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/*! OpenPGP.js v5.10.1 - 2023-08-29 - this is LGPL licensed code, see LICENSE/our website https://openpgpjs.org/ for more information. */
const globalThis = typeof window !== 'undefined' ? window : typeof global !== 'undefined' ? global : typeof self !== 'undefined' ? self : {};
import { c as createCommonjsModule, m as minimalisticAssert, i as inherits_browser, u as utils, b as common, d as common$1, _ as _224, e as _256, f as _384, g as _512, r as ripemd } from './openpgp.mjs';
import bn from './bn.mjs';
var utils_1 = createCommonjsModule(function (module, exports) {
var utils = exports;
function toArray(msg, enc) {
if (Array.isArray(msg))
return msg.slice();
if (!msg)
return [];
var res = [];
if (typeof msg !== 'string') {
for (var i = 0; i < msg.length; i++)
res[i] = msg[i] | 0;
return res;
}
if (enc === 'hex') {
msg = msg.replace(/[^a-z0-9]+/ig, '');
if (msg.length % 2 !== 0)
msg = '0' + msg;
for (var i = 0; i < msg.length; i += 2)
res.push(parseInt(msg[i] + msg[i + 1], 16));
} else {
for (var i = 0; i < msg.length; i++) {
var c = msg.charCodeAt(i);
var hi = c >> 8;
var lo = c & 0xff;
if (hi)
res.push(hi, lo);
else
res.push(lo);
}
}
return res;
}
utils.toArray = toArray;
function zero2(word) {
if (word.length === 1)
return '0' + word;
else
return word;
}
utils.zero2 = zero2;
function toHex(msg) {
var res = '';
for (var i = 0; i < msg.length; i++)
res += zero2(msg[i].toString(16));
return res;
}
utils.toHex = toHex;
utils.encode = function encode(arr, enc) {
if (enc === 'hex')
return toHex(arr);
else
return arr;
};
});
var utils_1$1 = createCommonjsModule(function (module, exports) {
var utils = exports;
utils.assert = minimalisticAssert;
utils.toArray = utils_1.toArray;
utils.zero2 = utils_1.zero2;
utils.toHex = utils_1.toHex;
utils.encode = utils_1.encode;
// Represent num in a w-NAF form
function getNAF(num, w) {
var naf = [];
var ws = 1 << (w + 1);
var k = num.clone();
while (k.cmpn(1) >= 0) {
var z;
if (k.isOdd()) {
var mod = k.andln(ws - 1);
if (mod > (ws >> 1) - 1)
z = (ws >> 1) - mod;
else
z = mod;
k.isubn(z);
} else {
z = 0;
}
naf.push(z);
// Optimization, shift by word if possible
var shift = (k.cmpn(0) !== 0 && k.andln(ws - 1) === 0) ? (w + 1) : 1;
for (var i = 1; i < shift; i++)
naf.push(0);
k.iushrn(shift);
}
return naf;
}
utils.getNAF = getNAF;
// Represent k1, k2 in a Joint Sparse Form
function getJSF(k1, k2) {
var jsf = [
[],
[]
];
k1 = k1.clone();
k2 = k2.clone();
var d1 = 0;
var d2 = 0;
while (k1.cmpn(-d1) > 0 || k2.cmpn(-d2) > 0) {
// First phase
var m14 = (k1.andln(3) + d1) & 3;
var m24 = (k2.andln(3) + d2) & 3;
if (m14 === 3)
m14 = -1;
if (m24 === 3)
m24 = -1;
var u1;
if ((m14 & 1) === 0) {
u1 = 0;
} else {
var m8 = (k1.andln(7) + d1) & 7;
if ((m8 === 3 || m8 === 5) && m24 === 2)
u1 = -m14;
else
u1 = m14;
}
jsf[0].push(u1);
var u2;
if ((m24 & 1) === 0) {
u2 = 0;
} else {
var m8 = (k2.andln(7) + d2) & 7;
if ((m8 === 3 || m8 === 5) && m14 === 2)
u2 = -m24;
else
u2 = m24;
}
jsf[1].push(u2);
// Second phase
if (2 * d1 === u1 + 1)
d1 = 1 - d1;
if (2 * d2 === u2 + 1)
d2 = 1 - d2;
k1.iushrn(1);
k2.iushrn(1);
}
return jsf;
}
utils.getJSF = getJSF;
function cachedProperty(obj, name, computer) {
var key = '_' + name;
obj.prototype[name] = function cachedProperty() {
return this[key] !== undefined ? this[key] :
this[key] = computer.call(this);
};
}
utils.cachedProperty = cachedProperty;
function parseBytes(bytes) {
return typeof bytes === 'string' ? utils.toArray(bytes, 'hex') :
bytes;
}
utils.parseBytes = parseBytes;
function intFromLE(bytes) {
return new bn(bytes, 'hex', 'le');
}
utils.intFromLE = intFromLE;
});
var r;
var brorand = function rand(len) {
if (!r)
r = new Rand(null);
return r.generate(len);
};
function Rand(rand) {
this.rand = rand;
}
var Rand_1 = Rand;
Rand.prototype.generate = function generate(len) {
return this._rand(len);
};
// Emulate crypto API using randy
Rand.prototype._rand = function _rand(n) {
if (this.rand.getBytes)
return this.rand.getBytes(n);
var res = new Uint8Array(n);
for (var i = 0; i < res.length; i++)
res[i] = this.rand.getByte();
return res;
};
if (typeof self === 'object') {
if (self.crypto && self.crypto.getRandomValues) {
// Modern browsers
Rand.prototype._rand = function _rand(n) {
var arr = new Uint8Array(n);
self.crypto.getRandomValues(arr);
return arr;
};
} else if (self.msCrypto && self.msCrypto.getRandomValues) {
// IE
Rand.prototype._rand = function _rand(n) {
var arr = new Uint8Array(n);
self.msCrypto.getRandomValues(arr);
return arr;
};
// Safari's WebWorkers do not have `crypto`
} else if (typeof window === 'object') {
// Old junk
Rand.prototype._rand = function() {
throw new Error('Not implemented yet');
};
}
} else {
// Node.js or Web worker with no crypto support
try {
var crypto = void('crypto');
if (typeof crypto.randomBytes !== 'function')
throw new Error('Not supported');
Rand.prototype._rand = function _rand(n) {
return crypto.randomBytes(n);
};
} catch (e) {
}
}
brorand.Rand = Rand_1;
var getNAF = utils_1$1.getNAF;
var getJSF = utils_1$1.getJSF;
var assert = utils_1$1.assert;
function BaseCurve(type, conf) {
this.type = type;
this.p = new bn(conf.p, 16);
// Use Montgomery, when there is no fast reduction for the prime
this.red = conf.prime ? bn.red(conf.prime) : bn.mont(this.p);
// Useful for many curves
this.zero = new bn(0).toRed(this.red);
this.one = new bn(1).toRed(this.red);
this.two = new bn(2).toRed(this.red);
// Curve configuration, optional
this.n = conf.n && new bn(conf.n, 16);
this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed);
// Temporary arrays
this._wnafT1 = new Array(4);
this._wnafT2 = new Array(4);
this._wnafT3 = new Array(4);
this._wnafT4 = new Array(4);
// Generalized Greg Maxwell's trick
var adjustCount = this.n && this.p.div(this.n);
if (!adjustCount || adjustCount.cmpn(100) > 0) {
this.redN = null;
} else {
this._maxwellTrick = true;
this.redN = this.n.toRed(this.red);
}
}
var base = BaseCurve;
BaseCurve.prototype.point = function point() {
throw new Error('Not implemented');
};
BaseCurve.prototype.validate = function validate() {
throw new Error('Not implemented');
};
BaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) {
assert(p.precomputed);
var doubles = p._getDoubles();
var naf = getNAF(k, 1);
var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);
I /= 3;
// Translate into more windowed form
var repr = [];
for (var j = 0; j < naf.length; j += doubles.step) {
var nafW = 0;
for (var k = j + doubles.step - 1; k >= j; k--)
nafW = (nafW << 1) + naf[k];
repr.push(nafW);
}
var a = this.jpoint(null, null, null);
var b = this.jpoint(null, null, null);
for (var i = I; i > 0; i--) {
for (var j = 0; j < repr.length; j++) {
var nafW = repr[j];
if (nafW === i)
b = b.mixedAdd(doubles.points[j]);
else if (nafW === -i)
b = b.mixedAdd(doubles.points[j].neg());
}
a = a.add(b);
}
return a.toP();
};
BaseCurve.prototype._wnafMul = function _wnafMul(p, k) {
var w = 4;
// Precompute window
var nafPoints = p._getNAFPoints(w);
w = nafPoints.wnd;
var wnd = nafPoints.points;
// Get NAF form
var naf = getNAF(k, w);
// Add `this`*(N+1) for every w-NAF index
var acc = this.jpoint(null, null, null);
for (var i = naf.length - 1; i >= 0; i--) {
// Count zeroes
for (var k = 0; i >= 0 && naf[i] === 0; i--)
k++;
if (i >= 0)
k++;
acc = acc.dblp(k);
if (i < 0)
break;
var z = naf[i];
assert(z !== 0);
if (p.type === 'affine') {
// J +- P
if (z > 0)
acc = acc.mixedAdd(wnd[(z - 1) >> 1]);
else
acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg());
} else {
// J +- J
if (z > 0)
acc = acc.add(wnd[(z - 1) >> 1]);
else
acc = acc.add(wnd[(-z - 1) >> 1].neg());
}
}
return p.type === 'affine' ? acc.toP() : acc;
};
BaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW,
points,
coeffs,
len,
jacobianResult) {
var wndWidth = this._wnafT1;
var wnd = this._wnafT2;
var naf = this._wnafT3;
// Fill all arrays
var max = 0;
for (var i = 0; i < len; i++) {
var p = points[i];
var nafPoints = p._getNAFPoints(defW);
wndWidth[i] = nafPoints.wnd;
wnd[i] = nafPoints.points;
}
// Comb small window NAFs
for (var i = len - 1; i >= 1; i -= 2) {
var a = i - 1;
var b = i;
if (wndWidth[a] !== 1 || wndWidth[b] !== 1) {
naf[a] = getNAF(coeffs[a], wndWidth[a]);
naf[b] = getNAF(coeffs[b], wndWidth[b]);
max = Math.max(naf[a].length, max);
max = Math.max(naf[b].length, max);
continue;
}
var comb = [
points[a], /* 1 */
null, /* 3 */
null, /* 5 */
points[b] /* 7 */
];
// Try to avoid Projective points, if possible
if (points[a].y.cmp(points[b].y) === 0) {
comb[1] = points[a].add(points[b]);
comb[2] = points[a].toJ().mixedAdd(points[b].neg());
} else if (points[a].y.cmp(points[b].y.redNeg()) === 0) {
comb[1] = points[a].toJ().mixedAdd(points[b]);
comb[2] = points[a].add(points[b].neg());
} else {
comb[1] = points[a].toJ().mixedAdd(points[b]);
comb[2] = points[a].toJ().mixedAdd(points[b].neg());
}
var index = [
-3, /* -1 -1 */
-1, /* -1 0 */
-5, /* -1 1 */
-7, /* 0 -1 */
0, /* 0 0 */
7, /* 0 1 */
5, /* 1 -1 */
1, /* 1 0 */
3 /* 1 1 */
];
var jsf = getJSF(coeffs[a], coeffs[b]);
max = Math.max(jsf[0].length, max);
naf[a] = new Array(max);
naf[b] = new Array(max);
for (var j = 0; j < max; j++) {
var ja = jsf[0][j] | 0;
var jb = jsf[1][j] | 0;
naf[a][j] = index[(ja + 1) * 3 + (jb + 1)];
naf[b][j] = 0;
wnd[a] = comb;
}
}
var acc = this.jpoint(null, null, null);
var tmp = this._wnafT4;
for (var i = max; i >= 0; i--) {
var k = 0;
while (i >= 0) {
var zero = true;
for (var j = 0; j < len; j++) {
tmp[j] = naf[j][i] | 0;
if (tmp[j] !== 0)
zero = false;
}
if (!zero)
break;
k++;
i--;
}
if (i >= 0)
k++;
acc = acc.dblp(k);
if (i < 0)
break;
for (var j = 0; j < len; j++) {
var z = tmp[j];
var p;
if (z === 0)
continue;
else if (z > 0)
p = wnd[j][(z - 1) >> 1];
else if (z < 0)
p = wnd[j][(-z - 1) >> 1].neg();
if (p.type === 'affine')
acc = acc.mixedAdd(p);
else
acc = acc.add(p);
}
}
// Zeroify references
for (var i = 0; i < len; i++)
wnd[i] = null;
if (jacobianResult)
return acc;
else
return acc.toP();
};
function BasePoint(curve, type) {
this.curve = curve;
this.type = type;
this.precomputed = null;
}
BaseCurve.BasePoint = BasePoint;
BasePoint.prototype.eq = function eq(/*other*/) {
throw new Error('Not implemented');
};
BasePoint.prototype.validate = function validate() {
return this.curve.validate(this);
};
BaseCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
bytes = utils_1$1.toArray(bytes, enc);
var len = this.p.byteLength();
// uncompressed, hybrid-odd, hybrid-even
if ((bytes[0] === 0x04 || bytes[0] === 0x06 || bytes[0] === 0x07) &&
bytes.length - 1 === 2 * len) {
if (bytes[0] === 0x06)
assert(bytes[bytes.length - 1] % 2 === 0);
else if (bytes[0] === 0x07)
assert(bytes[bytes.length - 1] % 2 === 1);
var res = this.point(bytes.slice(1, 1 + len),
bytes.slice(1 + len, 1 + 2 * len));
return res;
} else if ((bytes[0] === 0x02 || bytes[0] === 0x03) &&
bytes.length - 1 === len) {
return this.pointFromX(bytes.slice(1, 1 + len), bytes[0] === 0x03);
}
throw new Error('Unknown point format');
};
BasePoint.prototype.encodeCompressed = function encodeCompressed(enc) {
return this.encode(enc, true);
};
BasePoint.prototype._encode = function _encode(compact) {
var len = this.curve.p.byteLength();
var x = this.getX().toArray('be', len);
if (compact)
return [ this.getY().isEven() ? 0x02 : 0x03 ].concat(x);
return [ 0x04 ].concat(x, this.getY().toArray('be', len)) ;
};
BasePoint.prototype.encode = function encode(enc, compact) {
return utils_1$1.encode(this._encode(compact), enc);
};
BasePoint.prototype.precompute = function precompute(power) {
if (this.precomputed)
return this;
var precomputed = {
doubles: null,
naf: null,
beta: null
};
precomputed.naf = this._getNAFPoints(8);
precomputed.doubles = this._getDoubles(4, power);
precomputed.beta = this._getBeta();
this.precomputed = precomputed;
return this;
};
BasePoint.prototype._hasDoubles = function _hasDoubles(k) {
if (!this.precomputed)
return false;
var doubles = this.precomputed.doubles;
if (!doubles)
return false;
return doubles.points.length >= Math.ceil((k.bitLength() + 1) / doubles.step);
};
BasePoint.prototype._getDoubles = function _getDoubles(step, power) {
if (this.precomputed && this.precomputed.doubles)
return this.precomputed.doubles;
var doubles = [ this ];
var acc = this;
for (var i = 0; i < power; i += step) {
for (var j = 0; j < step; j++)
acc = acc.dbl();
doubles.push(acc);
}
return {
step: step,
points: doubles
};
};
BasePoint.prototype._getNAFPoints = function _getNAFPoints(wnd) {
if (this.precomputed && this.precomputed.naf)
return this.precomputed.naf;
var res = [ this ];
var max = (1 << wnd) - 1;
var dbl = max === 1 ? null : this.dbl();
for (var i = 1; i < max; i++)
res[i] = res[i - 1].add(dbl);
return {
wnd: wnd,
points: res
};
};
BasePoint.prototype._getBeta = function _getBeta() {
return null;
};
BasePoint.prototype.dblp = function dblp(k) {
var r = this;
for (var i = 0; i < k; i++)
r = r.dbl();
return r;
};
var assert$1 = utils_1$1.assert;
function ShortCurve(conf) {
base.call(this, 'short', conf);
this.a = new bn(conf.a, 16).toRed(this.red);
this.b = new bn(conf.b, 16).toRed(this.red);
this.tinv = this.two.redInvm();
this.zeroA = this.a.fromRed().cmpn(0) === 0;
this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;
// If the curve is endomorphic, precalculate beta and lambda
this.endo = this._getEndomorphism(conf);
this._endoWnafT1 = new Array(4);
this._endoWnafT2 = new Array(4);
}
inherits_browser(ShortCurve, base);
var short_1 = ShortCurve;
ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {
// No efficient endomorphism
if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)
return;
// Compute beta and lambda, that lambda * P = (beta * Px; Py)
var beta;
var lambda;
if (conf.beta) {
beta = new bn(conf.beta, 16).toRed(this.red);
} else {
var betas = this._getEndoRoots(this.p);
// Choose the smallest beta
beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];
beta = beta.toRed(this.red);
}
if (conf.lambda) {
lambda = new bn(conf.lambda, 16);
} else {
// Choose the lambda that is matching selected beta
var lambdas = this._getEndoRoots(this.n);
if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {
lambda = lambdas[0];
} else {
lambda = lambdas[1];
assert$1(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);
}
}
// Get basis vectors, used for balanced length-two representation
var basis;
if (conf.basis) {
basis = conf.basis.map(function(vec) {
return {
a: new bn(vec.a, 16),
b: new bn(vec.b, 16)
};
});
} else {
basis = this._getEndoBasis(lambda);
}
return {
beta: beta,
lambda: lambda,
basis: basis
};
};
ShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {
// Find roots of for x^2 + x + 1 in F
// Root = (-1 +- Sqrt(-3)) / 2
//
var red = num === this.p ? this.red : bn.mont(num);
var tinv = new bn(2).toRed(red).redInvm();
var ntinv = tinv.redNeg();
var s = new bn(3).toRed(red).redNeg().redSqrt().redMul(tinv);
var l1 = ntinv.redAdd(s).fromRed();
var l2 = ntinv.redSub(s).fromRed();
return [ l1, l2 ];
};
ShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {
// aprxSqrt >= sqrt(this.n)
var aprxSqrt = this.n.ushrn(Math.floor(this.n.bitLength() / 2));
// 3.74
// Run EGCD, until r(L + 1) < aprxSqrt
var u = lambda;
var v = this.n.clone();
var x1 = new bn(1);
var y1 = new bn(0);
var x2 = new bn(0);
var y2 = new bn(1);
// NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)
var a0;
var b0;
// First vector
var a1;
var b1;
// Second vector
var a2;
var b2;
var prevR;
var i = 0;
var r;
var x;
while (u.cmpn(0) !== 0) {
var q = v.div(u);
r = v.sub(q.mul(u));
x = x2.sub(q.mul(x1));
var y = y2.sub(q.mul(y1));
if (!a1 && r.cmp(aprxSqrt) < 0) {
a0 = prevR.neg();
b0 = x1;
a1 = r.neg();
b1 = x;
} else if (a1 && ++i === 2) {
break;
}
prevR = r;
v = u;
u = r;
x2 = x1;
x1 = x;
y2 = y1;
y1 = y;
}
a2 = r.neg();
b2 = x;
var len1 = a1.sqr().add(b1.sqr());
var len2 = a2.sqr().add(b2.sqr());
if (len2.cmp(len1) >= 0) {
a2 = a0;
b2 = b0;
}
// Normalize signs
if (a1.negative) {
a1 = a1.neg();
b1 = b1.neg();
}
if (a2.negative) {
a2 = a2.neg();
b2 = b2.neg();
}
return [
{ a: a1, b: b1 },
{ a: a2, b: b2 }
];
};
ShortCurve.prototype._endoSplit = function _endoSplit(k) {
var basis = this.endo.basis;
var v1 = basis[0];
var v2 = basis[1];
var c1 = v2.b.mul(k).divRound(this.n);
var c2 = v1.b.neg().mul(k).divRound(this.n);
var p1 = c1.mul(v1.a);
var p2 = c2.mul(v2.a);
var q1 = c1.mul(v1.b);
var q2 = c2.mul(v2.b);
// Calculate answer
var k1 = k.sub(p1).sub(p2);
var k2 = q1.add(q2).neg();
return { k1: k1, k2: k2 };
};
ShortCurve.prototype.pointFromX = function pointFromX(x, odd) {
x = new bn(x, 16);
if (!x.red)
x = x.toRed(this.red);
var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
var y = y2.redSqrt();
if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
throw new Error('invalid point');
// XXX Is there any way to tell if the number is odd without converting it
// to non-red form?
var isOdd = y.fromRed().isOdd();
if (odd && !isOdd || !odd && isOdd)
y = y.redNeg();
return this.point(x, y);
};
ShortCurve.prototype.validate = function validate(point) {
if (point.inf)
return true;
var x = point.x;
var y = point.y;
var ax = this.a.redMul(x);
var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);
return y.redSqr().redISub(rhs).cmpn(0) === 0;
};
ShortCurve.prototype._endoWnafMulAdd =
function _endoWnafMulAdd(points, coeffs, jacobianResult) {
var npoints = this._endoWnafT1;
var ncoeffs = this._endoWnafT2;
for (var i = 0; i < points.length; i++) {
var split = this._endoSplit(coeffs[i]);
var p = points[i];
var beta = p._getBeta();
if (split.k1.negative) {
split.k1.ineg();
p = p.neg(true);
}
if (split.k2.negative) {
split.k2.ineg();
beta = beta.neg(true);
}
npoints[i * 2] = p;
npoints[i * 2 + 1] = beta;
ncoeffs[i * 2] = split.k1;
ncoeffs[i * 2 + 1] = split.k2;
}
var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2, jacobianResult);
// Clean-up references to points and coefficients
for (var j = 0; j < i * 2; j++) {
npoints[j] = null;
ncoeffs[j] = null;
}
return res;
};
function Point(curve, x, y, isRed) {
base.BasePoint.call(this, curve, 'affine');
if (x === null && y === null) {
this.x = null;
this.y = null;
this.inf = true;
} else {
this.x = new bn(x, 16);
this.y = new bn(y, 16);
// Force redgomery representation when loading from JSON
if (isRed) {
this.x.forceRed(this.curve.red);
this.y.forceRed(this.curve.red);
}
if (!this.x.red)
this.x = this.x.toRed(this.curve.red);
if (!this.y.red)
this.y = this.y.toRed(this.curve.red);
this.inf = false;
}
}
inherits_browser(Point, base.BasePoint);
ShortCurve.prototype.point = function point(x, y, isRed) {
return new Point(this, x, y, isRed);
};
ShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {
return Point.fromJSON(this, obj, red);
};
Point.prototype._getBeta = function _getBeta() {
if (!this.curve.endo)
return;
var pre = this.precomputed;
if (pre && pre.beta)
return pre.beta;
var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);
if (pre) {
var curve = this.curve;
var endoMul = function(p) {
return curve.point(p.x.redMul(curve.endo.beta), p.y);
};
pre.beta = beta;
beta.precomputed = {
beta: null,
naf: pre.naf && {
wnd: pre.naf.wnd,
points: pre.naf.points.map(endoMul)
},
doubles: pre.doubles && {
step: pre.doubles.step,
points: pre.doubles.points.map(endoMul)
}
};
}
return beta;
};
Point.prototype.toJSON = function toJSON() {
if (!this.precomputed)
return [ this.x, this.y ];
return [ this.x, this.y, this.precomputed && {
doubles: this.precomputed.doubles && {
step: this.precomputed.doubles.step,
points: this.precomputed.doubles.points.slice(1)
},
naf: this.precomputed.naf && {
wnd: this.precomputed.naf.wnd,
points: this.precomputed.naf.points.slice(1)
}
} ];
};
Point.fromJSON = function fromJSON(curve, obj, red) {
if (typeof obj === 'string')
obj = JSON.parse(obj);
var res = curve.point(obj[0], obj[1], red);
if (!obj[2])
return res;
function obj2point(obj) {
return curve.point(obj[0], obj[1], red);
}
var pre = obj[2];
res.precomputed = {
beta: null,
doubles: pre.doubles && {
step: pre.doubles.step,
points: [ res ].concat(pre.doubles.points.map(obj2point))
},
naf: pre.naf && {
wnd: pre.naf.wnd,
points: [ res ].concat(pre.naf.points.map(obj2point))
}
};
return res;
};
Point.prototype.inspect = function inspect() {
if (this.isInfinity())
return '<EC Point Infinity>';
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
' y: ' + this.y.fromRed().toString(16, 2) + '>';
};
Point.prototype.isInfinity = function isInfinity() {
return this.inf;
};
Point.prototype.add = function add(p) {
// O + P = P
if (this.inf)
return p;
// P + O = P
if (p.inf)
return this;
// P + P = 2P
if (this.eq(p))
return this.dbl();
// P + (-P) = O
if (this.neg().eq(p))
return this.curve.point(null, null);
// P + Q = O
if (this.x.cmp(p.x) === 0)
return this.curve.point(null, null);
var c = this.y.redSub(p.y);
if (c.cmpn(0) !== 0)
c = c.redMul(this.x.redSub(p.x).redInvm());
var nx = c.redSqr().redISub(this.x).redISub(p.x);
var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
return this.curve.point(nx, ny);
};
Point.prototype.dbl = function dbl() {
if (this.inf)
return this;
// 2P = O
var ys1 = this.y.redAdd(this.y);
if (ys1.cmpn(0) === 0)
return this.curve.point(null, null);
var a = this.curve.a;
var x2 = this.x.redSqr();
var dyinv = ys1.redInvm();
var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);
var nx = c.redSqr().redISub(this.x.redAdd(this.x));
var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
return this.curve.point(nx, ny);
};
Point.prototype.getX = function getX() {
return this.x.fromRed();
};
Point.prototype.getY = function getY() {
return this.y.fromRed();
};
Point.prototype.mul = function mul(k) {
k = new bn(k, 16);
if (this.isInfinity())
return this;
else if (this._hasDoubles(k))
return this.curve._fixedNafMul(this, k);
else if (this.curve.endo)
return this.curve._endoWnafMulAdd([ this ], [ k ]);
else
return this.curve._wnafMul(this, k);
};
Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {
var points = [ this, p2 ];
var coeffs = [ k1, k2 ];
if (this.curve.endo)
return this.curve._endoWnafMulAdd(points, coeffs);
else
return this.curve._wnafMulAdd(1, points, coeffs, 2);
};
Point.prototype.jmulAdd = function jmulAdd(k1, p2, k2) {
var points = [ this, p2 ];
var coeffs = [ k1, k2 ];
if (this.curve.endo)
return this.curve._endoWnafMulAdd(points, coeffs, true);
else
return this.curve._wnafMulAdd(1, points, coeffs, 2, true);
};
Point.prototype.eq = function eq(p) {
return this === p ||
this.inf === p.inf &&
(this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);
};
Point.prototype.neg = function neg(_precompute) {
if (this.inf)
return this;
var res = this.curve.point(this.x, this.y.redNeg());
if (_precompute && this.precomputed) {
var pre = this.precomputed;
var negate = function(p) {
return p.neg();
};
res.precomputed = {
naf: pre.naf && {
wnd: pre.naf.wnd,
points: pre.naf.points.map(negate)
},
doubles: pre.doubles && {
step: pre.doubles.step,
points: pre.doubles.points.map(negate)
}
};
}
return res;
};
Point.prototype.toJ = function toJ() {
if (this.inf)
return this.curve.jpoint(null, null, null);
var res = this.curve.jpoint(this.x, this.y, this.curve.one);
return res;
};
function JPoint(curve, x, y, z) {
base.BasePoint.call(this, curve, 'jacobian');
if (x === null && y === null && z === null) {
this.x = this.curve.one;
this.y = this.curve.one;
this.z = new bn(0);
} else {
this.x = new bn(x, 16);
this.y = new bn(y, 16);
this.z = new bn(z, 16);
}
if (!this.x.red)
this.x = this.x.toRed(this.curve.red);
if (!this.y.red)
this.y = this.y.toRed(this.curve.red);
if (!this.z.red)
this.z = this.z.toRed(this.curve.red);
this.zOne = this.z === this.curve.one;
}
inherits_browser(JPoint, base.BasePoint);
ShortCurve.prototype.jpoint = function jpoint(x, y, z) {
return new JPoint(this, x, y, z);
};
JPoint.prototype.toP = function toP() {
if (this.isInfinity())
return this.curve.point(null, null);
var zinv = this.z.redInvm();
var zinv2 = zinv.redSqr();
var ax = this.x.redMul(zinv2);
var ay = this.y.redMul(zinv2).redMul(zinv);
return this.curve.point(ax, ay);
};
JPoint.prototype.neg = function neg() {
return this.curve.jpoint(this.x, this.y.redNeg(), this.z);
};
JPoint.prototype.add = function add(p) {
// O + P = P
if (this.isInfinity())
return p;
// P + O = P
if (p.isInfinity())
return this;
// 12M + 4S + 7A
var pz2 = p.z.redSqr();
var z2 = this.z.redSqr();
var u1 = this.x.redMul(pz2);
var u2 = p.x.redMul(z2);
var s1 = this.y.redMul(pz2.redMul(p.z));
var s2 = p.y.redMul(z2.redMul(this.z));
var h = u1.redSub(u2);
var r = s1.redSub(s2);
if (h.cmpn(0) === 0) {
if (r.cmpn(0) !== 0)
return this.curve.jpoint(null, null, null);
else
return this.dbl();
}
var h2 = h.redSqr();
var h3 = h2.redMul(h);
var v = u1.redMul(h2);
var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
var nz = this.z.redMul(p.z).redMul(h);
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype.mixedAdd = function mixedAdd(p) {
// O + P = P
if (this.isInfinity())
return p.toJ();
// P + O = P
if (p.isInfinity())
return this;
// 8M + 3S + 7A
var z2 = this.z.redSqr();
var u1 = this.x;
var u2 = p.x.redMul(z2);
var s1 = this.y;
var s2 = p.y.redMul(z2).redMul(this.z);
var h = u1.redSub(u2);
var r = s1.redSub(s2);
if (h.cmpn(0) === 0) {
if (r.cmpn(0) !== 0)
return this.curve.jpoint(null, null, null);
else
return this.dbl();
}
var h2 = h.redSqr();
var h3 = h2.redMul(h);
var v = u1.redMul(h2);
var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
var nz = this.z.redMul(h);
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype.dblp = function dblp(pow) {
if (pow === 0)
return this;
if (this.isInfinity())
return this;
if (!pow)
return this.dbl();
if (this.curve.zeroA || this.curve.threeA) {
var r = this;
for (var i = 0; i < pow; i++)
r = r.dbl();
return r;
}
// 1M + 2S + 1A + N * (4S + 5M + 8A)
// N = 1 => 6M + 6S + 9A
var a = this.curve.a;
var tinv = this.curve.tinv;
var jx = this.x;
var jy = this.y;
var jz = this.z;
var jz4 = jz.redSqr().redSqr();
// Reuse results
var jyd = jy.redAdd(jy);
for (var i = 0; i < pow; i++) {
var jx2 = jx.redSqr();
var jyd2 = jyd.redSqr();
var jyd4 = jyd2.redSqr();
var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
var t1 = jx.redMul(jyd2);
var nx = c.redSqr().redISub(t1.redAdd(t1));
var t2 = t1.redISub(nx);
var dny = c.redMul(t2);
dny = dny.redIAdd(dny).redISub(jyd4);
var nz = jyd.redMul(jz);
if (i + 1 < pow)
jz4 = jz4.redMul(jyd4);
jx = nx;
jz = nz;
jyd = dny;
}
return this.curve.jpoint(jx, jyd.redMul(tinv), jz);
};
JPoint.prototype.dbl = function dbl() {
if (this.isInfinity())
return this;
if (this.curve.zeroA)
return this._zeroDbl();
else if (this.curve.threeA)
return this._threeDbl();
else
return this._dbl();
};
JPoint.prototype._zeroDbl = function _zeroDbl() {
var nx;
var ny;
var nz;
// Z = 1
if (this.zOne) {
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
// #doubling-mdbl-2007-bl
// 1M + 5S + 14A
// XX = X1^2
var xx = this.x.redSqr();
// YY = Y1^2
var yy = this.y.redSqr();
// YYYY = YY^2
var yyyy = yy.redSqr();
// S = 2 * ((X1 + YY)^2 - XX - YYYY)
var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
s = s.redIAdd(s);
// M = 3 * XX + a; a = 0
var m = xx.redAdd(xx).redIAdd(xx);
// T = M ^ 2 - 2*S
var t = m.redSqr().redISub(s).redISub(s);
// 8 * YYYY
var yyyy8 = yyyy.redIAdd(yyyy);
yyyy8 = yyyy8.redIAdd(yyyy8);
yyyy8 = yyyy8.redIAdd(yyyy8);
// X3 = T
nx = t;
// Y3 = M * (S - T) - 8 * YYYY
ny = m.redMul(s.redISub(t)).redISub(yyyy8);
// Z3 = 2*Y1
nz = this.y.redAdd(this.y);
} else {
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
// #doubling-dbl-2009-l
// 2M + 5S + 13A
// A = X1^2
var a = this.x.redSqr();
// B = Y1^2
var b = this.y.redSqr();
// C = B^2
var c = b.redSqr();
// D = 2 * ((X1 + B)^2 - A - C)
var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);
d = d.redIAdd(d);
// E = 3 * A
var e = a.redAdd(a).redIAdd(a);
// F = E^2
var f = e.redSqr();
// 8 * C
var c8 = c.redIAdd(c);
c8 = c8.redIAdd(c8);
c8 = c8.redIAdd(c8);
// X3 = F - 2 * D
nx = f.redISub(d).redISub(d);
// Y3 = E * (D - X3) - 8 * C
ny = e.redMul(d.redISub(nx)).redISub(c8);
// Z3 = 2 * Y1 * Z1
nz = this.y.redMul(this.z);
nz = nz.redIAdd(nz);
}
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype._threeDbl = function _threeDbl() {
var nx;
var ny;
var nz;
// Z = 1
if (this.zOne) {
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
// #doubling-mdbl-2007-bl
// 1M + 5S + 15A
// XX = X1^2
var xx = this.x.redSqr();
// YY = Y1^2
var yy = this.y.redSqr();
// YYYY = YY^2
var yyyy = yy.redSqr();
// S = 2 * ((X1 + YY)^2 - XX - YYYY)
var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
s = s.redIAdd(s);
// M = 3 * XX + a
var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);
// T = M^2 - 2 * S
var t = m.redSqr().redISub(s).redISub(s);
// X3 = T
nx = t;
// Y3 = M * (S - T) - 8 * YYYY
var yyyy8 = yyyy.redIAdd(yyyy);
yyyy8 = yyyy8.redIAdd(yyyy8);
yyyy8 = yyyy8.redIAdd(yyyy8);
ny = m.redMul(s.redISub(t)).redISub(yyyy8);
// Z3 = 2 * Y1
nz = this.y.redAdd(this.y);
} else {
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
// 3M + 5S
// delta = Z1^2
var delta = this.z.redSqr();
// gamma = Y1^2
var gamma = this.y.redSqr();
// beta = X1 * gamma
var beta = this.x.redMul(gamma);
// alpha = 3 * (X1 - delta) * (X1 + delta)
var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));
alpha = alpha.redAdd(alpha).redIAdd(alpha);
// X3 = alpha^2 - 8 * beta
var beta4 = beta.redIAdd(beta);
beta4 = beta4.redIAdd(beta4);
var beta8 = beta4.redAdd(beta4);
nx = alpha.redSqr().redISub(beta8);
// Z3 = (Y1 + Z1)^2 - gamma - delta
nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);
// Y3 = alpha * (4 * beta - X3) - 8 * gamma^2
var ggamma8 = gamma.redSqr();
ggamma8 = ggamma8.redIAdd(ggamma8);
ggamma8 = ggamma8.redIAdd(ggamma8);
ggamma8 = ggamma8.redIAdd(ggamma8);
ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);
}
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype._dbl = function _dbl() {
var a = this.curve.a;
// 4M + 6S + 10A
var jx = this.x;
var jy = this.y;
var jz = this.z;
var jz4 = jz.redSqr().redSqr();
var jx2 = jx.redSqr();
var jy2 = jy.redSqr();
var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
var jxd4 = jx.redAdd(jx);
jxd4 = jxd4.redIAdd(jxd4);
var t1 = jxd4.redMul(jy2);
var nx = c.redSqr().redISub(t1.redAdd(t1));
var t2 = t1.redISub(nx);
var jyd8 = jy2.redSqr();
jyd8 = jyd8.redIAdd(jyd8);
jyd8 = jyd8.redIAdd(jyd8);
jyd8 = jyd8.redIAdd(jyd8);
var ny = c.redMul(t2).redISub(jyd8);
var nz = jy.redAdd(jy).redMul(jz);
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype.trpl = function trpl() {
if (!this.curve.zeroA)
return this.dbl().add(this);
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl
// 5M + 10S + ...
// XX = X1^2
var xx = this.x.redSqr();
// YY = Y1^2
var yy = this.y.redSqr();
// ZZ = Z1^2
var zz = this.z.redSqr();
// YYYY = YY^2
var yyyy = yy.redSqr();
// M = 3 * XX + a * ZZ2; a = 0
var m = xx.redAdd(xx).redIAdd(xx);
// MM = M^2
var mm = m.redSqr();
// E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM
var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
e = e.redIAdd(e);
e = e.redAdd(e).redIAdd(e);
e = e.redISub(mm);
// EE = E^2
var ee = e.redSqr();
// T = 16*YYYY
var t = yyyy.redIAdd(yyyy);
t = t.redIAdd(t);
t = t.redIAdd(t);
t = t.redIAdd(t);
// U = (M + E)^2 - MM - EE - T
var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);
// X3 = 4 * (X1 * EE - 4 * YY * U)
var yyu4 = yy.redMul(u);
yyu4 = yyu4.redIAdd(yyu4);
yyu4 = yyu4.redIAdd(yyu4);
var nx = this.x.redMul(ee).redISub(yyu4);
nx = nx.redIAdd(nx);
nx = nx.redIAdd(nx);
// Y3 = 8 * Y1 * (U * (T - U) - E * EE)
var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));
ny = ny.redIAdd(ny);
ny = ny.redIAdd(ny);
ny = ny.redIAdd(ny);
// Z3 = (Z1 + E)^2 - ZZ - EE
var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);
return this.curve.jpoint(nx, ny, nz);
};
JPoint.prototype.mul = function mul(k, kbase) {
k = new bn(k, kbase);
return this.curve._wnafMul(this, k);
};
JPoint.prototype.eq = function eq(p) {
if (p.type === 'affine')
return this.eq(p.toJ());
if (this === p)
return true;
// x1 * z2^2 == x2 * z1^2
var z2 = this.z.redSqr();
var pz2 = p.z.redSqr();
if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)
return false;
// y1 * z2^3 == y2 * z1^3
var z3 = z2.redMul(this.z);
var pz3 = pz2.redMul(p.z);
return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;
};
JPoint.prototype.eqXToP = function eqXToP(x) {
var zs = this.z.redSqr();
var rx = x.toRed(this.curve.red).redMul(zs);
if (this.x.cmp(rx) === 0)
return true;
var xc = x.clone();
var t = this.curve.redN.redMul(zs);
for (;;) {
xc.iadd(this.curve.n);
if (xc.cmp(this.curve.p) >= 0)
return false;
rx.redIAdd(t);
if (this.x.cmp(rx) === 0)
return true;
}
};
JPoint.prototype.inspect = function inspect() {
if (this.isInfinity())
return '<EC JPoint Infinity>';
return '<EC JPoint x: ' + this.x.toString(16, 2) +
' y: ' + this.y.toString(16, 2) +
' z: ' + this.z.toString(16, 2) + '>';
};
JPoint.prototype.isInfinity = function isInfinity() {
// XXX This code assumes that zero is always zero in red
return this.z.cmpn(0) === 0;
};
function MontCurve(conf) {
base.call(this, 'mont', conf);
this.a = new bn(conf.a, 16).toRed(this.red);
this.b = new bn(conf.b, 16).toRed(this.red);
this.i4 = new bn(4).toRed(this.red).redInvm();
this.two = new bn(2).toRed(this.red);
// Note: this implementation is according to the original paper
// by P. Montgomery, NOT the one by D. J. Bernstein.
this.a24 = this.i4.redMul(this.a.redAdd(this.two));
}
inherits_browser(MontCurve, base);
var mont = MontCurve;
MontCurve.prototype.validate = function validate(point) {
var x = point.normalize().x;
var x2 = x.redSqr();
var rhs = x2.redMul(x).redAdd(x2.redMul(this.a)).redAdd(x);
var y = rhs.redSqrt();
return y.redSqr().cmp(rhs) === 0;
};
function Point$1(curve, x, z) {
base.BasePoint.call(this, curve, 'projective');
if (x === null && z === null) {
this.x = this.curve.one;
this.z = this.curve.zero;
} else {
this.x = new bn(x, 16);
this.z = new bn(z, 16);
if (!this.x.red)
this.x = this.x.toRed(this.curve.red);
if (!this.z.red)
this.z = this.z.toRed(this.curve.red);
}
}
inherits_browser(Point$1, base.BasePoint);
MontCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
var bytes = utils_1$1.toArray(bytes, enc);
// TODO Curve448
// Montgomery curve points must be represented in the compressed format
// https://tools.ietf.org/html/draft-ietf-openpgp-rfc4880bis-02#appendix-B
if (bytes.length === 33 && bytes[0] === 0x40)
bytes = bytes.slice(1, 33).reverse(); // point must be little-endian
if (bytes.length !== 32)
throw new Error('Unknown point compression format');
return this.point(bytes, 1);
};
MontCurve.prototype.point = function point(x, z) {
return new Point$1(this, x, z);
};
MontCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
return Point$1.fromJSON(this, obj);
};
Point$1.prototype.precompute = function precompute() {
// No-op
};
Point$1.prototype._encode = function _encode(compact) {
var len = this.curve.p.byteLength();
// Note: the output should always be little-endian
// https://tools.ietf.org/html/draft-ietf-openpgp-rfc4880bis-02#appendix-B
if (compact) {
return [ 0x40 ].concat(this.getX().toArray('le', len));
} else {
return this.getX().toArray('be', len);
}
};
Point$1.fromJSON = function fromJSON(curve, obj) {
return new Point$1(curve, obj[0], obj[1] || curve.one);
};
Point$1.prototype.inspect = function inspect() {
if (this.isInfinity())
return '<EC Point Infinity>';
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
' z: ' + this.z.fromRed().toString(16, 2) + '>';
};
Point$1.prototype.isInfinity = function isInfinity() {
// XXX This code assumes that zero is always zero in red
return this.z.cmpn(0) === 0;
};
Point$1.prototype.dbl = function dbl() {
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3
// 2M + 2S + 4A
// A = X1 + Z1
var a = this.x.redAdd(this.z);
// AA = A^2
var aa = a.redSqr();
// B = X1 - Z1
var b = this.x.redSub(this.z);
// BB = B^2
var bb = b.redSqr();
// C = AA - BB
var c = aa.redSub(bb);
// X3 = AA * BB
var nx = aa.redMul(bb);
// Z3 = C * (BB + A24 * C)
var nz = c.redMul(bb.redAdd(this.curve.a24.redMul(c)));
return this.curve.point(nx, nz);
};
Point$1.prototype.add = function add() {
throw new Error('Not supported on Montgomery curve');
};
Point$1.prototype.diffAdd = function diffAdd(p, diff) {
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3
// 4M + 2S + 6A
// A = X2 + Z2
var a = this.x.redAdd(this.z);
// B = X2 - Z2
var b = this.x.redSub(this.z);
// C = X3 + Z3
var c = p.x.redAdd(p.z);
// D = X3 - Z3
var d = p.x.redSub(p.z);
// DA = D * A
var da = d.redMul(a);
// CB = C * B
var cb = c.redMul(b);
// X5 = Z1 * (DA + CB)^2
var nx = diff.z.redMul(da.redAdd(cb).redSqr());
// Z5 = X1 * (DA - CB)^2
var nz = diff.x.redMul(da.redISub(cb).redSqr());
return this.curve.point(nx, nz);
};
Point$1.prototype.mul = function mul(k) {
k = new bn(k, 16);
var t = k.clone();
var a = this; // (N / 2) * Q + Q
var b = this.curve.point(null, null); // (N / 2) * Q
var c = this; // Q
for (var bits = []; t.cmpn(0) !== 0; t.iushrn(1))
bits.push(t.andln(1));
for (var i = bits.length - 1; i >= 0; i--) {
if (bits[i] === 0) {
// N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q
a = a.diffAdd(b, c);
// N * Q = 2 * ((N / 2) * Q + Q))
b = b.dbl();
} else {
// N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)
b = a.diffAdd(b, c);
// N * Q + Q = 2 * ((N / 2) * Q + Q)
a = a.dbl();
}
}
return b;
};
Point$1.prototype.mulAdd = function mulAdd() {
throw new Error('Not supported on Montgomery curve');
};
Point$1.prototype.jumlAdd = function jumlAdd() {
throw new Error('Not supported on Montgomery curve');
};
Point$1.prototype.eq = function eq(other) {
return this.getX().cmp(other.getX()) === 0;
};
Point$1.prototype.normalize = function normalize() {
this.x = this.x.redMul(this.z.redInvm());
this.z = this.curve.one;
return this;
};
Point$1.prototype.getX = function getX() {
// Normalize coordinates
this.normalize();
return this.x.fromRed();
};
var assert$2 = utils_1$1.assert;
function EdwardsCurve(conf) {
// NOTE: Important as we are creating point in Base.call()
this.twisted = (conf.a | 0) !== 1;
this.mOneA = this.twisted && (conf.a | 0) === -1;
this.extended = this.mOneA;
base.call(this, 'edwards', conf);
this.a = new bn(conf.a, 16).umod(this.red.m);
this.a = this.a.toRed(this.red);
this.c = new bn(conf.c, 16).toRed(this.red);
this.c2 = this.c.redSqr();
this.d = new bn(conf.d, 16).toRed(this.red);
this.dd = this.d.redAdd(this.d);
assert$2(!this.twisted || this.c.fromRed().cmpn(1) === 0);
this.oneC = (conf.c | 0) === 1;
}
inherits_browser(EdwardsCurve, base);
var edwards = EdwardsCurve;
EdwardsCurve.prototype._mulA = function _mulA(num) {
if (this.mOneA)
return num.redNeg();
else
return this.a.redMul(num);
};
EdwardsCurve.prototype._mulC = function _mulC(num) {
if (this.oneC)
return num;
else
return this.c.redMul(num);
};
// Just for compatibility with Short curve
EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {
return this.point(x, y, z, t);
};
EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {
x = new bn(x, 16);
if (!x.red)
x = x.toRed(this.red);
var x2 = x.redSqr();
var rhs = this.c2.redSub(this.a.redMul(x2));
var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));
var y2 = rhs.redMul(lhs.redInvm());
var y = y2.redSqrt();
if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
throw new Error('invalid point');
var isOdd = y.fromRed().isOdd();
if (odd && !isOdd || !odd && isOdd)
y = y.redNeg();
return this.point(x, y);
};
EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {
y = new bn(y, 16);
if (!y.red)
y = y.toRed(this.red);
// x^2 = (y^2 - c^2) / (c^2 d y^2 - a)
var y2 = y.redSqr();
var lhs = y2.redSub(this.c2);
var rhs = y2.redMul(this.d).redMul(this.c2).redSub(this.a);
var x2 = lhs.redMul(rhs.redInvm());
if (x2.cmp(this.zero) === 0) {
if (odd)
throw new Error('invalid point');
else
return this.point(this.zero, y);
}
var x = x2.redSqrt();
if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)
throw new Error('invalid point');
if (x.fromRed().isOdd() !== odd)
x = x.redNeg();
return this.point(x, y);
};
EdwardsCurve.prototype.validate = function validate(point) {
if (point.isInfinity())
return true;
// Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
point.normalize();
var x2 = point.x.redSqr();
var y2 = point.y.redSqr();
var lhs = x2.redMul(this.a).redAdd(y2);
var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));
return lhs.cmp(rhs) === 0;
};
function Point$2(curve, x, y, z, t) {
base.BasePoint.call(this, curve, 'projective');
if (x === null && y === null && z === null) {
this.x = this.curve.zero;
this.y = this.curve.one;
this.z = this.curve.one;
this.t = this.curve.zero;
this.zOne = true;
} else {
this.x = new bn(x, 16);
this.y = new bn(y, 16);
this.z = z ? new bn(z, 16) : this.curve.one;
this.t = t && new bn(t, 16);
if (!this.x.red)
this.x = this.x.toRed(this.curve.red);
if (!this.y.red)
this.y = this.y.toRed(this.curve.red);
if (!this.z.red)
this.z = this.z.toRed(this.curve.red);
if (this.t && !this.t.red)
this.t = this.t.toRed(this.curve.red);
this.zOne = this.z === this.curve.one;
// Use extended coordinates
if (this.curve.extended && !this.t) {
this.t = this.x.redMul(this.y);
if (!this.zOne)
this.t = this.t.redMul(this.z.redInvm());
}
}
}
inherits_browser(Point$2, base.BasePoint);
EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
return Point$2.fromJSON(this, obj);
};
EdwardsCurve.prototype.point = function point(x, y, z, t) {
return new Point$2(this, x, y, z, t);
};
Point$2.fromJSON = function fromJSON(curve, obj) {
return new Point$2(curve, obj[0], obj[1], obj[2]);
};
Point$2.prototype.inspect = function inspect() {
if (this.isInfinity())
return '<EC Point Infinity>';
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
' y: ' + this.y.fromRed().toString(16, 2) +
' z: ' + this.z.fromRed().toString(16, 2) + '>';
};
Point$2.prototype.isInfinity = function isInfinity() {
// XXX This code assumes that zero is always zero in red
return this.x.cmpn(0) === 0 &&
(this.y.cmp(this.z) === 0 ||
(this.zOne && this.y.cmp(this.curve.c) === 0));
};
Point$2.prototype._extDbl = function _extDbl() {
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
// #doubling-dbl-2008-hwcd
// 4M + 4S
// A = X1^2
var a = this.x.redSqr();
// B = Y1^2
var b = this.y.redSqr();
// C = 2 * Z1^2
var c = this.z.redSqr();
c = c.redIAdd(c);
// D = a * A
var d = this.curve._mulA(a);
// E = (X1 + Y1)^2 - A - B
var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);
// G = D + B
var g = d.redAdd(b);
// F = G - C
var f = g.redSub(c);
// H = D - B
var h = d.redSub(b);
// X3 = E * F
var nx = e.redMul(f);
// Y3 = G * H
var ny = g.redMul(h);
// T3 = E * H
var nt = e.redMul(h);
// Z3 = F * G
var nz = f.redMul(g);
return this.curve.point(nx, ny, nz, nt);
};
Point$2.prototype._projDbl = function _projDbl() {
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
// #doubling-dbl-2008-bbjlp
// #doubling-dbl-2007-bl
// and others
// Generally 3M + 4S or 2M + 4S
// B = (X1 + Y1)^2
var b = this.x.redAdd(this.y).redSqr();
// C = X1^2
var c = this.x.redSqr();
// D = Y1^2
var d = this.y.redSqr();
var nx;
var ny;
var nz;
if (this.curve.twisted) {
// E = a * C
var e = this.curve._mulA(c);
// F = E + D
var f = e.redAdd(d);
if (this.zOne) {
// X3 = (B - C - D) * (F - 2)
nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));
// Y3 = F * (E - D)
ny = f.redMul(e.redSub(d));
// Z3 = F^2 - 2 * F
nz = f.redSqr().redSub(f).redSub(f);
} else {
// H = Z1^2
var h = this.z.redSqr();
// J = F - 2 * H
var j = f.redSub(h).redISub(h);
// X3 = (B-C-D)*J
nx = b.redSub(c).redISub(d).redMul(j);
// Y3 = F * (E - D)
ny = f.redMul(e.redSub(d));
// Z3 = F * J
nz = f.redMul(j);
}
} else {
// E = C + D
var e = c.redAdd(d);
// H = (c * Z1)^2
var h = this.curve._mulC(this.z).redSqr();
// J = E - 2 * H
var j = e.redSub(h).redSub(h);
// X3 = c * (B - E) * J
nx = this.curve._mulC(b.redISub(e)).redMul(j);
// Y3 = c * E * (C - D)
ny = this.curve._mulC(e).redMul(c.redISub(d));
// Z3 = E * J
nz = e.redMul(j);
}
return this.curve.point(nx, ny, nz);
};
Point$2.prototype.dbl = function dbl() {
if (this.isInfinity())
return this;
// Double in extended coordinates
if (this.curve.extended)
return this._extDbl();
else
return this._projDbl();
};
Point$2.prototype._extAdd = function _extAdd(p) {
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
// #addition-add-2008-hwcd-3
// 8M
// A = (Y1 - X1) * (Y2 - X2)
var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));
// B = (Y1 + X1) * (Y2 + X2)
var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));
// C = T1 * k * T2
var c = this.t.redMul(this.curve.dd).redMul(p.t);
// D = Z1 * 2 * Z2
var d = this.z.redMul(p.z.redAdd(p.z));
// E = B - A
var e = b.redSub(a);
// F = D - C
var f = d.redSub(c);
// G = D + C
var g = d.redAdd(c);
// H = B + A
var h = b.redAdd(a);
// X3 = E * F
var nx = e.redMul(f);
// Y3 = G * H
var ny = g.redMul(h);
// T3 = E * H
var nt = e.redMul(h);
// Z3 = F * G
var nz = f.redMul(g);
return this.curve.point(nx, ny, nz, nt);
};
Point$2.prototype._projAdd = function _projAdd(p) {
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
// #addition-add-2008-bbjlp
// #addition-add-2007-bl
// 10M + 1S
// A = Z1 * Z2
var a = this.z.redMul(p.z);
// B = A^2
var b = a.redSqr();
// C = X1 * X2
var c = this.x.redMul(p.x);
// D = Y1 * Y2
var d = this.y.redMul(p.y);
// E = d * C * D
var e = this.curve.d.redMul(c).redMul(d);
// F = B - E
var f = b.redSub(e);
// G = B + E
var g = b.redAdd(e);
// X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);
var nx = a.redMul(f).redMul(tmp);
var ny;
var nz;
if (this.curve.twisted) {
// Y3 = A * G * (D - a * C)
ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));
// Z3 = F * G
nz = f.redMul(g);
} else {
// Y3 = A * G * (D - C)
ny = a.redMul(g).redMul(d.redSub(c));
// Z3 = c * F * G
nz = this.curve._mulC(f).redMul(g);
}
return this.curve.point(nx, ny, nz);
};
Point$2.prototype.add = function add(p) {
if (this.isInfinity())
return p;
if (p.isInfinity())
return this;
if (this.curve.extended)
return this._extAdd(p);
else
return this._projAdd(p);
};
Point$2.prototype.mul = function mul(k) {
if (this._hasDoubles(k))
return this.curve._fixedNafMul(this, k);
else
return this.curve._wnafMul(this, k);
};
Point$2.prototype.mulAdd = function mulAdd(k1, p, k2) {
return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, false);
};
Point$2.prototype.jmulAdd = function jmulAdd(k1, p, k2) {
return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, true);
};
Point$2.prototype.normalize = function normalize() {
if (this.zOne)
return this;
// Normalize coordinates
var zi = this.z.redInvm();
this.x = this.x.redMul(zi);
this.y = this.y.redMul(zi);
if (this.t)
this.t = this.t.redMul(zi);
this.z = this.curve.one;
this.zOne = true;
return this;
};
Point$2.prototype.neg = function neg() {
return this.curve.point(this.x.redNeg(),
this.y,
this.z,
this.t && this.t.redNeg());
};
Point$2.prototype.getX = function getX() {
this.normalize();
return this.x.fromRed();
};
Point$2.prototype.getY = function getY() {
this.normalize();
return this.y.fromRed();
};
Point$2.prototype.eq = function eq(other) {
return this === other ||
this.getX().cmp(other.getX()) === 0 &&
this.getY().cmp(other.getY()) === 0;
};
Point$2.prototype.eqXToP = function eqXToP(x) {
var rx = x.toRed(this.curve.red).redMul(this.z);
if (this.x.cmp(rx) === 0)
return true;
var xc = x.clone();
var t = this.curve.redN.redMul(this.z);
for (;;) {
xc.iadd(this.curve.n);
if (xc.cmp(this.curve.p) >= 0)
return false;
rx.redIAdd(t);
if (this.x.cmp(rx) === 0)
return true;
}
};
// Compatibility with BaseCurve
Point$2.prototype.toP = Point$2.prototype.normalize;
Point$2.prototype.mixedAdd = Point$2.prototype.add;
var curve_1 = createCommonjsModule(function (module, exports) {
var curve = exports;
curve.base = base;
curve.short = short_1;
curve.mont = mont;
curve.edwards = edwards;
});
var rotl32 = utils.rotl32;
var sum32 = utils.sum32;
var sum32_5 = utils.sum32_5;
var ft_1 = common.ft_1;
var BlockHash = common$1.BlockHash;
var sha1_K = [
0x5A827999, 0x6ED9EBA1,
0x8F1BBCDC, 0xCA62C1D6
];
function SHA1() {
if (!(this instanceof SHA1))
return new SHA1();
BlockHash.call(this);
this.h = [
0x67452301, 0xefcdab89, 0x98badcfe,
0x10325476, 0xc3d2e1f0 ];
this.W = new Array(80);
}
utils.inherits(SHA1, BlockHash);
var _1 = SHA1;
SHA1.blockSize = 512;
SHA1.outSize = 160;
SHA1.hmacStrength = 80;
SHA1.padLength = 64;
SHA1.prototype._update = function _update(msg, start) {
var W = this.W;
for (var i = 0; i < 16; i++)
W[i] = msg[start + i];
for(; i < W.length; i++)
W[i] = rotl32(W[i - 3] ^ W[i - 8] ^ W[i - 14] ^ W[i - 16], 1);
var a = this.h[0];
var b = this.h[1];
var c = this.h[2];
var d = this.h[3];
var e = this.h[4];
for (i = 0; i < W.length; i++) {
var s = ~~(i / 20);
var t = sum32_5(rotl32(a, 5), ft_1(s, b, c, d), e, W[i], sha1_K[s]);
e = d;
d = c;
c = rotl32(b, 30);
b = a;
a = t;
}
this.h[0] = sum32(this.h[0], a);
this.h[1] = sum32(this.h[1], b);
this.h[2] = sum32(this.h[2], c);
this.h[3] = sum32(this.h[3], d);
this.h[4] = sum32(this.h[4], e);
};
SHA1.prototype._digest = function digest(enc) {
if (enc === 'hex')
return utils.toHex32(this.h, 'big');
else
return utils.split32(this.h, 'big');
};
var sha1 = _1;
var sha224 = _224;
var sha256 = _256;
var sha384 = _384;
var sha512 = _512;
var sha = {
sha1: sha1,
sha224: sha224,
sha256: sha256,
sha384: sha384,
sha512: sha512
};
function Hmac(hash, key, enc) {
if (!(this instanceof Hmac))
return new Hmac(hash, key, enc);
this.Hash = hash;
this.blockSize = hash.blockSize / 8;
this.outSize = hash.outSize / 8;
this.inner = null;
this.outer = null;
this._init(utils.toArray(key, enc));
}
var hmac = Hmac;
Hmac.prototype._init = function init(key) {
// Shorten key, if needed
if (key.length > this.blockSize)
key = new this.Hash().update(key).digest();
minimalisticAssert(key.length <= this.blockSize);
// Add padding to key
for (var i = key.length; i < this.blockSize; i++)
key.push(0);
for (i = 0; i < key.length; i++)
key[i] ^= 0x36;
this.inner = new this.Hash().update(key);
// 0x36 ^ 0x5c = 0x6a
for (i = 0; i < key.length; i++)
key[i] ^= 0x6a;
this.outer = new this.Hash().update(key);
};
Hmac.prototype.update = function update(msg, enc) {
this.inner.update(msg, enc);
return this;
};
Hmac.prototype.digest = function digest(enc) {
this.outer.update(this.inner.digest());
return this.outer.digest(enc);
};
var hash_1 = createCommonjsModule(function (module, exports) {
var hash = exports;
hash.utils = utils;
hash.common = common$1;
hash.sha = sha;
hash.ripemd = ripemd;
hash.hmac = hmac;
// Proxy hash functions to the main object
hash.sha1 = hash.sha.sha1;
hash.sha256 = hash.sha.sha256;
hash.sha224 = hash.sha.sha224;
hash.sha384 = hash.sha.sha384;
hash.sha512 = hash.sha.sha512;
hash.ripemd160 = hash.ripemd.ripemd160;
});
var secp256k1 = {
doubles: {
step: 4,
points: [
[
'e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a',
'f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821'
],
[
'8282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508',
'11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf'
],
[
'175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739',
'd3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695'
],
[
'363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640',
'4e273adfc732221953b445397f3363145b9a89008199ecb62003c7f3bee9de9'
],
[
'8b4b5f165df3c2be8c6244b5b745638843e4a781a15bcd1b69f79a55dffdf80c',
'4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36'
],
[
'723cbaa6e5db996d6bf771c00bd548c7b700dbffa6c0e77bcb6115925232fcda',
'96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f'
],
[
'eebfa4d493bebf98ba5feec812c2d3b50947961237a919839a533eca0e7dd7fa',
'5d9a8ca3970ef0f269ee7edaf178089d9ae4cdc3a711f712ddfd4fdae1de8999'
],
[
'100f44da696e71672791d0a09b7bde459f1215a29b3c03bfefd7835b39a48db0',
'cdd9e13192a00b772ec8f3300c090666b7ff4a18ff5195ac0fbd5cd62bc65a09'
],
[
'e1031be262c7ed1b1dc9227a4a04c017a77f8d4464f3b3852c8acde6e534fd2d',
'9d7061928940405e6bb6a4176597535af292dd419e1ced79a44f18f29456a00d'
],
[
'feea6cae46d55b530ac2839f143bd7ec5cf8b266a41d6af52d5e688d9094696d',
'e57c6b6c97dce1bab06e4e12bf3ecd5c981c8957cc41442d3155debf18090088'
],
[
'da67a91d91049cdcb367be4be6ffca3cfeed657d808583de33fa978bc1ec6cb1',
'9bacaa35481642bc41f463f7ec9780e5dec7adc508f740a17e9ea8e27a68be1d'
],
[
'53904faa0b334cdda6e000935ef22151ec08d0f7bb11069f57545ccc1a37b7c0',
'5bc087d0bc80106d88c9eccac20d3c1c13999981e14434699dcb096b022771c8'
],
[
'8e7bcd0bd35983a7719cca7764ca906779b53a043a9b8bcaeff959f43ad86047',
'10b7770b2a3da4b3940310420ca9514579e88e2e47fd68b3ea10047e8460372a'
],
[
'385eed34c1cdff21e6d0818689b81bde71a7f4f18397e6690a841e1599c43862',
'283bebc3e8ea23f56701de19e9ebf4576b304eec2086dc8cc0458fe5542e5453'
],
[
'6f9d9b803ecf191637c73a4413dfa180fddf84a5947fbc9c606ed86c3fac3a7',
'7c80c68e603059ba69b8e2a30e45c4d47ea4dd2f5c281002d86890603a842160'
],
[
'3322d401243c4e2582a2147c104d6ecbf774d163db0f5e5313b7e0e742d0e6bd',
'56e70797e9664ef5bfb019bc4ddaf9b72805f63ea2873af624f3a2e96c28b2a0'
],
[
'85672c7d2de0b7da2bd1770d89665868741b3f9af7643397721d74d28134ab83',
'7c481b9b5b43b2eb6374049bfa62c2e5e77f17fcc5298f44c8e3094f790313a6'
],
[
'948bf809b1988a46b06c9f1919413b10f9226c60f668832ffd959af60c82a0a',
'53a562856dcb6646dc6b74c5d1c3418c6d4dff08c97cd2bed4cb7f88d8c8e589'
],
[
'6260ce7f461801c34f067ce0f02873a8f1b0e44dfc69752accecd819f38fd8e8',
'bc2da82b6fa5b571a7f09049776a1ef7ecd292238051c198c1a84e95b2b4ae17'
],
[
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'4571534baa94d3b5f9f98d09fb990bddbd5f5b03ec481f10e0e5dc841d755bda'
],
[
'e06372b0f4a207adf5ea905e8f1771b4e7e8dbd1c6a6c5b725866a0ae4fce725',
'7a908974bce18cfe12a27bb2ad5a488cd7484a7787104870b27034f94eee31dd'
],
[
'213c7a715cd5d45358d0bbf9dc0ce02204b10bdde2a3f58540ad6908d0559754',
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],
[
'4e7c272a7af4b34e8dbb9352a5419a87e2838c70adc62cddf0cc3a3b08fbd53c',
'17749c766c9d0b18e16fd09f6def681b530b9614bff7dd33e0b3941817dcaae6'
],
[
'fea74e3dbe778b1b10f238ad61686aa5c76e3db2be43057632427e2840fb27b6',
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],
[
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],
[
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],
[
'd895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b',
'febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f'
],
[
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],
[
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],
[
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],
[
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'e507a3620a38261affdcbd9427222b839aefabe1582894d991d4d48cb6ef150'
],
[
'8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da',
'662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82'
],
[
'e4f3fb0176af85d65ff99ff9198c36091f48e86503681e3e6686fd5053231e11',
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],
[
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],
[
'e7a26ce69dd4829f3e10cec0a9e98ed3143d084f308b92c0997fddfc60cb3e41',
'2a758e300fa7984b471b006a1aafbb18d0a6b2c0420e83e20e8a9421cf2cfd51'
],
[
'b6459e0ee3662ec8d23540c223bcbdc571cbcb967d79424f3cf29eb3de6b80ef',
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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],
[
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'e82d86fb6443fcb7565aee58b2948220a70f750af484ca52d4142174dcf89405'
],
[
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],
[
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],
[
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],
[
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],
[
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],
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],
[
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]
]
},
naf: {
wnd: 7,
points: [
[
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],
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],
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[
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[
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[
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],
[
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],
[
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[
'93144423ace3451ed29e0fb9ac2af211cb6e84a601df5993c419859fff5df04a',
'7c10dfb164c3425f5c71a3f9d7992038f1065224f72bb9d1d902a6d13037b47c'
],
[
'b015f8044f5fcbdcf21ca26d6c34fb8197829205c7b7d2a7cb66418c157b112c',
'ab8c1e086d04e813744a655b2df8d5f83b3cdc6faa3088c1d3aea1454e3a1d5f'
],
[
'd5e9e1da649d97d89e4868117a465a3a4f8a18de57a140d36b3f2af341a21b52',
'4cb04437f391ed73111a13cc1d4dd0db1693465c2240480d8955e8592f27447a'
],
[
'd3ae41047dd7ca065dbf8ed77b992439983005cd72e16d6f996a5316d36966bb',
'bd1aeb21ad22ebb22a10f0303417c6d964f8cdd7df0aca614b10dc14d125ac46'
],
[
'463e2763d885f958fc66cdd22800f0a487197d0a82e377b49f80af87c897b065',
'bfefacdb0e5d0fd7df3a311a94de062b26b80c61fbc97508b79992671ef7ca7f'
],
[
'7985fdfd127c0567c6f53ec1bb63ec3158e597c40bfe747c83cddfc910641917',
'603c12daf3d9862ef2b25fe1de289aed24ed291e0ec6708703a5bd567f32ed03'
],
[
'74a1ad6b5f76e39db2dd249410eac7f99e74c59cb83d2d0ed5ff1543da7703e9',
'cc6157ef18c9c63cd6193d83631bbea0093e0968942e8c33d5737fd790e0db08'
],
[
'30682a50703375f602d416664ba19b7fc9bab42c72747463a71d0896b22f6da3',
'553e04f6b018b4fa6c8f39e7f311d3176290d0e0f19ca73f17714d9977a22ff8'
],
[
'9e2158f0d7c0d5f26c3791efefa79597654e7a2b2464f52b1ee6c1347769ef57',
'712fcdd1b9053f09003a3481fa7762e9ffd7c8ef35a38509e2fbf2629008373'
],
[
'176e26989a43c9cfeba4029c202538c28172e566e3c4fce7322857f3be327d66',
'ed8cc9d04b29eb877d270b4878dc43c19aefd31f4eee09ee7b47834c1fa4b1c3'
],
[
'75d46efea3771e6e68abb89a13ad747ecf1892393dfc4f1b7004788c50374da8',
'9852390a99507679fd0b86fd2b39a868d7efc22151346e1a3ca4726586a6bed8'
],
[
'809a20c67d64900ffb698c4c825f6d5f2310fb0451c869345b7319f645605721',
'9e994980d9917e22b76b061927fa04143d096ccc54963e6a5ebfa5f3f8e286c1'
],
[
'1b38903a43f7f114ed4500b4eac7083fdefece1cf29c63528d563446f972c180',
'4036edc931a60ae889353f77fd53de4a2708b26b6f5da72ad3394119daf408f9'
]
]
}
};
var curves_1 = createCommonjsModule(function (module, exports) {
var curves = exports;
var assert = utils_1$1.assert;
function PresetCurve(options) {
if (options.type === 'short')
this.curve = new curve_1.short(options);
else if (options.type === 'edwards')
this.curve = new curve_1.edwards(options);
else if (options.type === 'mont')
this.curve = new curve_1.mont(options);
else throw new Error('Unknown curve type.');
this.g = this.curve.g;
this.n = this.curve.n;
this.hash = options.hash;
assert(this.g.validate(), 'Invalid curve');
assert(this.g.mul(this.n).isInfinity(), 'Invalid curve, n*G != O');
}
curves.PresetCurve = PresetCurve;
function defineCurve(name, options) {
Object.defineProperty(curves, name, {
configurable: true,
enumerable: true,
get: function() {
var curve = new PresetCurve(options);
Object.defineProperty(curves, name, {
configurable: true,
enumerable: true,
value: curve
});
return curve;
}
});
}
defineCurve('p192', {
type: 'short',
prime: 'p192',
p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',
a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',
b: '64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1',
n: 'ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831',
hash: hash_1.sha256,
gRed: false,
g: [
'188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012',
'07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811'
]
});
defineCurve('p224', {
type: 'short',
prime: 'p224',
p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',
a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',
b: 'b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4',
n: 'ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d',
hash: hash_1.sha256,
gRed: false,
g: [
'b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21',
'bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34'
]
});
defineCurve('p256', {
type: 'short',
prime: null,
p: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff',
a: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc',
b: '5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b',
n: 'ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551',
hash: hash_1.sha256,
gRed: false,
g: [
'6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296',
'4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5'
]
});
defineCurve('p384', {
type: 'short',
prime: null,
p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'fffffffe ffffffff 00000000 00000000 ffffffff',
a: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'fffffffe ffffffff 00000000 00000000 fffffffc',
b: 'b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f ' +
'5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef',
n: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 ' +
'f4372ddf 581a0db2 48b0a77a ecec196a ccc52973',
hash: hash_1.sha384,
gRed: false,
g: [
'aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 ' +
'5502f25d bf55296c 3a545e38 72760ab7',
'3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 ' +
'0a60b1ce 1d7e819d 7a431d7c 90ea0e5f'
]
});
defineCurve('p521', {
type: 'short',
prime: null,
p: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'ffffffff ffffffff ffffffff ffffffff ffffffff',
a: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'ffffffff ffffffff ffffffff ffffffff fffffffc',
b: '00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b ' +
'99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd ' +
'3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00',
n: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
'ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 ' +
'f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409',
hash: hash_1.sha512,
gRed: false,
g: [
'000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 ' +
'053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 ' +
'a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66',
'00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 ' +
'579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 ' +
'3fad0761 353c7086 a272c240 88be9476 9fd16650'
]
});
// https://tools.ietf.org/html/rfc7748#section-4.1
defineCurve('curve25519', {
type: 'mont',
prime: 'p25519',
p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
a: '76d06',
b: '1',
n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
cofactor: '8',
hash: hash_1.sha256,
gRed: false,
g: [
'9'
]
});
defineCurve('ed25519', {
type: 'edwards',
prime: 'p25519',
p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
a: '-1',
c: '1',
// -121665 * (121666^(-1)) (mod P)
d: '52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3',
n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
cofactor: '8',
hash: hash_1.sha256,
gRed: false,
g: [
'216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a',
// 4/5
'6666666666666666666666666666666666666666666666666666666666666658'
]
});
// https://tools.ietf.org/html/rfc5639#section-3.4
defineCurve('brainpoolP256r1', {
type: 'short',
prime: null,
p: 'A9FB57DB A1EEA9BC 3E660A90 9D838D72 6E3BF623 D5262028 2013481D 1F6E5377',
a: '7D5A0975 FC2C3057 EEF67530 417AFFE7 FB8055C1 26DC5C6C E94A4B44 F330B5D9',
b: '26DC5C6C E94A4B44 F330B5D9 BBD77CBF 95841629 5CF7E1CE 6BCCDC18 FF8C07B6',
n: 'A9FB57DB A1EEA9BC 3E660A90 9D838D71 8C397AA3 B561A6F7 901E0E82 974856A7',
hash: hash_1.sha256, // or 384, or 512
gRed: false,
g: [
'8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262',
'547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997'
]
});
// https://tools.ietf.org/html/rfc5639#section-3.6
defineCurve('brainpoolP384r1', {
type: 'short',
prime: null,
p: '8CB91E82 A3386D28 0F5D6F7E 50E641DF 152F7109 ED5456B4 12B1DA19 7FB71123' +
'ACD3A729 901D1A71 87470013 3107EC53',
a: '7BC382C6 3D8C150C 3C72080A CE05AFA0 C2BEA28E 4FB22787 139165EF BA91F90F' +
'8AA5814A 503AD4EB 04A8C7DD 22CE2826',
b: '04A8C7DD 22CE2826 8B39B554 16F0447C 2FB77DE1 07DCD2A6 2E880EA5 3EEB62D5' +
'7CB43902 95DBC994 3AB78696 FA504C11',
n: '8CB91E82 A3386D28 0F5D6F7E 50E641DF 152F7109 ED5456B3 1F166E6C AC0425A7' +
'CF3AB6AF 6B7FC310 3B883202 E9046565',
hash: hash_1.sha384, // or 512
gRed: false,
g: [
'1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10' +
'E8E826E03436D646AAEF87B2E247D4AF1E',
'8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129' +
'280E4646217791811142820341263C5315'
]
});
// https://tools.ietf.org/html/rfc5639#section-3.7
defineCurve('brainpoolP512r1', {
type: 'short',
prime: null,
p: 'AADD9DB8 DBE9C48B 3FD4E6AE 33C9FC07 CB308DB3 B3C9D20E D6639CCA 70330871' +
'7D4D9B00 9BC66842 AECDA12A E6A380E6 2881FF2F 2D82C685 28AA6056 583A48F3',
a: '7830A331 8B603B89 E2327145 AC234CC5 94CBDD8D 3DF91610 A83441CA EA9863BC' +
'2DED5D5A A8253AA1 0A2EF1C9 8B9AC8B5 7F1117A7 2BF2C7B9 E7C1AC4D 77FC94CA',
b: '3DF91610 A83441CA EA9863BC 2DED5D5A A8253AA1 0A2EF1C9 8B9AC8B5 7F1117A7' +
'2BF2C7B9 E7C1AC4D 77FC94CA DC083E67 984050B7 5EBAE5DD 2809BD63 8016F723',
n: 'AADD9DB8 DBE9C48B 3FD4E6AE 33C9FC07 CB308DB3 B3C9D20E D6639CCA 70330870' +
'553E5C41 4CA92619 41866119 7FAC1047 1DB1D381 085DDADD B5879682 9CA90069',
hash: hash_1.sha512,
gRed: false,
g: [
'81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009' +
'8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822',
'7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81' +
'11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892'
]
});
// https://en.bitcoin.it/wiki/Secp256k1
var pre;
try {
pre = secp256k1;
} catch (e) {
pre = undefined;
}
defineCurve('secp256k1', {
type: 'short',
prime: 'k256',
p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f',
a: '0',
b: '7',
n: 'ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141',
h: '1',
hash: hash_1.sha256,
// Precomputed endomorphism
beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',
lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',
basis: [
{
a: '3086d221a7d46bcde86c90e49284eb15',
b: '-e4437ed6010e88286f547fa90abfe4c3'
},
{
a: '114ca50f7a8e2f3f657c1108d9d44cfd8',
b: '3086d221a7d46bcde86c90e49284eb15'
}
],
gRed: false,
g: [
'79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
'483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',
pre
]
});
});
function HmacDRBG(options) {
if (!(this instanceof HmacDRBG))
return new HmacDRBG(options);
this.hash = options.hash;
this.predResist = !!options.predResist;
this.outLen = this.hash.outSize;
this.minEntropy = options.minEntropy || this.hash.hmacStrength;
this._reseed = null;
this.reseedInterval = null;
this.K = null;
this.V = null;
var entropy = utils_1.toArray(options.entropy, options.entropyEnc || 'hex');
var nonce = utils_1.toArray(options.nonce, options.nonceEnc || 'hex');
var pers = utils_1.toArray(options.pers, options.persEnc || 'hex');
minimalisticAssert(entropy.length >= (this.minEntropy / 8),
'Not enough entropy. Minimum is: ' + this.minEntropy + ' bits');
this._init(entropy, nonce, pers);
}
var hmacDrbg = HmacDRBG;
HmacDRBG.prototype._init = function init(entropy, nonce, pers) {
var seed = entropy.concat(nonce).concat(pers);
this.K = new Array(this.outLen / 8);
this.V = new Array(this.outLen / 8);
for (var i = 0; i < this.V.length; i++) {
this.K[i] = 0x00;
this.V[i] = 0x01;
}
this._update(seed);
this._reseed = 1;
this.reseedInterval = 0x1000000000000; // 2^48
};
HmacDRBG.prototype._hmac = function hmac() {
return new hash_1.hmac(this.hash, this.K);
};
HmacDRBG.prototype._update = function update(seed) {
var kmac = this._hmac()
.update(this.V)
.update([ 0x00 ]);
if (seed)
kmac = kmac.update(seed);
this.K = kmac.digest();
this.V = this._hmac().update(this.V).digest();
if (!seed)
return;
this.K = this._hmac()
.update(this.V)
.update([ 0x01 ])
.update(seed)
.digest();
this.V = this._hmac().update(this.V).digest();
};
HmacDRBG.prototype.reseed = function reseed(entropy, entropyEnc, add, addEnc) {
// Optional entropy enc
if (typeof entropyEnc !== 'string') {
addEnc = add;
add = entropyEnc;
entropyEnc = null;
}
entropy = utils_1.toArray(entropy, entropyEnc);
add = utils_1.toArray(add, addEnc);
minimalisticAssert(entropy.length >= (this.minEntropy / 8),
'Not enough entropy. Minimum is: ' + this.minEntropy + ' bits');
this._update(entropy.concat(add || []));
this._reseed = 1;
};
HmacDRBG.prototype.generate = function generate(len, enc, add, addEnc) {
if (this._reseed > this.reseedInterval)
throw new Error('Reseed is required');
// Optional encoding
if (typeof enc !== 'string') {
addEnc = add;
add = enc;
enc = null;
}
// Optional additional data
if (add) {
add = utils_1.toArray(add, addEnc || 'hex');
this._update(add);
}
var temp = [];
while (temp.length < len) {
this.V = this._hmac().update(this.V).digest();
temp = temp.concat(this.V);
}
var res = temp.slice(0, len);
this._update(add);
this._reseed++;
return utils_1.encode(res, enc);
};
var assert$3 = utils_1$1.assert;
function KeyPair(ec, options) {
this.ec = ec;
this.priv = null;
this.pub = null;
// KeyPair(ec, { priv: ..., pub: ... })
if (options.priv)
this._importPrivate(options.priv, options.privEnc);
if (options.pub)
this._importPublic(options.pub, options.pubEnc);
}
var key = KeyPair;
KeyPair.fromPublic = function fromPublic(ec, pub, enc) {
if (pub instanceof KeyPair)
return pub;
return new KeyPair(ec, {
pub: pub,
pubEnc: enc
});
};
KeyPair.fromPrivate = function fromPrivate(ec, priv, enc) {
if (priv instanceof KeyPair)
return priv;
return new KeyPair(ec, {
priv: priv,
privEnc: enc
});
};
// TODO: should not validate for X25519
KeyPair.prototype.validate = function validate() {
var pub = this.getPublic();
if (pub.isInfinity())
return { result: false, reason: 'Invalid public key' };
if (!pub.validate())
return { result: false, reason: 'Public key is not a point' };
if (!pub.mul(this.ec.curve.n).isInfinity())
return { result: false, reason: 'Public key * N != O' };
return { result: true, reason: null };
};
KeyPair.prototype.getPublic = function getPublic(enc, compact) {
if (!this.pub)
this.pub = this.ec.g.mul(this.priv);
if (!enc)
return this.pub;
return this.pub.encode(enc, compact);
};
KeyPair.prototype.getPrivate = function getPrivate(enc) {
if (enc === 'hex')
return this.priv.toString(16, 2);
else
return this.priv;
};
KeyPair.prototype._importPrivate = function _importPrivate(key, enc) {
this.priv = new bn(key, enc || 16);
// For Curve25519/Curve448 we have a specific procedure.
// TODO Curve448
if (this.ec.curve.type === 'mont') {
var one = this.ec.curve.one;
var mask = one.ushln(255 - 3).sub(one).ushln(3);
this.priv = this.priv.or(one.ushln(255 - 1));
this.priv = this.priv.and(mask);
} else
// Ensure that the priv won't be bigger than n, otherwise we may fail
// in fixed multiplication method
this.priv = this.priv.umod(this.ec.curve.n);
};
KeyPair.prototype._importPublic = function _importPublic(key, enc) {
if (key.x || key.y) {
// Montgomery points only have an `x` coordinate.
// Weierstrass/Edwards points on the other hand have both `x` and
// `y` coordinates.
if (this.ec.curve.type === 'mont') {
assert$3(key.x, 'Need x coordinate');
} else if (this.ec.curve.type === 'short' ||
this.ec.curve.type === 'edwards') {
assert$3(key.x && key.y, 'Need both x and y coordinate');
}
this.pub = this.ec.curve.point(key.x, key.y);
return;
}
this.pub = this.ec.curve.decodePoint(key, enc);
};
// ECDH
KeyPair.prototype.derive = function derive(pub) {
return pub.mul(this.priv).getX();
};
// ECDSA
KeyPair.prototype.sign = function sign(msg, enc, options) {
return this.ec.sign(msg, this, enc, options);
};
KeyPair.prototype.verify = function verify(msg, signature) {
return this.ec.verify(msg, signature, this);
};
KeyPair.prototype.inspect = function inspect() {
return '<Key priv: ' + (this.priv && this.priv.toString(16, 2)) +
' pub: ' + (this.pub && this.pub.inspect()) + ' >';
};
var assert$4 = utils_1$1.assert;
function Signature(options, enc) {
if (options instanceof Signature)
return options;
if (this._importDER(options, enc))
return;
assert$4(options.r && options.s, 'Signature without r or s');
this.r = new bn(options.r, 16);
this.s = new bn(options.s, 16);
if (options.recoveryParam === undefined)
this.recoveryParam = null;
else
this.recoveryParam = options.recoveryParam;
}
var signature = Signature;
function Position() {
this.place = 0;
}
function getLength(buf, p) {
var initial = buf[p.place++];
if (!(initial & 0x80)) {
return initial;
}
var octetLen = initial & 0xf;
var val = 0;
for (var i = 0, off = p.place; i < octetLen; i++, off++) {
val <<= 8;
val |= buf[off];
}
p.place = off;
return val;
}
function rmPadding(buf) {
var i = 0;
var len = buf.length - 1;
while (!buf[i] && !(buf[i + 1] & 0x80) && i < len) {
i++;
}
if (i === 0) {
return buf;
}
return buf.slice(i);
}
Signature.prototype._importDER = function _importDER(data, enc) {
data = utils_1$1.toArray(data, enc);
var p = new Position();
if (data[p.place++] !== 0x30) {
return false;
}
var len = getLength(data, p);
if ((len + p.place) !== data.length) {
return false;
}
if (data[p.place++] !== 0x02) {
return false;
}
var rlen = getLength(data, p);
var r = data.slice(p.place, rlen + p.place);
p.place += rlen;
if (data[p.place++] !== 0x02) {
return false;
}
var slen = getLength(data, p);
if (data.length !== slen + p.place) {
return false;
}
var s = data.slice(p.place, slen + p.place);
if (r[0] === 0 && (r[1] & 0x80)) {
r = r.slice(1);
}
if (s[0] === 0 && (s[1] & 0x80)) {
s = s.slice(1);
}
this.r = new bn(r);
this.s = new bn(s);
this.recoveryParam = null;
return true;
};
function constructLength(arr, len) {
if (len < 0x80) {
arr.push(len);
return;
}
var octets = 1 + (Math.log(len) / Math.LN2 >>> 3);
arr.push(octets | 0x80);
while (--octets) {
arr.push((len >>> (octets << 3)) & 0xff);
}
arr.push(len);
}
Signature.prototype.toDER = function toDER(enc) {
var r = this.r.toArray();
var s = this.s.toArray();
// Pad values
if (r[0] & 0x80)
r = [ 0 ].concat(r);
// Pad values
if (s[0] & 0x80)
s = [ 0 ].concat(s);
r = rmPadding(r);
s = rmPadding(s);
while (!s[0] && !(s[1] & 0x80)) {
s = s.slice(1);
}
var arr = [ 0x02 ];
constructLength(arr, r.length);
arr = arr.concat(r);
arr.push(0x02);
constructLength(arr, s.length);
var backHalf = arr.concat(s);
var res = [ 0x30 ];
constructLength(res, backHalf.length);
res = res.concat(backHalf);
return utils_1$1.encode(res, enc);
};
var assert$5 = utils_1$1.assert;
function EC(options) {
if (!(this instanceof EC))
return new EC(options);
// Shortcut `elliptic.ec(curve-name)`
if (typeof options === 'string') {
assert$5(curves_1.hasOwnProperty(options), 'Unknown curve ' + options);
options = curves_1[options];
}
// Shortcut for `elliptic.ec(elliptic.curves.curveName)`
if (options instanceof curves_1.PresetCurve)
options = { curve: options };
this.curve = options.curve.curve;
this.n = this.curve.n;
this.nh = this.n.ushrn(1);
this.g = this.curve.g;
// Point on curve
this.g = options.curve.g;
this.g.precompute(options.curve.n.bitLength() + 1);
// Hash function for DRBG
this.hash = options.hash || options.curve.hash;
}
var ec = EC;
EC.prototype.keyPair = function keyPair(options) {
return new key(this, options);
};
EC.prototype.keyFromPrivate = function keyFromPrivate(priv, enc) {
return key.fromPrivate(this, priv, enc);
};
EC.prototype.keyFromPublic = function keyFromPublic(pub, enc) {
return key.fromPublic(this, pub, enc);
};
EC.prototype.genKeyPair = function genKeyPair(options) {
if (!options)
options = {};
// Instantiate Hmac_DRBG
var drbg = new hmacDrbg({
hash: this.hash,
pers: options.pers,
persEnc: options.persEnc || 'utf8',
entropy: options.entropy || brorand(this.hash.hmacStrength),
entropyEnc: options.entropy && options.entropyEnc || 'utf8',
nonce: this.n.toArray()
});
// Key generation for curve25519 is simpler
if (this.curve.type === 'mont') {
var priv = new bn(drbg.generate(32));
return this.keyFromPrivate(priv);
}
var bytes = this.n.byteLength();
var ns2 = this.n.sub(new bn(2));
do {
var priv = new bn(drbg.generate(bytes));
if (priv.cmp(ns2) > 0)
continue;
priv.iaddn(1);
return this.keyFromPrivate(priv);
} while (true);
};
EC.prototype._truncateToN = function truncateToN(msg, truncOnly, bitSize) {
bitSize = bitSize || msg.byteLength() * 8;
var delta = bitSize - this.n.bitLength();
if (delta > 0)
msg = msg.ushrn(delta);
if (!truncOnly && msg.cmp(this.n) >= 0)
return msg.sub(this.n);
else
return msg;
};
EC.prototype.truncateMsg = function truncateMSG(msg) {
// Bit size is only determined correctly for Uint8Arrays and hex strings
var bitSize;
if (msg instanceof Uint8Array) {
bitSize = msg.byteLength * 8;
msg = this._truncateToN(new bn(msg, 16), false, bitSize);
} else if (typeof msg === 'string') {
bitSize = msg.length * 4;
msg = this._truncateToN(new bn(msg, 16), false, bitSize);
} else {
msg = this._truncateToN(new bn(msg, 16));
}
return msg;
};
EC.prototype.sign = function sign(msg, key, enc, options) {
if (typeof enc === 'object') {
options = enc;
enc = null;
}
if (!options)
options = {};
key = this.keyFromPrivate(key, enc);
msg = this.truncateMsg(msg);
// Zero-extend key to provide enough entropy
var bytes = this.n.byteLength();
var bkey = key.getPrivate().toArray('be', bytes);
// Zero-extend nonce to have the same byte size as N
var nonce = msg.toArray('be', bytes);
// Instantiate Hmac_DRBG
var drbg = new hmacDrbg({
hash: this.hash,
entropy: bkey,
nonce: nonce,
pers: options.pers,
persEnc: options.persEnc || 'utf8'
});
// Number of bytes to generate
var ns1 = this.n.sub(new bn(1));
for (var iter = 0; true; iter++) {
var k = options.k ?
options.k(iter) :
new bn(drbg.generate(this.n.byteLength()));
k = this._truncateToN(k, true);
if (k.cmpn(1) <= 0 || k.cmp(ns1) >= 0)
continue;
var kp = this.g.mul(k);
if (kp.isInfinity())
continue;
var kpX = kp.getX();
var r = kpX.umod(this.n);
if (r.cmpn(0) === 0)
continue;
var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg));
s = s.umod(this.n);
if (s.cmpn(0) === 0)
continue;
var recoveryParam = (kp.getY().isOdd() ? 1 : 0) |
(kpX.cmp(r) !== 0 ? 2 : 0);
// Use complement of `s`, if it is > `n / 2`
if (options.canonical && s.cmp(this.nh) > 0) {
s = this.n.sub(s);
recoveryParam ^= 1;
}
return new signature({ r: r, s: s, recoveryParam: recoveryParam });
}
};
EC.prototype.verify = function verify(msg, signature$1, key, enc) {
key = this.keyFromPublic(key, enc);
signature$1 = new signature(signature$1, 'hex');
// Fallback to the old code
var ret = this._verify(this.truncateMsg(msg), signature$1, key) ||
this._verify(this._truncateToN(new bn(msg, 16)), signature$1, key);
return ret;
};
EC.prototype._verify = function _verify(msg, signature, key) {
// Perform primitive values validation
var r = signature.r;
var s = signature.s;
if (r.cmpn(1) < 0 || r.cmp(this.n) >= 0)
return false;
if (s.cmpn(1) < 0 || s.cmp(this.n) >= 0)
return false;
// Validate signature
var sinv = s.invm(this.n);
var u1 = sinv.mul(msg).umod(this.n);
var u2 = sinv.mul(r).umod(this.n);
if (!this.curve._maxwellTrick) {
var p = this.g.mulAdd(u1, key.getPublic(), u2);
if (p.isInfinity())
return false;
return p.getX().umod(this.n).cmp(r) === 0;
}
// NOTE: Greg Maxwell's trick, inspired by:
// https://git.io/vad3K
var p = this.g.jmulAdd(u1, key.getPublic(), u2);
if (p.isInfinity())
return false;
// Compare `p.x` of Jacobian point with `r`,
// this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the
// inverse of `p.z^2`
return p.eqXToP(r);
};
EC.prototype.recoverPubKey = function(msg, signature$1, j, enc) {
assert$5((3 & j) === j, 'The recovery param is more than two bits');
signature$1 = new signature(signature$1, enc);
var n = this.n;
var e = new bn(msg);
var r = signature$1.r;
var s = signature$1.s;
// A set LSB signifies that the y-coordinate is odd
var isYOdd = j & 1;
var isSecondKey = j >> 1;
if (r.cmp(this.curve.p.umod(this.curve.n)) >= 0 && isSecondKey)
throw new Error('Unable to find sencond key candinate');
// 1.1. Let x = r + jn.
if (isSecondKey)
r = this.curve.pointFromX(r.add(this.curve.n), isYOdd);
else
r = this.curve.pointFromX(r, isYOdd);
var rInv = signature$1.r.invm(n);
var s1 = n.sub(e).mul(rInv).umod(n);
var s2 = s.mul(rInv).umod(n);
// 1.6.1 Compute Q = r^-1 (sR - eG)
// Q = r^-1 (sR + -eG)
return this.g.mulAdd(s1, r, s2);
};
EC.prototype.getKeyRecoveryParam = function(e, signature$1, Q, enc) {
signature$1 = new signature(signature$1, enc);
if (signature$1.recoveryParam !== null)
return signature$1.recoveryParam;
for (var i = 0; i < 4; i++) {
var Qprime;
try {
Qprime = this.recoverPubKey(e, signature$1, i);
} catch (e) {
continue;
}
if (Qprime.eq(Q))
return i;
}
throw new Error('Unable to find valid recovery factor');
};
var assert$6 = utils_1$1.assert;
var parseBytes = utils_1$1.parseBytes;
var cachedProperty = utils_1$1.cachedProperty;
/**
* @param {EDDSA} eddsa - instance
* @param {Object} params - public/private key parameters
*
* @param {Array<Byte>} [params.secret] - secret seed bytes
* @param {Point} [params.pub] - public key point (aka `A` in eddsa terms)
* @param {Array<Byte>} [params.pub] - public key point encoded as bytes
*
*/
function KeyPair$1(eddsa, params) {
this.eddsa = eddsa;
if (params.hasOwnProperty('secret'))
this._secret = parseBytes(params.secret);
if (eddsa.isPoint(params.pub))
this._pub = params.pub;
else {
this._pubBytes = parseBytes(params.pub);
if (this._pubBytes && this._pubBytes.length === 33 &&
this._pubBytes[0] === 0x40)
this._pubBytes = this._pubBytes.slice(1, 33);
if (this._pubBytes && this._pubBytes.length !== 32)
throw new Error('Unknown point compression format');
}
}
KeyPair$1.fromPublic = function fromPublic(eddsa, pub) {
if (pub instanceof KeyPair$1)
return pub;
return new KeyPair$1(eddsa, { pub: pub });
};
KeyPair$1.fromSecret = function fromSecret(eddsa, secret) {
if (secret instanceof KeyPair$1)
return secret;
return new KeyPair$1(eddsa, { secret: secret });
};
KeyPair$1.prototype.secret = function secret() {
return this._secret;
};
cachedProperty(KeyPair$1, 'pubBytes', function pubBytes() {
return this.eddsa.encodePoint(this.pub());
});
cachedProperty(KeyPair$1, 'pub', function pub() {
if (this._pubBytes)
return this.eddsa.decodePoint(this._pubBytes);
return this.eddsa.g.mul(this.priv());
});
cachedProperty(KeyPair$1, 'privBytes', function privBytes() {
var eddsa = this.eddsa;
var hash = this.hash();
var lastIx = eddsa.encodingLength - 1;
// https://tools.ietf.org/html/rfc8032#section-5.1.5
var a = hash.slice(0, eddsa.encodingLength);
a[0] &= 248;
a[lastIx] &= 127;
a[lastIx] |= 64;
return a;
});
cachedProperty(KeyPair$1, 'priv', function priv() {
return this.eddsa.decodeInt(this.privBytes());
});
cachedProperty(KeyPair$1, 'hash', function hash() {
return this.eddsa.hash().update(this.secret()).digest();
});
cachedProperty(KeyPair$1, 'messagePrefix', function messagePrefix() {
return this.hash().slice(this.eddsa.encodingLength);
});
KeyPair$1.prototype.sign = function sign(message) {
assert$6(this._secret, 'KeyPair can only verify');
return this.eddsa.sign(message, this);
};
KeyPair$1.prototype.verify = function verify(message, sig) {
return this.eddsa.verify(message, sig, this);
};
KeyPair$1.prototype.getSecret = function getSecret(enc) {
assert$6(this._secret, 'KeyPair is public only');
return utils_1$1.encode(this.secret(), enc);
};
KeyPair$1.prototype.getPublic = function getPublic(enc, compact) {
return utils_1$1.encode((compact ? [ 0x40 ] : []).concat(this.pubBytes()), enc);
};
var key$1 = KeyPair$1;
var assert$7 = utils_1$1.assert;
var cachedProperty$1 = utils_1$1.cachedProperty;
var parseBytes$1 = utils_1$1.parseBytes;
/**
* @param {EDDSA} eddsa - eddsa instance
* @param {Array<Bytes>|Object} sig -
* @param {Array<Bytes>|Point} [sig.R] - R point as Point or bytes
* @param {Array<Bytes>|bn} [sig.S] - S scalar as bn or bytes
* @param {Array<Bytes>} [sig.Rencoded] - R point encoded
* @param {Array<Bytes>} [sig.Sencoded] - S scalar encoded
*/
function Signature$1(eddsa, sig) {
this.eddsa = eddsa;
if (typeof sig !== 'object')
sig = parseBytes$1(sig);
if (Array.isArray(sig)) {
sig = {
R: sig.slice(0, eddsa.encodingLength),
S: sig.slice(eddsa.encodingLength)
};
}
assert$7(sig.R && sig.S, 'Signature without R or S');
if (eddsa.isPoint(sig.R))
this._R = sig.R;
if (sig.S instanceof bn)
this._S = sig.S;
this._Rencoded = Array.isArray(sig.R) ? sig.R : sig.Rencoded;
this._Sencoded = Array.isArray(sig.S) ? sig.S : sig.Sencoded;
}
cachedProperty$1(Signature$1, 'S', function S() {
return this.eddsa.decodeInt(this.Sencoded());
});
cachedProperty$1(Signature$1, 'R', function R() {
return this.eddsa.decodePoint(this.Rencoded());
});
cachedProperty$1(Signature$1, 'Rencoded', function Rencoded() {
return this.eddsa.encodePoint(this.R());
});
cachedProperty$1(Signature$1, 'Sencoded', function Sencoded() {
return this.eddsa.encodeInt(this.S());
});
Signature$1.prototype.toBytes = function toBytes() {
return this.Rencoded().concat(this.Sencoded());
};
Signature$1.prototype.toHex = function toHex() {
return utils_1$1.encode(this.toBytes(), 'hex').toUpperCase();
};
var signature$1 = Signature$1;
var assert$8 = utils_1$1.assert;
var parseBytes$2 = utils_1$1.parseBytes;
function EDDSA(curve) {
assert$8(curve === 'ed25519', 'only tested with ed25519 so far');
if (!(this instanceof EDDSA))
return new EDDSA(curve);
var curve = curves_1[curve].curve;
this.curve = curve;
this.g = curve.g;
this.g.precompute(curve.n.bitLength() + 1);
this.pointClass = curve.point().constructor;
this.encodingLength = Math.ceil(curve.n.bitLength() / 8);
this.hash = hash_1.sha512;
}
var eddsa = EDDSA;
/**
* @param {Array|String} message - message bytes
* @param {Array|String|KeyPair} secret - secret bytes or a keypair
* @returns {Signature} - signature
*/
EDDSA.prototype.sign = function sign(message, secret) {
message = parseBytes$2(message);
var key = this.keyFromSecret(secret);
var r = this.hashInt(key.messagePrefix(), message);
var R = this.g.mul(r);
var Rencoded = this.encodePoint(R);
var s_ = this.hashInt(Rencoded, key.pubBytes(), message)
.mul(key.priv());
var S = r.add(s_).umod(this.curve.n);
return this.makeSignature({ R: R, S: S, Rencoded: Rencoded });
};
/**
* @param {Array} message - message bytes
* @param {Array|String|Signature} sig - sig bytes
* @param {Array|String|Point|KeyPair} pub - public key
* @returns {Boolean} - true if public key matches sig of message
*/
EDDSA.prototype.verify = function verify(message, sig, pub) {
message = parseBytes$2(message);
sig = this.makeSignature(sig);
var key = this.keyFromPublic(pub);
var h = this.hashInt(sig.Rencoded(), key.pubBytes(), message);
var SG = this.g.mul(sig.S());
var RplusAh = sig.R().add(key.pub().mul(h));
return RplusAh.eq(SG);
};
EDDSA.prototype.hashInt = function hashInt() {
var hash = this.hash();
for (var i = 0; i < arguments.length; i++)
hash.update(arguments[i]);
return utils_1$1.intFromLE(hash.digest()).umod(this.curve.n);
};
EDDSA.prototype.keyPair = function keyPair(options) {
return new key$1(this, options);
};
EDDSA.prototype.keyFromPublic = function keyFromPublic(pub) {
return key$1.fromPublic(this, pub);
};
EDDSA.prototype.keyFromSecret = function keyFromSecret(secret) {
return key$1.fromSecret(this, secret);
};
EDDSA.prototype.genKeyPair = function genKeyPair(options) {
if (!options)
options = {};
// Instantiate Hmac_DRBG
var drbg = new hmacDrbg({
hash: this.hash,
pers: options.pers,
persEnc: options.persEnc || 'utf8',
entropy: options.entropy || brorand(this.hash.hmacStrength),
entropyEnc: options.entropy && options.entropyEnc || 'utf8',
nonce: this.curve.n.toArray()
});
return this.keyFromSecret(drbg.generate(32));
};
EDDSA.prototype.makeSignature = function makeSignature(sig) {
if (sig instanceof signature$1)
return sig;
return new signature$1(this, sig);
};
/**
* * https://tools.ietf.org/html/draft-josefsson-eddsa-ed25519-03#section-5.2
*
* EDDSA defines methods for encoding and decoding points and integers. These are
* helper convenience methods, that pass along to utility functions implied
* parameters.
*
*/
EDDSA.prototype.encodePoint = function encodePoint(point) {
var enc = point.getY().toArray('le', this.encodingLength);
enc[this.encodingLength - 1] |= point.getX().isOdd() ? 0x80 : 0;
return enc;
};
EDDSA.prototype.decodePoint = function decodePoint(bytes) {
bytes = utils_1$1.parseBytes(bytes);
var lastIx = bytes.length - 1;
var normed = bytes.slice(0, lastIx).concat(bytes[lastIx] & ~0x80);
var xIsOdd = (bytes[lastIx] & 0x80) !== 0;
var y = utils_1$1.intFromLE(normed);
return this.curve.pointFromY(y, xIsOdd);
};
EDDSA.prototype.encodeInt = function encodeInt(num) {
return num.toArray('le', this.encodingLength);
};
EDDSA.prototype.decodeInt = function decodeInt(bytes) {
return utils_1$1.intFromLE(bytes);
};
EDDSA.prototype.isPoint = function isPoint(val) {
return val instanceof this.pointClass;
};
var elliptic_1 = createCommonjsModule(function (module, exports) {
var elliptic = exports;
elliptic.utils = utils_1$1;
elliptic.rand = brorand;
elliptic.curve = curve_1;
elliptic.curves = curves_1;
// Protocols
elliptic.ec = ec;
elliptic.eddsa = eddsa;
});
export default elliptic_1;
export { elliptic_1 as __moduleExports };
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