1 files changed, 203 insertions, 0 deletions
diff --git a/vendor/github.com/btcsuite/btcd/btcec/gensecp256k1.go b/vendor/github.com/btcsuite/btcd/btcec/gensecp256k1.go
new file mode 100644
index 000000000..1928702da
--- /dev/null
+++ b/vendor/github.com/btcsuite/btcd/btcec/gensecp256k1.go
@@ -0,0 +1,203 @@
+// Copyright (c) 2014-2015 The btcsuite developers
+// Use of this source code is governed by an ISC
+// license that can be found in the LICENSE file.
+
+// This file is ignored during the regular build due to the following build tag.
+// This build tag is set during go generate.
+// +build gensecp256k1
+
+package btcec
+
+// References:
+//   [GECC]: Guide to Elliptic Curve Cryptography (Hankerson, Menezes, Vanstone)
+
+import (
+	"encoding/binary"
+	"math/big"
+)
+
+// secp256k1BytePoints are dummy points used so the code which generates the
+// real values can compile.
+var secp256k1BytePoints = ""
+
+// getDoublingPoints returns all the possible G^(2^i) for i in
+// 0..n-1 where n is the curve's bit size (256 in the case of secp256k1)
+// the coordinates are recorded as Jacobian coordinates.
+func (curve *KoblitzCurve) getDoublingPoints() [][3]fieldVal {
+	doublingPoints := make([][3]fieldVal, curve.BitSize)
+
+	// initialize px, py, pz to the Jacobian coordinates for the base point
+	px, py := curve.bigAffineToField(curve.Gx, curve.Gy)
+	pz := new(fieldVal).SetInt(1)
+	for i := 0; i < curve.BitSize; i++ {
+		doublingPoints[i] = [3]fieldVal{*px, *py, *pz}
+		// P = 2*P
+		curve.doubleJacobian(px, py, pz, px, py, pz)
+	}
+	return doublingPoints
+}
+
+// SerializedBytePoints returns a serialized byte slice which contains all of
+// the possible points per 8-bit window.  This is used to when generating
+// secp256k1.go.
+func (curve *KoblitzCurve) SerializedBytePoints() []byte {
+	doublingPoints := curve.getDoublingPoints()
+
+	// Segregate the bits into byte-sized windows
+	serialized := make([]byte, curve.byteSize*256*3*10*4)
+	offset := 0
+	for byteNum := 0; byteNum < curve.byteSize; byteNum++ {
+		// Grab the 8 bits that make up this byte from doublingPoints.
+		startingBit := 8 * (curve.byteSize - byteNum - 1)
+		computingPoints := doublingPoints[startingBit : startingBit+8]
+
+		// Compute all points in this window and serialize them.
+		for i := 0; i < 256; i++ {
+			px, py, pz := new(fieldVal), new(fieldVal), new(fieldVal)
+			for j := 0; j < 8; j++ {
+				if i>>uint(j)&1 == 1 {
+					curve.addJacobian(px, py, pz, &computingPoints[j][0],
+						&computingPoints[j][1], &computingPoints[j][2], px, py, pz)
+				}
+			}
+			for i := 0; i < 10; i++ {
+				binary.LittleEndian.PutUint32(serialized[offset:], px.n[i])
+				offset += 4
+			}
+			for i := 0; i < 10; i++ {
+				binary.LittleEndian.PutUint32(serialized[offset:], py.n[i])
+				offset += 4
+			}
+			for i := 0; i < 10; i++ {
+				binary.LittleEndian.PutUint32(serialized[offset:], pz.n[i])
+				offset += 4
+			}
+		}
+	}
+
+	return serialized
+}
+
+// sqrt returns the square root of the provided big integer using Newton's
+// method.  It's only compiled and used during generation of pre-computed
+// values, so speed is not a huge concern.
+func sqrt(n *big.Int) *big.Int {
+	// Initial guess = 2^(log_2(n)/2)
+	guess := big.NewInt(2)
+	guess.Exp(guess, big.NewInt(int64(n.BitLen()/2)), nil)
+
+	// Now refine using Newton's method.
+	big2 := big.NewInt(2)
+	prevGuess := big.NewInt(0)
+	for {
+		prevGuess.Set(guess)
+		guess.Add(guess, new(big.Int).Div(n, guess))
+		guess.Div(guess, big2)
+		if guess.Cmp(prevGuess) == 0 {
+			break
+		}
+	}
+	return guess
+}
+
+// EndomorphismVectors runs the first 3 steps of algorithm 3.74 from [GECC] to
+// generate the linearly independent vectors needed to generate a balanced
+// length-two representation of a multiplier such that k = k1 + k2λ (mod N) and
+// returns them.  Since the values will always be the same given the fact that N
+// and λ are fixed, the final results can be accelerated by storing the
+// precomputed values with the curve.
+func (curve *KoblitzCurve) EndomorphismVectors() (a1, b1, a2, b2 *big.Int) {
+	bigMinus1 := big.NewInt(-1)
+
+	// This section uses an extended Euclidean algorithm to generate a
+	// sequence of equations:
+	//  s[i] * N + t[i] * λ = r[i]
+
+	nSqrt := sqrt(curve.N)
+	u, v := new(big.Int).Set(curve.N), new(big.Int).Set(curve.lambda)
+	x1, y1 := big.NewInt(1), big.NewInt(0)
+	x2, y2 := big.NewInt(0), big.NewInt(1)
+	q, r := new(big.Int), new(big.Int)
+	qu, qx1, qy1 := new(big.Int), new(big.Int), new(big.Int)
+	s, t := new(big.Int), new(big.Int)
+	ri, ti := new(big.Int), new(big.Int)
+	a1, b1, a2, b2 = new(big.Int), new(big.Int), new(big.Int), new(big.Int)
+	found, oneMore := false, false
+	for u.Sign() != 0 {
+		// q = v/u
+		q.Div(v, u)
+
+		// r = v - q*u
+		qu.Mul(q, u)
+		r.Sub(v, qu)
+
+		// s = x2 - q*x1
+		qx1.Mul(q, x1)
+		s.Sub(x2, qx1)
+
+		// t = y2 - q*y1
+		qy1.Mul(q, y1)
+		t.Sub(y2, qy1)
+
+		// v = u, u = r, x2 = x1, x1 = s, y2 = y1, y1 = t
+		v.Set(u)
+		u.Set(r)
+		x2.Set(x1)
+		x1.Set(s)
+		y2.Set(y1)
+		y1.Set(t)
+
+		// As soon as the remainder is less than the sqrt of n, the
+		// values of a1 and b1 are known.
+		if !found && r.Cmp(nSqrt) < 0 {
+			// When this condition executes ri and ti represent the
+			// r[i] and t[i] values such that i is the greatest
+			// index for which r >= sqrt(n).  Meanwhile, the current
+			// r and t values are r[i+1] and t[i+1], respectively.
+
+			// a1 = r[i+1], b1 = -t[i+1]
+			a1.Set(r)
+			b1.Mul(t, bigMinus1)
+			found = true
+			oneMore = true
+
+			// Skip to the next iteration so ri and ti are not
+			// modified.
+			continue
+
+		} else if oneMore {
+			// When this condition executes ri and ti still
+			// represent the r[i] and t[i] values while the current
+			// r and t are r[i+2] and t[i+2], respectively.
+
+			// sum1 = r[i]^2 + t[i]^2
+			rSquared := new(big.Int).Mul(ri, ri)
+			tSquared := new(big.Int).Mul(ti, ti)
+			sum1 := new(big.Int).Add(rSquared, tSquared)
+
+			// sum2 = r[i+2]^2 + t[i+2]^2
+			r2Squared := new(big.Int).Mul(r, r)
+			t2Squared := new(big.Int).Mul(t, t)
+			sum2 := new(big.Int).Add(r2Squared, t2Squared)
+
+			// if (r[i]^2 + t[i]^2) <= (r[i+2]^2 + t[i+2]^2)
+			if sum1.Cmp(sum2) <= 0 {
+				// a2 = r[i], b2 = -t[i]
+				a2.Set(ri)
+				b2.Mul(ti, bigMinus1)
+			} else {
+				// a2 = r[i+2], b2 = -t[i+2]
+				a2.Set(r)
+				b2.Mul(t, bigMinus1)
+			}
+
+			// All done.
+			break
+		}
+
+		ri.Set(r)
+		ti.Set(t)
+	}
+
+	return a1, b1, a2, b2
+}