]> Cypherpunks repositories - gostls13.git/commitdiff
crypto/ecdsa,crypto/elliptic: improve tests and benchmarks
authorFilippo Valsorda <filippo@golang.org>
Sat, 1 May 2021 03:10:26 +0000 (23:10 -0400)
committerFilippo Valsorda <filippo@golang.org>
Thu, 6 May 2021 02:21:55 +0000 (02:21 +0000)
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>
src/crypto/ecdsa/ecdsa_s390x.go
src/crypto/ecdsa/ecdsa_s390x_test.go
src/crypto/ecdsa/ecdsa_test.go
src/crypto/elliptic/elliptic_test.go
src/crypto/elliptic/fuzz_test.go
src/crypto/elliptic/p224_test.go
src/crypto/elliptic/p256_test.go [new file with mode: 0644]

index 0a1d73e7a46bfdc9a7f3f26dff7e476327d0d5c2..1480d1bf6f62913cb73c87f3e295208e5c7ed695 100644 (file)
@@ -21,12 +21,18 @@ import (
 //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
        }
index e8b16b3668bd1f8d8531e4494d5487b9599ac432..f5633fb8a62dec57d7e48f96774dadc92577948f 100644 (file)
@@ -13,6 +13,9 @@ import (
 )
 
 func TestNoAsm(t *testing.T) {
+       testingDisableKDSA = true
+       defer func() { testingDisableKDSA = false }()
+
        curves := [...]elliptic.Curve{
                elliptic.P256(),
                elliptic.P384(),
@@ -20,15 +23,11 @@ func TestNoAsm(t *testing.T) {
        }
 
        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, &params, name)
-               testSignAndVerify(t, &params, name)
-               testNonceSafety(t, &params, name)
-               testINDCCA(t, &params, name)
-               testNegativeInputs(t, &params, 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) })
        }
 }
index 0c1ff6d2008b22688a8a9a8deba462d084a516ef..556818acf4d14ac411cfc3393746e8bb075dca56 100644 (file)
@@ -21,216 +21,148 @@ import (
        "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 {
@@ -351,10 +283,14 @@ func TestVectors(t *testing.T) {
        }
 }
 
-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
@@ -363,35 +299,103 @@ func testNegativeInputs(t *testing.T, curve elliptic.Curve, tag string) {
        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)
+                       }
+               }
+       })
 }
index e80e7731aaaed03b15dcb698722738a99c4cf8e2..0d43b736f9ae5dac936d26b467d8c442b2a7f156 100644 (file)
@@ -8,414 +8,60 @@ import (
        "bytes"
        "crypto/rand"
        "encoding/hex"
-       "fmt"
        "math/big"
        "testing"
 )
 
-func TestOnCurve(t *testing.T) {
-       p224 := P224()
-       if !p224.IsOnCurve(p224.Params().Gx, p224.Params().Gy) {
-               t.Errorf("FAIL")
-       }
-}
-
-func TestOffCurve(t *testing.T) {
-       p224 := P224()
-       x, y := new(big.Int).SetInt64(1), new(big.Int).SetInt64(1)
-       if p224.IsOnCurve(x, y) {
-               t.Errorf("FAIL: point off curve is claimed to be on the curve")
+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) {
@@ -455,199 +101,66 @@ 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")
+               }
        }
 }
 
@@ -677,27 +190,14 @@ func TestMarshalCompressed(t *testing.T) {
                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) {
@@ -721,3 +221,46 @@ 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)
+               }
+       })
+}
index f5c9841a126f903723b0f285a720c87049e5bdee..8ff3bf3cc245056169cc4c74d74de4db0d390217 100644 (file)
@@ -14,7 +14,6 @@ import (
 )
 
 func TestFuzz(t *testing.T) {
-
        p256 := P256()
        p256Generic := p256.Params()
 
index c3141b6ab4de0b00ec7382cff55b2d47b8ab1d0d..b213b273d23d887b5c6e6d888e29872022d45f3c 100644 (file)
@@ -5,6 +5,8 @@
 package elliptic
 
 import (
+       "encoding/hex"
+       "fmt"
        "math/big"
        "math/bits"
        "math/rand"
@@ -312,3 +314,316 @@ func TestP224Invert(t *testing.T) {
                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")
+       }
+}
diff --git a/src/crypto/elliptic/p256_test.go b/src/crypto/elliptic/p256_test.go
new file mode 100644 (file)
index 0000000..1435f5e
--- /dev/null
@@ -0,0 +1,155 @@
+// 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)
+       }
+}