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'use strict';
var BN = require('bn.js');
var elliptic = require('../../elliptic');
var utils = elliptic.utils;
var getNAF = utils.getNAF;
var getJSF = utils.getJSF;
var assert = utils.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);
}
}
module.exports = 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.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.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;
};