		"d4c01040dba19628931bc8855370317c722cbd9ca6156985f1c2e9ce",
   190  	},
   191  	{
   192  		"13479966930919337728895168462090683249159702977113823384618282123295",
   193  		"ef353bf5c73cd551b96d596fbc9a67f16d61dd9fe56af19de1fba9cd",
   194  		"21771b9cdce3e8430c09b3838be70b48c21e15bc09ee1f2d7945b91f",
   195  	},
   196  	{
   197  		"50210731791415612487756441341851895584393717453129007497216",
   198  		"4036052a3091eb481046ad3289c95d3ac905ca0023de2c03ecd451cf",
   199  		"d768165a38a2b96f812586a9d59d4136035d9c853a5bf2e1c86a4993",
   200  	},
   201  	{
   202  		"26959946667150639794667015087019625940457807714424391721682722368041",
   203  		"fcc7f2b45df1cd5a3c0c0731ca47a8af75cfb0347e8354eefe782455",
   204  		"f2a28eefd8b345832116f1e574f2c6b2c895aa8c24941f40d8b80ad1",
   205  	},
   206  	{
   207  		"26959946667150639794667015087019625940457807714424391721682722368042",
   208  		"a1e81c04f30ce201c7c9ace785ed44cc33b455a022f2acdbc6cae83c",
   209  		"230e093c24f638f533dac6e2b6d01da3b5e7f45429315ca93fb8e634",
   210  	},
   211  	{
   212  		"26959946667150639794667015087019625940457807714424391721682722368043",
   213  		"c9ff61b040874c0568479216824a15eab1a838a797d189746226e4cc",
   214  		"156729f1a003647030666054e208180f8f7b0df2249e44fba5931fff",
   215  	},
   216  	{
   217  		"26959946667150639794667015087019625940457807714424391721682722368044",
   218  		"b8357c3a6ceef288310e17b8bfeff9200846ca8c1942497c484403bc",
   219  		"eb610599f95942df1082e4f9426d086fb9c6231ae8b24933aab5db",
   220  	},
   221  	{
   222  		"26959946667150639794667015087019625940457807714424391721682722368045",
   223  		"b6ec4fe1777382404ef679997ba8d1cc5cd8e85349259f590c4c66d",
   224  		"cc662b9bcba6f94ee4ff1c9c10bd6ddd0d138df2d099a282152a4b7f",
   225  	},
   226  	{
   227  		"26959946667150639794667015087019625940457807714424391721682722368046",
   228  		"baa4d8635511a7d288aebeedd12ce529ff102c91f97f867e21916bf9",
   229  		"6865a0b8a607f0b04b13d1cb0aa992a5a97f5ee8ca1849efb9ed8678",
   230  	},
   231  	{
   232  		"26959946667150639794667015087019625940457807714424391721682722368047",
   233  		"a53640c83dc208603ded83e4ecf758f24c357d7cf48088b2ce01e9fa",
   234  		"2a7eb328dbe663b5a468b5bc97a040a3745396ba636b964370dc3352",
   235  	},
   236  	{
   237  		"26959946667150639794667015087019625940457807714424391721682722368048",
   238  		"34e8e17a430e43289793c383fac9774247b40e9ebd3366981fcfaeca",
   239  		"dad7e608e380480434ea641cc82c82cbc92801469c8db0204f13489a",
   240  	},
   241  	{
   242  		"26959946667150639794667015087019625940457807714424391721682722368049",
   243  		"6e31ee1dc137f81b056752e4deab1443a481033e9b4c93a3044f4f7a",
   244  		"df82220fc7a4021549165325725f94c3410ddb56c54e161fc9ef62ee",
   245  	},
   246  	{
   247  		"26959946667150639794667015087019625940457807714424391721682722368050",
   248  		"ef53b6294aca431f0f3c22dc82eb9050324f1d88d377e716448e507c",
   249  		"df4aefffbf6d1699c930481cd102127c9a3d992048ab05929b6e5927",
   250  	},
   251  	{
   252  		"26959946667150639794667015087019625940457807714424391721682722368051",
   253  		"aea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd",
   254  		"c644cf154cc81f5ade49345e541b4d4b5c1adb3eb5c01c14ee949aa2",
   255  	},
   256  	{
   257  		"26959946667150639794667015087019625940457807714424391721682722368052",
   258  		"2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d",
   259  		"c8e8cd1b0be40b0877cfca1958603122f1e6914f84b7e8e968ae8b9e",
   260  	},
   261  	{
   262  		"26959946667150639794667015087019625940457807714424391721682722368053",
   263  		"858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550",
   264  		"fb9232c15a3bc7673a3a03b0253824c53d0fd1411b1cabe2e187fb87",
   265  	},
   266  	{
   267  		"26959946667150639794667015087019625940457807714424391721682722368054",
   268  		"db2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28",
   269  		"f0c5cff7ab680d09ee11dae84e9c1072ac48ea2e744b1b7f72fd469e",
   270  	},
   271  	{
   272  		"26959946667150639794667015087019625940457807714424391721682722368055",
   273  		"1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408",
   274  		"76050f3348af2664aac3a8b05281304ebc7a7914c6ad50a4b4eac383",
   275  	},
   276  	{
   277  		"26959946667150639794667015087019625940457807714424391721682722368056",
   278  		"31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa",
   279  		"d817400e8ba9ca13a45f360e3d121eaaeb39af82d6001c8186f5f866",
   280  	},
   281  	{
   282  		"26959946667150639794667015087019625940457807714424391721682722368057",
   283  		"ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
   284  		"fb7da7f5f13a43b81774373c879cd32d6934c05fa758eeb14fcfab38",
   285  	},
   286  	{
   287  		"26959946667150639794667015087019625940457807714424391721682722368058",
   288  		"df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
   289  		"5c080fc3522f41bbb3f55a97cfecf21f882ce8cbb1e50ca6e67e56dc",
   290  	},
   291  	{
   292  		"26959946667150639794667015087019625940457807714424391721682722368059",
   293  		"706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
   294  		"e3d4895843da188fd58fb0567976d7b50359d6b78530c8f62d1b1746",
   295  	},
   296  	{
   297  		"26959946667150639794667015087019625940457807714424391721682722368060",
   298  		"b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
   299  		"42c89c774a08dc04b3dd201932bc8a5ea5f8b89bbb2a7e667aff81cd",
   300  	},
   301  }
   302  
   303  type scalarMultTest struct {
   304  	k          string
   305  	xIn, yIn   string
   306  	xOut, yOut string
   307  }
   308  
   309  var p256MultTests = []scalarMultTest{
   310  	{
   311  		"2a265f8bcbdcaf94d58519141e578124cb40d64a501fba9c11847b28965bc737",
   312  		"023819813ac969847059028ea88a1f30dfbcde03fc791d3a252c6b41211882ea",
   313  		"f93e4ae433cc12cf2a43fc0ef26400c0e125508224cdb649380f25479148a4ad",
   314  		"4d4de80f1534850d261075997e3049321a0864082d24a917863366c0724f5ae3",
   315  		"a22d2b7f7818a3563e0f7a76c9bf0921ac55e06e2e4d11795b233824b1db8cc0",
   316  	},
   317  	{
   318  		"313f72ff9fe811bf573176231b286a3bdb6f1b14e05c40146590727a71c3bccd",
   319  		"cc11887b2d66cbae8f4d306627192522932146b42f01d3c6f92bd5c8ba739b06",
   320  		"a2f08a029cd06b46183085bae9248b0ed15b70280c7ef13a457f5af382426031",
   321  		"831c3f6b5f762d2f461901577af41354ac5f228c2591f84f8a6e51e2e3f17991",
   322  		"93f90934cd0ef2c698cc471c60a93524e87ab31ca2412252337f364513e43684",
   323  	},
   324  }
   325  
   326  func TestBaseMult(t *testing.T) {
   327  	p224 := P224()
   328  	for i, e := range p224BaseMultTests {
   329  		k, ok := new(big.Int).SetString(e.k, 10)
   330  		if !ok {
   331  			t.Errorf("%d: bad value for k: %s", i, e.k)
   332  		}
   333  		x, y := p224.ScalarBaseMult(k.Bytes())
   334  		if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
   335  			t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
   336  		}
   337  		if testing.Short() && i > 5 {
   338  			break
   339  		}
   340  	}
   341  }
   342  
   343  func TestGenericBaseMult(t *testing.T) {
   344  	// We use the P224 CurveParams directly in order to test the generic implementation.
   345  	p224 := P224().Params()
   346  	for i, e := range p224BaseMultTests {
   347  		k, ok := new(big.Int).SetString(e.k, 10)
   348  		if !ok {
   349  			t.Errorf("%d: bad value for k: %s", i, e.k)
   350  		}
   351  		x, y := p224.ScalarBaseMult(k.Bytes())
   352  		if fmt.Sprintf("%x", x) != e.x || fmt.Sprintf("%x", y) != e.y {
   353  			t.Errorf("%d: bad output for k=%s: got (%x, %x), want (%s, %s)", i, e.k, x, y, e.x, e.y)
   354  		}
   355  		if testing.Short() && i > 5 {
   356  			break
   357  		}
   358  	}
   359  }
   360  
   361  func TestP256BaseMult(t *testing.T) {
   362  	p256 := P256()
   363  	p256Generic := p256.Params()
   364  
   365  	scalars := make([]*big.Int, 0, len(p224BaseMultTests)+1)
   366  	for _, e := range p224BaseMultTests {
   367  		k, _ := new(big.Int).SetString(e.k, 10)
   368  		scalars = append(scalars, k)
   369  	}
   370  	k := new(big.Int).SetInt64(1)
   371  	k.Lsh(k, 500)
   372  	scalars = append(scalars, k)
   373  
   374  	for i, k := range scalars {
   375  		x, y := p256.ScalarBaseMult(k.Bytes())
   376  		x2, y2 := p256Generic.ScalarBaseMult(k.Bytes())
   377  		if x.Cmp(x2) != 0 || y.Cmp(y2) != 0 {
   378  			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, x, y, x2, y2)
   379  		}
   380  
   381  		if testing.Short() && i > 5 {
   382  			break
   383  		}
   384  	}
   385  }
   386  
   387  func TestP256Mult(t *testing.T) {
   388  	p256 := P256()
   389  	p256Generic := p256.Params()
   390  
   391  	for i, e := range p224BaseMultTests {
   392  		x, _ := new(big.Int).SetString(e.x, 16)
   393  		y, _ := new(big.Int).SetString(e.y, 16)
   394  		k, _ := new(big.Int).SetString(e.k, 10)
   395  
   396  		xx, yy := p256.ScalarMult(x, y, k.Bytes())
   397  		xx2, yy2 := p256Generic.ScalarMult(x, y, k.Bytes())
   398  		if xx.Cmp(xx2) != 0 || yy.Cmp(yy2) != 0 {
   399  			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, xx2, yy2)
   400  		}
   401  		if testing.Short() && i > 5 {
   402  			break
   403  		}
   404  	}
   405  
   406  	for i, e := range p256MultTests {
   407  		x, _ := new(big.Int).SetString(e.xIn, 16)
   408  		y, _ := new(big.Int).SetString(e.yIn, 16)
   409  		k, _ := new(big.Int).SetString(e.k, 16)
   410  		expectedX, _ := new(big.Int).SetString(e.xOut, 16)
   411  		expectedY, _ := new(big.Int).SetString(e.yOut, 16)
   412  
   413  		xx, yy := p256.ScalarMult(x, y, k.Bytes())
   414  		if xx.Cmp(expectedX) != 0 || yy.Cmp(expectedY) != 0 {
   415  			t.Errorf("#%d: got (%x, %x), want (%x, %x)", i, xx, yy, expectedX, expectedY)
   416  		}
   417  	}
   418  }
   419  
   420  func TestInfinity(t *testing.T) {
   421  	tests := []struct {
   422  		name  string
   423  		curve Curve
   424  	}{
   425  		{"p224", P224()},
   426  		{"p256", P256()},
   427  	}
   428  
   429  	for _, test := range tests {
   430  		curve := test.curve
   431  		x, y := curve.ScalarBaseMult(nil)
   432  		if x.Sign() != 0 || y.Sign() != 0 {
   433  			t.Errorf("%s: x^0 != ∞", test.name)
   434  		}
   435  		x.SetInt64(0)
   436  		y.SetInt64(0)
   437  
   438  		x2, y2 := curve.Double(x, y)
   439  		if x2.Sign() != 0 || y2.Sign() != 0 {
   440  			t.Errorf("%s: 2∞ != ∞", test.name)
   441  		}
   442  
   443  		baseX := curve.Params().Gx
   444  		baseY := curve.Params().Gy
   445  
   446  		x3, y3 := curve.Add(baseX, baseY, x, y)
   447  		if x3.Cmp(baseX) != 0 || y3.Cmp(baseY) != 0 {
   448  			t.Errorf("%s: x+∞ != x", test.name)
   449  		}
   450  
   451  		x4, y4 := curve.Add(x, y, baseX, baseY)
   452  		if x4.Cmp(baseX) != 0 || y4.Cmp(baseY) != 0 {
   453  			t.Errorf("%s: ∞+x != x", test.name)
   454  		}
   455  	}
   456  }
   457  
   458  type synthCombinedMult struct {
   459  	Curve
   460  }
   461  
   462  func (s synthCombinedMult) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) {
   463  	x1, y1 := s.ScalarBaseMult(baseScalar)
   464  	x2, y2 := s.ScalarMult(bigX, bigY, scalar)
   465  	return s.Add(x1, y1, x2, y2)
   466  }
   467  
   468  func TestCombinedMult(t *testing.T) {
   469  	type combinedMult interface {
   470  		Curve
   471  		CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
   472  	}
   473  
   474  	p256, ok := P256().(combinedMult)
   475  	if !ok {
   476  		p256 = &synthCombinedMult{P256()}
   477  	}
   478  
   479  	gx := p256.Params().Gx
   480  	gy := p256.Params().Gy
   481  
   482  	zero := make([]byte, 32)
   483  	one := make([]byte, 32)
   484  	one[31] = 1
   485  	two := make([]byte, 32)
   486  	two[31] = 2
   487  
   488  	// 0×G + 0×G = ∞
   489  	x, y := p256.CombinedMult(gx, gy, zero, zero)
   490  	if x.Sign() != 0 || y.Sign() != 0 {
   491  		t.Errorf("0×G + 0×G = (%d, %d), should be ∞", x, y)
   492  	}
   493  
   494  	// 1×G + 0×G = G
   495  	x, y = p256.CombinedMult(gx, gy, one, zero)
   496  	if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
   497  		t.Errorf("1×G + 0×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
   498  	}
   499  
   500  	// 0×G + 1×G = G
   501  	x, y = p256.CombinedMult(gx, gy, zero, one)
   502  	if x.Cmp(gx) != 0 || y.Cmp(gy) != 0 {
   503  		t.Errorf("0×G + 1×G = (%d, %d), should be (%d, %d)", x, y, gx, gy)
   504  	}
   505  
   506  	// 1×G + 1×G = 2×G
   507  	x, y = p256.CombinedMult(gx, gy, one, one)
   508  	ggx, ggy := p256.ScalarBaseMult(two)
   509  	if x.Cmp(ggx) != 0 || y.Cmp(ggy) != 0 {
   510  		t.Errorf("1×G + 1×G = (%d, %d), should be (%d, %d)", x, y, ggx, ggy)
   511  	}
   512  
   513  	minusOne := new(big.Int).Sub(p256.Params().N, big.NewInt(1))
   514  	// 1×G + (-1)×G = ∞
   515  	x, y = p256.CombinedMult(gx, gy, one, minusOne.Bytes())
   516  	if x.Sign() != 0 || y.Sign() != 0 {
   517  		t.Errorf("1×G + (-1)×G = (%d, %d), should be ∞", x, y)
   518  	}
   519  }
   520  
   521  func BenchmarkBaseMult(b *testing.B) {
   522  	b.ResetTimer()
   523  	p224 := P224()
   524  	e := p224BaseMultTests[25]
   525  	k, _ := new(big.Int).SetString(e.k, 10)
   526  	b.ReportAllocs()
   527  	b.StartTimer()
   528  	b.RunParallel(func(pb *testing.PB) {
   529  		for pb.Next() {
   530  			p224.ScalarBaseMult(k.Bytes())
   531  		}
   532  	})
   533  }
   534  
   535  func BenchmarkBaseMultP256(b *testing.B) {
   536  	b.ResetTimer()
   537  	p256 := P256()
   538  	e := p224BaseMultTests[25]
   539  	k, _ := new(big.Int).SetString(e.k, 10)
   540  	b.ReportAllocs()
   541  	b.StartTimer()
   542  	b.RunParallel(func(pb *testing.PB) {
   543  		for pb.Next() {
   544  			p256.ScalarBaseMult(k.Bytes())
   545  		}
   546  	})
   547  }
   548  
   549  func BenchmarkScalarMultP256(b *testing.B) {
   550  	b.ResetTimer()
   551  	p256 := P256()
   552  	_, x, y, _ := GenerateKey(p256, rand.Reader)
   553  	priv, _, _, _ := GenerateKey(p256, rand.Reader)
   554  
   555  	b.ReportAllocs()
   556  	b.StartTimer()
   557  	b.RunParallel(func(pb *testing.PB) {
   558  		for pb.Next() {
   559  			p256.ScalarMult(x, y, priv)
   560  		}
   561  	})
   562  }
   563  
   564  func TestMarshal(t *testing.T) {
   565  	p224 := P224()
   566  	_, x, y, err := GenerateKey(p224, rand.Reader)
   567  	if err != nil {
   568  		t.Error(err)
   569  		return
   570  	}
   571  	serialized := Marshal(p224, x, y)
   572  	xx, yy := Unmarshal(p224, serialized)
   573  	if xx == nil {
   574  		t.Error("failed to unmarshal")
   575  		return
   576  	}
   577  	if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
   578  		t.Error("unmarshal returned different values")
   579  		return
   580  	}
   581  }
   582  
   583  func TestP224Overflow(t *testing.T) {
   584  	// This tests for a specific bug in the P224 implementation.
   585  	p224 := P224()
   586  	pointData, _ := hex.DecodeString("049B535B45FB0A2072398A6831834624C7E32CCFD5A4B933BCEAF77F1DD945E08BBE5178F5EDF5E733388F196D2A631D2E075BB16CBFEEA15B")
   587  	x, y := Unmarshal(p224, pointData)
   588  	if !p224.IsOnCurve(x, y) {
   589  		t.Error("P224 failed to validate a correct point")
   590  	}
   591  }
   592  
   593  // See https://golang.org/issues/20482
   594  func TestUnmarshalToLargeCoordinates(t *testing.T) {
   595  	curve := P256()
   596  	p := curve.Params().P
   597  
   598  	invalidX, invalidY := make([]byte, 65), make([]byte, 65)
   599  	invalidX[0], invalidY[0] = 4, 4 // uncompressed encoding
   600  
   601  	// Set x to be greater than curve's parameter P – specifically, to P+5.
   602  	// Set y to mod_sqrt(x^3 - 3x + B)) so that (x mod P = 5 , y) is on the
   603  	// curve.
   604  	x := new(big.Int).Add(p, big.NewInt(5))
   605  	y, _ := new(big.Int).SetString("31468013646237722594854082025316614106172411895747863909393730389177298123724", 10)
   606  
   607  	copy(invalidX[1:], x.Bytes())
   608  	copy(invalidX[33:], y.Bytes())
   609  
   610  	if X, Y := Unmarshal(curve, invalidX); X != nil || Y != nil {
   611  		t.Errorf("Unmarshal accepts invalid X coordinate")
   612  	}
   613  
   614  	// 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.
   615  	x, _ = new(big.Int).SetString("31931927535157963707678568152204072984517581467226068221761862915403492091210", 10)
   616  	y, _ = new(big.Int).SetString("5208467867388784005506817585327037698770365050895731383201516607147", 10)
   617  	y.Add(y, p)
   618  
   619  	if p.Cmp(y) > 0 || y.BitLen() != 256 {
   620  		t.Fatal("y not within expected range")
   621  	}
   622  
   623  	// marshal
   624  	copy(invalidY[1:], x.Bytes())
   625  	copy(invalidY[33:], y.Bytes())
   626  
   627  	if X, Y := Unmarshal(curve, invalidY); X != nil || Y != nil {
   628  		t.Errorf("Unmarshal accepts invalid Y coordinate")
   629  	}
   630  }
   631  

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