crypto/elliptic: add package

elliptic implements several standard elliptic curves over prime fields.

R=r, r2
CC=golang-dev
https://golang.org/cl/3065041

src/pkg/Makefile

@@ -32,6 +32,7 @@ DIRS=\
 	crypto/block\
 	crypto/blowfish\
 	crypto/cast5\
+	crypto/elliptic\
 	crypto/hmac\
 	crypto/md4\
 	crypto/md5\

src/pkg/crypto/elliptic/Makefile

+# Copyright 2010 The Go Authors. All rights reserved.
+# Use of this source code is governed by a BSD-style
+# license that can be found in the LICENSE file.
+
+include ../../../Make.inc
+
+TARG=crypto/elliptic
+GOFILES=\
+	elliptic.go\
+
+include ../../../Make.pkg

src/pkg/crypto/elliptic/elliptic.go

+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// The elliptic package implements several standard elliptic curves over prime
+// fields
+package elliptic
+
+// WARNING: this implementation is simple but slow and not constant time.
+// A significant speedup could be obtained by using either a projective or
+// Jacobian transform.
+
+import (
+	"big"
+	"sync"
+)
+
+// A Curve represents a short-form Weierstrass curve with a=-3.
+// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
+type Curve struct {
+	P      *big.Int // the order of the underlying field
+	B      *big.Int // the constant of the curve equation
+	Gx, Gy *big.Int // (x,y) of the base point
+}
+
+// IsOnCurve returns true if the given (x,y) lies on the curve.
+func (curve *Curve) IsOnCurve(x, y *big.Int) bool {
+	// y² = x³ - 3x + b
+	y2 := new(big.Int).Mul(y, y)
+	y2.Mod(y2, curve.P)
+
+	x3 := new(big.Int).Mul(x, x)
+	x3.Mul(x3, x)
+
+	threeX := new(big.Int).Lsh(x, 1)
+	threeX.Add(threeX, x)
+
+	x3.Sub(x3, threeX)
+	x3.Add(x3, curve.B)
+	x3.Mod(x3, curve.P)
+
+	return x3.Cmp(y2) == 0
+}
+
+// Add returns the sum of (x1,y1) and (x2,y2)
+func (curve *Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	// x = (y2-y1)²/(x2-x1)²-x1-x2
+	y2my1 := new(big.Int).Sub(y2, y1)
+	if y2my1.Sign() < 0 {
+		y2my1.Add(y2my1, curve.P)
+	}
+	y2my1sq := new(big.Int).Mul(y2my1, y2my1)
+	x2mx1 := new(big.Int).Sub(x2, x1)
+	if x2mx1.Sign() < 0 {
+		x2mx1.Add(x2mx1, curve.P)
+	}
+	x2mx1sq := new(big.Int).Mul(x2mx1, x2mx1)
+	x2mx1sqinv := new(big.Int).ModInverse(x2mx1sq, curve.P)
+
+	x := new(big.Int).Mul(y2my1sq, x2mx1sqinv)
+	x.Sub(x, x1)
+	x.Sub(x, x2)
+	x.Mod(x, curve.P)
+
+	// y = (2x1+x2)*(y2-y1)/(x2-x1)-(y2-y1)³/(x2-x1)³-y1
+	y := new(big.Int).Lsh(x1, 1)
+	y.Add(y, x2)
+	x2mx1inv := new(big.Int).ModInverse(x2mx1, curve.P)
+	x2mx1inv.Mul(y2my1, x2mx1inv)
+	y.Mul(y, x2mx1inv)
+
+	y2my1sq.Mul(y2my1sq, y2my1)
+	x2mx1sq.Mul(x2mx1sq, x2mx1)
+	x2mx1sqinv.ModInverse(x2mx1sq, curve.P)
+	y2my1sq.Mul(y2my1sq, x2mx1sqinv)
+	y.Sub(y, y2my1sq)
+	y.Sub(y, y1)
+	y.Mod(y, curve.P)
+
+	return x, y
+}
+
+// Double returns 2*(x,y)
+func (curve *Curve) Double(x, y *big.Int) (*big.Int, *big.Int) {
+	// x = (3x²-3)²/(2y)²-x-x
+	threexsqm3 := new(big.Int).Mul(x, x)
+	three := new(big.Int).SetInt64(3)
+	threexsqm3.Mul(threexsqm3, three)
+	threexsqm3.Sub(threexsqm3, three)
+	threexsqm3sq := new(big.Int).Mul(threexsqm3, threexsqm3)
+
+	twoy := new(big.Int).Lsh(y, 1)
+	twoysq := new(big.Int).Mul(twoy, twoy)
+	twoysqinv := new(big.Int).ModInverse(twoysq, curve.P)
+
+	outx := new(big.Int).Mul(threexsqm3sq, twoysqinv)
+	outx.Sub(outx, x)
+	outx.Sub(outx, x)
+	outx.Mod(outx, curve.P)
+
+	// y = 3x*(3x²-3)/(2y)-(3x²-3)³/(2y)³-y
+	outy := new(big.Int).Mul(x, three)
+	outy.Mul(outy, threexsqm3)
+	twoyinv := new(big.Int).ModInverse(twoy, curve.P)
+	outy.Mul(outy, twoyinv)
+
+	threexsqm3sq.Mul(threexsqm3sq, threexsqm3)
+	twoysq.Mul(twoysq, twoy)
+	twoysqinv.ModInverse(twoysq, curve.P)
+	threexsqm3sq.Mul(threexsqm3sq, twoysqinv)
+	outy.Sub(outy, threexsqm3sq)
+	outy.Sub(outy, y)
+	outy.Mod(outy, curve.P)
+
+	return outx, outy
+}
+
+// ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
+func (curve *Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	// We have a slight problem in that the identity of the group (the
+	// point at infinity) cannot be represented in (x, y) form on a finite
+	// machine. Thus the standard add/double algorithm has to be tweaked
+	// slightly: our initial state is not the identity, but x, and we
+	// ignore the first true bit in |k|.  If we don't find any true bits in
+	// |k|, then we return nil, nil, because we cannot return the identity
+	// element.
+
+	x := Bx
+	y := By
+
+	seenFirstTrue := false
+	for _, byte := range k {
+		for bitNum := 0; bitNum < 8; bitNum++ {
+			if seenFirstTrue {
+				x, y = curve.Double(x, y)
+			}
+			if byte&0x80 == 0x80 {
+				if !seenFirstTrue {
+					seenFirstTrue = true
+				} else {
+					x, y = curve.Add(Bx, By, x, y)
+				}
+			}
+			byte <<= 1
+		}
+	}
+
+	if !seenFirstTrue {
+		return nil, nil
+	}
+
+	return x, y
+}
+
+// ScalarBaseMult returns k*G, where G is the base point of the group and k is
+// an integer in big-endian form.
+func (curve *Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	return curve.ScalarMult(curve.Gx, curve.Gy, k)
+}
+
+var initonce sync.Once
+var p224 *Curve
+var p256 *Curve
+var p384 *Curve
+var p521 *Curve
+
+func initAll() {
+	initP224()
+	initP256()
+	initP384()
+	initP521()
+}
+
+func initP224() {
+	// See FIPS 186-3, section D.2.2
+	p224 = new(Curve)
+	p224.P, _ = new(big.Int).SetString("26959946667150639794667015087019630673557916260026308143510066298881", 10)
+	p224.B, _ = new(big.Int).SetString("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16)
+	p224.Gx, _ = new(big.Int).SetString("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16)
+	p224.Gy, _ = new(big.Int).SetString("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16)
+}
+
+func initP256() {
+	// See FIPS 186-3, section D.2.3
+	p256 = new(Curve)
+	p256.P, _ = new(big.Int).SetString("115792089210356248762697446949407573530086143415290314195533631308867097853951", 10)
+	p256.B, _ = new(big.Int).SetString("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16)
+	p256.Gx, _ = new(big.Int).SetString("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16)
+	p256.Gy, _ = new(big.Int).SetString("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16)
+}
+
+func initP384() {
+	// See FIPS 186-3, section D.2.4
+	p384 = new(Curve)
+	p384.P, _ = new(big.Int).SetString("39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319", 10)
+	p384.B, _ = new(big.Int).SetString("b3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef", 16)
+	p384.Gx, _ = new(big.Int).SetString("aa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7", 16)
+	p384.Gy, _ = new(big.Int).SetString("3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f", 16)
+}
+
+func initP521() {
+	// See FIPS 186-3, section D.2.5
+	p521 = new(Curve)
+	p521.P, _ = new(big.Int).SetString("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", 10)
+	p521.B, _ = new(big.Int).SetString("051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 16)
+	p521.Gx, _ = new(big.Int).SetString("c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", 16)
+	p521.Gy, _ = new(big.Int).SetString("11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", 16)
+}
+
+// P224 returns a Curve which implements P-224 (see FIPS 186-3, section D.2.2)
+func P224() *Curve {
+	initonce.Do(initAll)
+	return p224
+}
+
+// P256 returns a Curve which implements P-256 (see FIPS 186-3, section D.2.3)
+func P256() *Curve {
+	initonce.Do(initAll)
+	return p256
+}
+
+// P384 returns a Curve which implements P-384 (see FIPS 186-3, section D.2.4)
+func P384() *Curve {
+	initonce.Do(initAll)
+	return p384
+}
+
+// P256 returns a Curve which implements P-521 (see FIPS 186-3, section D.2.5)
+func P521() *Curve {
+	initonce.Do(initAll)
+	return p521
+}

src/pkg/crypto/elliptic/elliptic_test.go

+// Copyright 2010 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package elliptic
+
+import (
+	"big"
+	"fmt"
+	"testing"
+)
+
+func TestOnCurve(t *testing.T) {
+	p224 := P224()
+	if !p224.IsOnCurve(p224.Gx, p224.Gy) {
+		t.Errorf("FAIL")
+	}
+}
+
+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 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", 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, %s), want (%s, %s)", i, e.k, x, y, e.x, e.y)
+		}
+	}
+}