From: Adam Langley Date: Fri, 12 Nov 2010 19:55:32 +0000 (-0500) Subject: crypto/elliptic: add package X-Git-Tag: weekly.2010-11-23~30 X-Git-Url: http://www.git.cypherpunks.su/?a=commitdiff_plain;h=fb784785f5c871c7c6d6c90637fa05ca23c16ef9;p=gostls13.git crypto/elliptic: add package elliptic implements several standard elliptic curves over prime fields. R=r, r2 CC=golang-dev https://golang.org/cl/3065041 --- diff --git a/src/pkg/Makefile b/src/pkg/Makefile index 05bddb4429..cfb16d2004 100644 --- a/src/pkg/Makefile +++ b/src/pkg/Makefile @@ -32,6 +32,7 @@ DIRS=\ crypto/block\ crypto/blowfish\ crypto/cast5\ + crypto/elliptic\ crypto/hmac\ crypto/md4\ crypto/md5\ diff --git a/src/pkg/crypto/elliptic/Makefile b/src/pkg/crypto/elliptic/Makefile new file mode 100644 index 0000000000..4db5d7de5f --- /dev/null +++ b/src/pkg/crypto/elliptic/Makefile @@ -0,0 +1,11 @@ +# 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 diff --git a/src/pkg/crypto/elliptic/elliptic.go b/src/pkg/crypto/elliptic/elliptic.go new file mode 100644 index 0000000000..0dca53b4b5 --- /dev/null +++ b/src/pkg/crypto/elliptic/elliptic.go @@ -0,0 +1,232 @@ +// 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 +} diff --git a/src/pkg/crypto/elliptic/elliptic_test.go b/src/pkg/crypto/elliptic/elliptic_test.go new file mode 100644 index 0000000000..797bc6cb41 --- /dev/null +++ b/src/pkg/crypto/elliptic/elliptic_test.go @@ -0,0 +1,300 @@ +// 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", + 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"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) + } + } +}