Ensured all tests and benchmarks run over all curves.
Change-Id: Idcbe14a50c60ff6c2cd56793bced6b428d049c39
Reviewed-on: https://go-review.googlesource.com/c/go/+/315272
Trust: Filippo Valsorda <filippo@golang.org>
Trust: Katie Hockman <katie@golang.org>
Run-TryBot: Filippo Valsorda <filippo@golang.org>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Katie Hockman <katie@golang.org>
Reviewed-by: Roland Shoemaker <roland@golang.org>
//go:noescape
func kdsa(fc uint64, params *[4096]byte) (errn uint64)
+// testingDisableKDSA forces the generic fallback path. It must only be set in tests.
+var testingDisableKDSA bool
+
// canUseKDSA checks if KDSA instruction is available, and if it is, it checks
// the name of the curve to see if it matches the curves supported(P-256, P-384, P-521).
// Then, based on the curve name, a function code and a block size will be assigned.
// If KDSA instruction is not available or if the curve is not supported, canUseKDSA
// will set ok to false.
func canUseKDSA(c elliptic.Curve) (functionCode uint64, blockSize int, ok bool) {
+ if testingDisableKDSA {
+ return 0, 0, false
+ }
if !cpu.S390X.HasECDSA {
return 0, 0, false
}
)
func TestNoAsm(t *testing.T) {
+ testingDisableKDSA = true
+ defer func() { testingDisableKDSA = false }()
+
curves := [...]elliptic.Curve{
elliptic.P256(),
elliptic.P384(),
}
for _, curve := range curves {
- // override the name of the curve to stop the assembly path being taken
- params := *curve.Params()
- name := params.Name
- params.Name = name + "_GENERIC_OVERRIDE"
-
- testKeyGeneration(t, ¶ms, name)
- testSignAndVerify(t, ¶ms, name)
- testNonceSafety(t, ¶ms, name)
- testINDCCA(t, ¶ms, name)
- testNegativeInputs(t, ¶ms, name)
+ name := curve.Params().Name
+ t.Run(name, func(t *testing.T) { testKeyGeneration(t, curve) })
+ t.Run(name, func(t *testing.T) { testSignAndVerify(t, curve) })
+ t.Run(name, func(t *testing.T) { testNonceSafety(t, curve) })
+ t.Run(name, func(t *testing.T) { testINDCCA(t, curve) })
+ t.Run(name, func(t *testing.T) { testNegativeInputs(t, curve) })
}
}
"testing"
)
-func testKeyGeneration(t *testing.T, c elliptic.Curve, tag string) {
- priv, err := GenerateKey(c, rand.Reader)
- if err != nil {
- t.Errorf("%s: error: %s", tag, err)
- return
+func testAllCurves(t *testing.T, f func(*testing.T, elliptic.Curve)) {
+ tests := []struct {
+ name string
+ curve elliptic.Curve
+ }{
+ {"P256", elliptic.P256()},
+ {"P224", elliptic.P224()},
+ {"P384", elliptic.P384()},
+ {"P521", elliptic.P521()},
}
- if !c.IsOnCurve(priv.PublicKey.X, priv.PublicKey.Y) {
- t.Errorf("%s: public key invalid: %s", tag, err)
- }
-}
-
-func TestKeyGeneration(t *testing.T) {
- testKeyGeneration(t, elliptic.P224(), "p224")
if testing.Short() {
- return
+ tests = tests[:1]
+ }
+ for _, test := range tests {
+ curve := test.curve
+ t.Run(test.name, func(t *testing.T) {
+ t.Parallel()
+ f(t, curve)
+ })
}
- testKeyGeneration(t, elliptic.P256(), "p256")
- testKeyGeneration(t, elliptic.P384(), "p384")
- testKeyGeneration(t, elliptic.P521(), "p521")
-}
-
-func BenchmarkSignP256(b *testing.B) {
- b.ResetTimer()
- p256 := elliptic.P256()
- hashed := []byte("testing")
- priv, _ := GenerateKey(p256, rand.Reader)
-
- b.ReportAllocs()
- b.ResetTimer()
- b.RunParallel(func(pb *testing.PB) {
- for pb.Next() {
- _, _, _ = Sign(rand.Reader, priv, hashed)
- }
- })
}
-func BenchmarkSignP384(b *testing.B) {
- b.ResetTimer()
- p384 := elliptic.P384()
- hashed := []byte("testing")
- priv, _ := GenerateKey(p384, rand.Reader)
-
- b.ReportAllocs()
- b.ResetTimer()
- b.RunParallel(func(pb *testing.PB) {
- for pb.Next() {
- _, _, _ = Sign(rand.Reader, priv, hashed)
- }
- })
+func TestKeyGeneration(t *testing.T) {
+ testAllCurves(t, testKeyGeneration)
}
-func BenchmarkVerifyP256(b *testing.B) {
- b.ResetTimer()
- p256 := elliptic.P256()
- hashed := []byte("testing")
- priv, _ := GenerateKey(p256, rand.Reader)
- r, s, _ := Sign(rand.Reader, priv, hashed)
-
- b.ReportAllocs()
- b.ResetTimer()
- b.RunParallel(func(pb *testing.PB) {
- for pb.Next() {
- Verify(&priv.PublicKey, hashed, r, s)
- }
- })
+func testKeyGeneration(t *testing.T, c elliptic.Curve) {
+ priv, err := GenerateKey(c, rand.Reader)
+ if err != nil {
+ t.Fatal(err)
+ }
+ if !c.IsOnCurve(priv.PublicKey.X, priv.PublicKey.Y) {
+ t.Errorf("public key invalid: %s", err)
+ }
}
-func BenchmarkKeyGeneration(b *testing.B) {
- b.ResetTimer()
- p256 := elliptic.P256()
-
- b.ReportAllocs()
- b.ResetTimer()
- b.RunParallel(func(pb *testing.PB) {
- for pb.Next() {
- GenerateKey(p256, rand.Reader)
- }
- })
+func TestSignAndVerify(t *testing.T) {
+ testAllCurves(t, testSignAndVerify)
}
-func testSignAndVerify(t *testing.T, c elliptic.Curve, tag string) {
+func testSignAndVerify(t *testing.T, c elliptic.Curve) {
priv, _ := GenerateKey(c, rand.Reader)
hashed := []byte("testing")
r, s, err := Sign(rand.Reader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
if !Verify(&priv.PublicKey, hashed, r, s) {
- t.Errorf("%s: Verify failed", tag)
+ t.Errorf("Verify failed")
}
hashed[0] ^= 0xff
if Verify(&priv.PublicKey, hashed, r, s) {
- t.Errorf("%s: Verify always works!", tag)
+ t.Errorf("Verify always works!")
}
}
-func TestSignAndVerify(t *testing.T) {
- testSignAndVerify(t, elliptic.P224(), "p224")
- if testing.Short() {
- return
- }
- testSignAndVerify(t, elliptic.P256(), "p256")
- testSignAndVerify(t, elliptic.P384(), "p384")
- testSignAndVerify(t, elliptic.P521(), "p521")
+func TestSignAndVerifyASN1(t *testing.T) {
+ testAllCurves(t, testSignAndVerifyASN1)
}
-func testSignAndVerifyASN1(t *testing.T, c elliptic.Curve, tag string) {
+func testSignAndVerifyASN1(t *testing.T, c elliptic.Curve) {
priv, _ := GenerateKey(c, rand.Reader)
hashed := []byte("testing")
sig, err := SignASN1(rand.Reader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
if !VerifyASN1(&priv.PublicKey, hashed, sig) {
- t.Errorf("%s: VerifyASN1 failed", tag)
+ t.Errorf("VerifyASN1 failed")
}
hashed[0] ^= 0xff
if VerifyASN1(&priv.PublicKey, hashed, sig) {
- t.Errorf("%s: VerifyASN1 always works!", tag)
+ t.Errorf("VerifyASN1 always works!")
}
}
-func TestSignAndVerifyASN1(t *testing.T) {
- testSignAndVerifyASN1(t, elliptic.P224(), "p224")
- if testing.Short() {
- return
- }
- testSignAndVerifyASN1(t, elliptic.P256(), "p256")
- testSignAndVerifyASN1(t, elliptic.P384(), "p384")
- testSignAndVerifyASN1(t, elliptic.P521(), "p521")
+func TestNonceSafety(t *testing.T) {
+ testAllCurves(t, testNonceSafety)
}
-func testNonceSafety(t *testing.T, c elliptic.Curve, tag string) {
+func testNonceSafety(t *testing.T, c elliptic.Curve) {
priv, _ := GenerateKey(c, rand.Reader)
hashed := []byte("testing")
r0, s0, err := Sign(zeroReader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
hashed = []byte("testing...")
r1, s1, err := Sign(zeroReader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
if s0.Cmp(s1) == 0 {
// This should never happen.
- t.Errorf("%s: the signatures on two different messages were the same", tag)
+ t.Errorf("the signatures on two different messages were the same")
}
if r0.Cmp(r1) == 0 {
- t.Errorf("%s: the nonce used for two different messages was the same", tag)
+ t.Errorf("the nonce used for two different messages was the same")
}
}
-func TestNonceSafety(t *testing.T) {
- testNonceSafety(t, elliptic.P224(), "p224")
- if testing.Short() {
- return
- }
- testNonceSafety(t, elliptic.P256(), "p256")
- testNonceSafety(t, elliptic.P384(), "p384")
- testNonceSafety(t, elliptic.P521(), "p521")
+func TestINDCCA(t *testing.T) {
+ testAllCurves(t, testINDCCA)
}
-func testINDCCA(t *testing.T, c elliptic.Curve, tag string) {
+func testINDCCA(t *testing.T, c elliptic.Curve) {
priv, _ := GenerateKey(c, rand.Reader)
hashed := []byte("testing")
r0, s0, err := Sign(rand.Reader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
r1, s1, err := Sign(rand.Reader, priv, hashed)
if err != nil {
- t.Errorf("%s: error signing: %s", tag, err)
+ t.Errorf("error signing: %s", err)
return
}
if s0.Cmp(s1) == 0 {
- t.Errorf("%s: two signatures of the same message produced the same result", tag)
+ t.Errorf("two signatures of the same message produced the same result")
}
if r0.Cmp(r1) == 0 {
- t.Errorf("%s: two signatures of the same message produced the same nonce", tag)
- }
-}
-
-func TestINDCCA(t *testing.T) {
- testINDCCA(t, elliptic.P224(), "p224")
- if testing.Short() {
- return
+ t.Errorf("two signatures of the same message produced the same nonce")
}
- testINDCCA(t, elliptic.P256(), "p256")
- testINDCCA(t, elliptic.P384(), "p384")
- testINDCCA(t, elliptic.P521(), "p521")
}
func fromHex(s string) *big.Int {
}
}
-func testNegativeInputs(t *testing.T, curve elliptic.Curve, tag string) {
+func TestNegativeInputs(t *testing.T) {
+ testAllCurves(t, testNegativeInputs)
+}
+
+func testNegativeInputs(t *testing.T, curve elliptic.Curve) {
key, err := GenerateKey(curve, rand.Reader)
if err != nil {
- t.Errorf("failed to generate key for %q", tag)
+ t.Errorf("failed to generate key")
}
var hash [32]byte
r.Neg(r)
if Verify(&key.PublicKey, hash[:], r, r) {
- t.Errorf("bogus signature accepted for %q", tag)
+ t.Errorf("bogus signature accepted")
}
}
-func TestNegativeInputs(t *testing.T) {
- testNegativeInputs(t, elliptic.P224(), "p224")
- testNegativeInputs(t, elliptic.P256(), "p256")
- testNegativeInputs(t, elliptic.P384(), "p384")
- testNegativeInputs(t, elliptic.P521(), "p521")
+func TestZeroHashSignature(t *testing.T) {
+ testAllCurves(t, testZeroHashSignature)
}
-func TestZeroHashSignature(t *testing.T) {
+func testZeroHashSignature(t *testing.T, curve elliptic.Curve) {
zeroHash := make([]byte, 64)
- for _, curve := range []elliptic.Curve{elliptic.P224(), elliptic.P256(), elliptic.P384(), elliptic.P521()} {
- privKey, err := GenerateKey(curve, rand.Reader)
+ privKey, err := GenerateKey(curve, rand.Reader)
+ if err != nil {
+ panic(err)
+ }
+
+ // Sign a hash consisting of all zeros.
+ r, s, err := Sign(rand.Reader, privKey, zeroHash)
+ if err != nil {
+ panic(err)
+ }
+
+ // Confirm that it can be verified.
+ if !Verify(&privKey.PublicKey, zeroHash, r, s) {
+ t.Errorf("zero hash signature verify failed for %T", curve)
+ }
+}
+
+func benchmarkAllCurves(t *testing.B, f func(*testing.B, elliptic.Curve)) {
+ tests := []struct {
+ name string
+ curve elliptic.Curve
+ }{
+ {"P256", elliptic.P256()},
+ {"P224", elliptic.P224()},
+ {"P384", elliptic.P384()},
+ {"P521", elliptic.P521()},
+ }
+ for _, test := range tests {
+ curve := test.curve
+ t.Run(test.name, func(t *testing.B) {
+ f(t, curve)
+ })
+ }
+}
+
+func BenchmarkSign(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve elliptic.Curve) {
+ priv, err := GenerateKey(curve, rand.Reader)
if err != nil {
- panic(err)
+ b.Fatal(err)
}
+ hashed := []byte("testing")
+
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ sig, err := SignASN1(rand.Reader, priv, hashed)
+ if err != nil {
+ b.Fatal(err)
+ }
+ // Prevent the compiler from optimizing out the operation.
+ hashed[0] = sig[0]
+ }
+ })
+}
- // Sign a hash consisting of all zeros.
- r, s, err := Sign(rand.Reader, privKey, zeroHash)
+func BenchmarkVerify(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve elliptic.Curve) {
+ priv, err := GenerateKey(curve, rand.Reader)
+ if err != nil {
+ b.Fatal(err)
+ }
+ hashed := []byte("testing")
+ r, s, err := Sign(rand.Reader, priv, hashed)
if err != nil {
- panic(err)
+ b.Fatal(err)
}
- // Confirm that it can be verified.
- if !Verify(&privKey.PublicKey, zeroHash, r, s) {
- t.Errorf("zero hash signature verify failed for %T", curve)
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ if !Verify(&priv.PublicKey, hashed, r, s) {
+ b.Fatal("verify failed")
+ }
}
- }
+ })
+}
+
+func BenchmarkGenerateKey(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve elliptic.Curve) {
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ if _, err := GenerateKey(curve, rand.Reader); err != nil {
+ b.Fatal(err)
+ }
+ }
+ })
}
"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")
+func testAllCurves(t *testing.T, f func(*testing.T, Curve)) {
+ tests := []struct {
+ name string
+ curve Curve
+ }{
+ {"P256", P256()},
+ {"P256/Params", P256().Params()},
+ {"P224", P224()},
+ {"P224/Params", P224().Params()},
+ {"P384", P384()},
+ {"P384/Params", P384().Params()},
+ {"P521", P521()},
+ {"P521/Params", P521().Params()},
}
- 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")
+ if testing.Short() {
+ tests = tests[:1]
}
-}
-
-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
- }
+ for _, test := range tests {
+ curve := test.curve
+ t.Run(test.name, func(t *testing.T) {
+ t.Parallel()
+ f(t, curve)
+ })
}
}
-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 TestOnCurve(t *testing.T) {
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ if !curve.IsOnCurve(curve.Params().Gx, curve.Params().Gy) {
+ t.Error("basepoint is not on the curve")
}
- }
+ })
}
-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)
+func TestOffCurve(t *testing.T) {
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
+ if curve.IsOnCurve(x, y) {
+ t.Errorf("point off curve is claimed to be on the curve")
}
-
- if testing.Short() && i > 5 {
- break
+ b := Marshal(curve, x, y)
+ x1, y1 := Unmarshal(curve, b)
+ if x1 != nil || y1 != nil {
+ t.Errorf("unmarshaling a point not on the curve succeeded")
}
- }
+ })
}
-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) {
+ testAllCurves(t, testInfinity)
}
func testInfinity(t *testing.T, curve Curve) {
}
}
-func TestInfinity(t *testing.T) {
- tests := []struct {
- name string
- curve Curve
- }{
- {"P-224", P224()},
- {"P-256", P256()},
- {"P-256/Generic", P256().Params()},
- {"P-384", P384()},
- {"P-521", P521()},
- }
- if testing.Short() {
- tests = tests[:1]
- }
- for _, test := range tests {
- curve := test.curve
- t.Run(test.name, func(t *testing.T) {
- testInfinity(t, curve)
- })
- }
-}
-
-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 TestMarshal(t *testing.T) {
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ _, x, y, err := GenerateKey(curve, rand.Reader)
+ if err != nil {
+ t.Fatal(err)
}
- })
-}
-
-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())
+ serialized := Marshal(curve, x, y)
+ xx, yy := Unmarshal(curve, serialized)
+ if xx == nil {
+ t.Fatal("failed to unmarshal")
}
- })
-}
-
-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)
+ if xx.Cmp(x) != 0 || yy.Cmp(y) != 0 {
+ t.Fatal("unmarshal returned different values")
}
})
}
-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")
- }
+func TestUnmarshalToLargeCoordinates(t *testing.T) {
+ // See https://golang.org/issues/20482.
+ testAllCurves(t, testUnmarshalToLargeCoordinates)
}
-// See https://golang.org/issues/20482
-func TestUnmarshalToLargeCoordinates(t *testing.T) {
- curve := P256()
+func testUnmarshalToLargeCoordinates(t *testing.T, curve Curve) {
p := curve.Params().P
-
- invalidX, invalidY := make([]byte, 65), make([]byte, 65)
- invalidX[0], invalidY[0] = 4, 4 // uncompressed encoding
+ byteLen := (p.BitLen() + 7) / 8
// 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)
+ y := curve.Params().polynomial(x)
+ y.ModSqrt(y, p)
- copy(invalidX[1:], x.Bytes())
- copy(invalidX[33:], y.Bytes())
+ invalid := make([]byte, byteLen*2+1)
+ invalid[0] = 4 // uncompressed encoding
+ x.FillBytes(invalid[1 : 1+byteLen])
+ y.FillBytes(invalid[1+byteLen:])
- if X, Y := Unmarshal(curve, invalidX); X != nil || Y != nil {
+ if X, Y := Unmarshal(curve, invalid); 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 curve == p256 {
+ // 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")
- }
+ 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())
+ // marshal
+ x.FillBytes(invalid[1 : 1+byteLen])
+ y.FillBytes(invalid[1+byteLen:])
- if X, Y := Unmarshal(curve, invalidY); X != nil || Y != nil {
- t.Errorf("Unmarshal accepts invalid Y coordinate")
+ if X, Y := Unmarshal(curve, invalid); X != nil || Y != nil {
+ t.Errorf("Unmarshal accepts invalid Y coordinate")
+ }
}
}
t.Skip("skipping other curves on short test")
}
- t.Run("P-224", func(t *testing.T) {
- _, x, y, err := GenerateKey(P224(), rand.Reader)
+ testAllCurves(t, func(t *testing.T, curve Curve) {
+ _, x, y, err := GenerateKey(curve, 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)
+ testMarshalCompressed(t, curve, x, y, nil)
})
+
}
func testMarshalCompressed(t *testing.T, curve Curve, x, y *big.Int, want []byte) {
t.Errorf("point did not round-trip correctly: got (%v, %v), want (%v, %v)", X, Y, x, y)
}
}
+
+func benchmarkAllCurves(t *testing.B, f func(*testing.B, Curve)) {
+ tests := []struct {
+ name string
+ curve Curve
+ }{
+ {"P256", P256()},
+ {"P224", P224()},
+ {"P384", P384()},
+ {"P521", P521()},
+ }
+ for _, test := range tests {
+ curve := test.curve
+ t.Run(test.name, func(t *testing.B) {
+ f(t, curve)
+ })
+ }
+}
+
+func BenchmarkScalarBaseMult(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
+ priv, _, _, _ := GenerateKey(curve, rand.Reader)
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x, _ := curve.ScalarBaseMult(priv)
+ // Prevent the compiler from optimizing out the operation.
+ priv[0] ^= byte(x.Bits()[0])
+ }
+ })
+}
+
+func BenchmarkScalarMult(b *testing.B) {
+ benchmarkAllCurves(b, func(b *testing.B, curve Curve) {
+ _, x, y, _ := GenerateKey(curve, rand.Reader)
+ priv, _, _, _ := GenerateKey(curve, rand.Reader)
+ b.ReportAllocs()
+ b.ResetTimer()
+ for i := 0; i < b.N; i++ {
+ x, y = curve.ScalarMult(x, y, priv)
+ }
+ })
+}
)
func TestFuzz(t *testing.T) {
-
p256 := P256()
p256Generic := p256.Params()
package elliptic
import (
+ "encoding/hex"
+ "fmt"
"math/big"
"math/bits"
"math/rand"
t.Errorf("p224Invert(a) * a = %x, expected 1", out)
}
}
+
+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",
+ },
+}
+
+func TestP224BaseMult(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 TestP224GenericBaseMult(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 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")
+ }
+}
--- /dev/null
+// Copyright 2021 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 (
+ "math/big"
+ "testing"
+)
+
+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 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)
+ }
+ }
+}
+
+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 TestP256CombinedMult(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)
+ }
+}