381 lines
12 KiB
JavaScript
381 lines
12 KiB
JavaScript
sjcl.ecc = {};
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/**
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* Represents a point on a curve in affine coordinates.
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* @constructor
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* @param {sjcl.ecc.curve} curve The curve that this point lies on.
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* @param {bigInt} x The x coordinate.
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* @param {bigInt} y The y coordinate.
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*/
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sjcl.ecc.point = function(curve,x,y) {
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if (x === undefined) {
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this.isIdentity = true;
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} else {
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this.x = x;
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this.y = y;
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this.isIdentity = false;
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}
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this.curve = curve;
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};
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sjcl.ecc.point.prototype = {
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toJac: function() {
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return new sjcl.ecc.pointJac(this.curve, this.x, this.y, new this.curve.field(1));
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},
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mult: function(k) {
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return this.toJac().mult(k, this).toAffine();
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},
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/**
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* Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
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* @param {bigInt} k The coefficient to multiply this by.
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* @param {bigInt} k2 The coefficient to multiply affine2 this by.
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* @param {sjcl.ecc.point} affine The other point in affine coordinates.
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* @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
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*/
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mult2: function(k, k2, affine2) {
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return this.toJac().mult2(k, this, k2, affine2).toAffine();
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},
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multiples: function() {
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var m, i, j;
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if (this._multiples === undefined) {
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j = this.toJac().doubl();
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m = this._multiples = [new sjcl.ecc.point(this.curve), this, j.toAffine()];
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for (i=3; i<16; i++) {
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j = j.add(this);
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m.push(j.toAffine());
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}
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}
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return this._multiples;
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},
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isValid: function() {
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return this.y.square().equals(this.curve.b.add(this.x.mul(this.curve.a.add(this.x.square()))));
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},
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toBits: function() {
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return sjcl.bitArray.concat(this.x.toBits(), this.y.toBits());
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}
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};
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/**
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* Represents a point on a curve in Jacobian coordinates. Coordinates can be specified as bigInts or strings (which
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* will be converted to bigInts).
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*
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* @constructor
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* @param {bigInt/string} x The x coordinate.
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* @param {bigInt/string} y The y coordinate.
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* @param {bigInt/string} z The z coordinate.
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* @param {sjcl.ecc.curve} curve The curve that this point lies on.
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*/
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sjcl.ecc.pointJac = function(curve, x, y, z) {
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if (x === undefined) {
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this.isIdentity = true;
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} else {
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this.x = x;
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this.y = y;
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this.z = z;
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this.isIdentity = false;
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}
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this.curve = curve;
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};
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sjcl.ecc.pointJac.prototype = {
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/**
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* Adds S and T and returns the result in Jacobian coordinates. Note that S must be in Jacobian coordinates and T must be in affine coordinates.
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* @param {sjcl.ecc.pointJac} S One of the points to add, in Jacobian coordinates.
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* @param {sjcl.ecc.point} T The other point to add, in affine coordinates.
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* @return {sjcl.ecc.pointJac} The sum of the two points, in Jacobian coordinates.
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*/
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add: function(T) {
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var S = this, sz2, c, d, c2, x1, x2, x, y1, y2, y, z;
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if (S.curve !== T.curve) {
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throw("sjcl.ecc.add(): Points must be on the same curve to add them!");
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}
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if (S.isIdentity) {
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return T.toJac();
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} else if (T.isIdentity) {
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return S;
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}
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sz2 = S.z.square();
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c = T.x.mul(sz2).subM(S.x);
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if (c.equals(0)) {
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if (S.y.equals(T.y.mul(sz2.mul(S.z)))) {
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// same point
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return S.doubl();
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} else {
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// inverses
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return new sjcl.ecc.pointJac(S.curve);
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}
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}
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d = T.y.mul(sz2.mul(S.z)).subM(S.y);
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c2 = c.square();
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x1 = d.square();
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x2 = c.square().mul(c).addM( S.x.add(S.x).mul(c2) );
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x = x1.subM(x2);
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y1 = S.x.mul(c2).subM(x).mul(d);
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y2 = S.y.mul(c.square().mul(c));
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y = y1.subM(y2);
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z = S.z.mul(c);
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return new sjcl.ecc.pointJac(this.curve,x,y,z);
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},
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/**
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* doubles this point.
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* @return {sjcl.ecc.pointJac} The doubled point.
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*/
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doubl: function() {
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if (this.isIdentity) { return this; }
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var
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y2 = this.y.square(),
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a = y2.mul(this.x.mul(4)),
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b = y2.square().mul(8),
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z2 = this.z.square(),
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c = this.x.sub(z2).mul(3).mul(this.x.add(z2)),
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x = c.square().subM(a).subM(a),
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y = a.sub(x).mul(c).subM(b),
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z = this.y.add(this.y).mul(this.z);
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return new sjcl.ecc.pointJac(this.curve, x, y, z);
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},
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/**
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* Returns a copy of this point converted to affine coordinates.
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* @return {sjcl.ecc.point} The converted point.
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*/
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toAffine: function() {
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if (this.isIdentity || this.z.equals(0)) {
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return new sjcl.ecc.point(this.curve);
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}
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var zi = this.z.inverse(), zi2 = zi.square();
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return new sjcl.ecc.point(this.curve, this.x.mul(zi2).fullReduce(), this.y.mul(zi2.mul(zi)).fullReduce());
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},
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/**
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* Multiply this point by k and return the answer in Jacobian coordinates.
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* @param {bigInt} k The coefficient to multiply by.
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* @param {sjcl.ecc.point} affine This point in affine coordinates.
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* @return {sjcl.ecc.pointJac} The result of the multiplication, in Jacobian coordinates.
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*/
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mult: function(k, affine) {
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if (typeof(k) === "number") {
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k = [k];
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} else if (k.limbs !== undefined) {
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k = k.normalize().limbs;
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}
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var i, j, out = new sjcl.ecc.point(this.curve).toJac(), multiples = affine.multiples();
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for (i=k.length-1; i>=0; i--) {
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for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
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out = out.doubl().doubl().doubl().doubl().add(multiples[k[i]>>j & 0xF]);
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}
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}
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return out;
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},
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/**
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* Multiply this point by k, added to affine2*k2, and return the answer in Jacobian coordinates.
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* @param {bigInt} k The coefficient to multiply this by.
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* @param {sjcl.ecc.point} affine This point in affine coordinates.
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* @param {bigInt} k2 The coefficient to multiply affine2 this by.
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* @param {sjcl.ecc.point} affine The other point in affine coordinates.
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* @return {sjcl.ecc.pointJac} The result of the multiplication and addition, in Jacobian coordinates.
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*/
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mult2: function(k1, affine, k2, affine2) {
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if (typeof(k1) === "number") {
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k1 = [k1];
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} else if (k1.limbs !== undefined) {
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k1 = k1.normalize().limbs;
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}
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if (typeof(k2) === "number") {
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k2 = [k2];
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} else if (k2.limbs !== undefined) {
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k2 = k2.normalize().limbs;
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}
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var i, j, out = new sjcl.ecc.point(this.curve).toJac(), m1 = affine.multiples(),
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m2 = affine2.multiples(), l1, l2;
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for (i=Math.max(k1.length,k2.length)-1; i>=0; i--) {
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l1 = k1[i] | 0;
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l2 = k2[i] | 0;
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for (j=sjcl.bn.prototype.radix-4; j>=0; j-=4) {
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out = out.doubl().doubl().doubl().doubl().add(m1[l1>>j & 0xF]).add(m2[l2>>j & 0xF]);
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}
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}
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return out;
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},
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isValid: function() {
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var z2 = this.z.square(), z4 = z2.square(), z6 = z4.mul(z2);
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return this.y.square().equals(
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this.curve.b.mul(z6).add(this.x.mul(
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this.curve.a.mul(z4).add(this.x.square()))));
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}
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};
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/**
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* Construct an elliptic curve. Most users will not use this and instead start with one of the NIST curves defined below.
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*
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* @constructor
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* @param {bigInt} p The prime modulus.
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* @param {bigInt} r The prime order of the curve.
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* @param {bigInt} a The constant a in the equation of the curve y^2 = x^3 + ax + b (for NIST curves, a is always -3).
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* @param {bigInt} x The x coordinate of a base point of the curve.
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* @param {bigInt} y The y coordinate of a base point of the curve.
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*/
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sjcl.ecc.curve = function(Field, r, a, b, x, y) {
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this.field = Field;
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this.r = Field.prototype.modulus.sub(r);
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this.a = new Field(a);
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this.b = new Field(b);
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this.G = new sjcl.ecc.point(this, new Field(x), new Field(y));
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};
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sjcl.ecc.curve.prototype.fromBits = function (bits) {
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var w = sjcl.bitArray, l = this.field.prototype.exponent + 7 & -8,
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p = new sjcl.ecc.point(this, this.field.fromBits(w.bitSlice(bits, 0, l)),
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this.field.fromBits(w.bitSlice(bits, l, 2*l)));
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if (!p.isValid()) {
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throw new sjcl.exception.corrupt("not on the curve!");
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}
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return p;
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};
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sjcl.ecc.curves = {
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c192: new sjcl.ecc.curve(
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sjcl.bn.prime.p192,
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"0x662107c8eb94364e4b2dd7ce",
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-3,
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"0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1",
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"0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012",
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"0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811"),
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c224: new sjcl.ecc.curve(
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sjcl.bn.prime.p224,
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"0xe95c1f470fc1ec22d6baa3a3d5c4",
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-3,
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"0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4",
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"0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21",
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"0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"),
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c256: new sjcl.ecc.curve(
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sjcl.bn.prime.p256,
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"0x4319055358e8617b0c46353d039cdaae",
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-3,
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"0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
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"0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
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"0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"),
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c384: new sjcl.ecc.curve(
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sjcl.bn.prime.p384,
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"0x389cb27e0bc8d21fa7e5f24cb74f58851313e696333ad68c",
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-3,
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"0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef",
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"0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7",
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"0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f")
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};
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/* Diffie-Hellman-like public-key system */
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sjcl.ecc._dh = function(cn) {
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sjcl.ecc[cn] = {
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publicKey: function(curve, point) {
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this._curve = curve;
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if (point instanceof Array) {
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this._point = curve.fromBits(point);
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} else {
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this._point = point;
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}
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},
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secretKey: function(curve, exponent) {
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this._curve = curve;
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this._exponent = exponent;
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},
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generateKeys: function(curve, paranoia) {
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if (curve === undefined) {
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curve = 256;
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}
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if (typeof curve === "number") {
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curve = sjcl.ecc.curves['c'+curve];
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if (curve === undefined) {
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throw new sjcl.exception.invalid("no such curve");
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}
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}
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var sec = sjcl.bn.random(curve.r, paranoia), pub = curve.G.mult(sec);
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return { pub: new sjcl.ecc[cn].publicKey(curve, pub),
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sec: new sjcl.ecc[cn].secretKey(curve, sec) };
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}
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};
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};
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sjcl.ecc._dh("elGamal");
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sjcl.ecc.elGamal.publicKey.prototype = {
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kem: function(paranoia) {
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var sec = sjcl.bn.random(this._curve.r, paranoia),
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tag = this._curve.G.mult(sec).toBits(),
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key = sjcl.hash.sha256.hash(this._point.mult(sec).toBits());
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return { key: key, tag: tag };
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}
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};
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sjcl.ecc.elGamal.secretKey.prototype = {
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unkem: function(tag) {
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return sjcl.hash.sha256.hash(this._curve.fromBits(tag).mult(this._exponent).toBits());
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},
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dh: function(pk) {
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return sjcl.hash.sha256.hash(pk._point.mult(this._exponent).toBits());
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}
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};
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sjcl.ecc._dh("ecdsa");
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sjcl.ecc.ecdsa.secretKey.prototype = {
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sign: function(hash, paranoia) {
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var R = this._curve.r,
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l = R.bitLength(),
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k = sjcl.bn.random(R.sub(1), paranoia).add(1),
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r = this._curve.G.mult(k).x.mod(R),
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s = sjcl.bn.fromBits(hash).add(r.mul(this._exponent)).inverseMod(R).mul(k).mod(R);
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return sjcl.bitArray.concat(r.toBits(l), s.toBits(l));
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}
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};
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sjcl.ecc.ecdsa.publicKey.prototype = {
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verify: function(hash, rs) {
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var w = sjcl.bitArray,
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R = this._curve.r,
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l = R.bitLength(),
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r = sjcl.bn.fromBits(w.bitSlice(rs,0,l)),
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s = sjcl.bn.fromBits(w.bitSlice(rs,l,2*l)),
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hG = sjcl.bn.fromBits(hash).mul(s).mod(R),
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hA = r.mul(s).mod(R),
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r2 = this._curve.G.mult2(hG, hA, this._point).x;
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if (r.equals(0) || s.equals(0) || r.greaterEquals(R) || s.greaterEquals(R) || !r2.equals(r)) {
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throw (new sjcl.exception.corrupt("signature didn't check out"));
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}
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return true;
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}
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};
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