@okxweb3/crypto-lib/dist/elliptic/curve/short.js

A base package for @okxweb3/coin-*

'use strict';
var utils = require('../utils');
var BN = require('bn.js/lib/bn');
var inherits = require('inherits');
var Base = require('./base');
var assert = utils.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;
    this.endo = this._getEndomorphism(conf);
    this._endoWnafT1 = new Array(4);
    this._endoWnafT2 = new Array(4);
}
inherits(ShortCurve, Base);
module.exports = ShortCurve;
ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {
    if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)
        return;
    var beta;
    var lambda;
    if (conf.beta) {
        beta = new BN(conf.beta, 16).toRed(this.red);
    }
    else {
        var betas = this._getEndoRoots(this.p);
        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 {
        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(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);
        }
    }
    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) {
    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) {
    var aprxSqrt = this.n.ushrn(Math.floor(this.n.bitLength() / 2));
    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);
    var a0;
    var b0;
    var a1;
    var b1;
    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;
    }
    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);
    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');
    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);
        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);
        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(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) {
    if (this.inf)
        return p;
    if (p.inf)
        return this;
    if (this.eq(p))
        return this.dbl();
    if (this.neg().eq(p))
        return this.curve.point(null, null);
    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;
    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(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) {
    if (this.isInfinity())
        return p;
    if (p.isInfinity())
        return this;
    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) {
    if (this.isInfinity())
        return p.toJ();
    if (p.isInfinity())
        return this;
    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();
    var i;
    if (this.curve.zeroA || this.curve.threeA) {
        var r = this;
        for (i = 0; i < pow; i++)
            r = r.dbl();
        return r;
    }
    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();
    var jyd = jy.redAdd(jy);
    for (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;
    if (this.zOne) {
        var xx = this.x.redSqr();
        var yy = this.y.redSqr();
        var yyyy = yy.redSqr();
        var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
        s = s.redIAdd(s);
        var m = xx.redAdd(xx).redIAdd(xx);
        var t = m.redSqr().redISub(s).redISub(s);
        var yyyy8 = yyyy.redIAdd(yyyy);
        yyyy8 = yyyy8.redIAdd(yyyy8);
        yyyy8 = yyyy8.redIAdd(yyyy8);
        nx = t;
        ny = m.redMul(s.redISub(t)).redISub(yyyy8);
        nz = this.y.redAdd(this.y);
    }
    else {
        var a = this.x.redSqr();
        var b = this.y.redSqr();
        var c = b.redSqr();
        var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);
        d = d.redIAdd(d);
        var e = a.redAdd(a).redIAdd(a);
        var f = e.redSqr();
        var c8 = c.redIAdd(c);
        c8 = c8.redIAdd(c8);
        c8 = c8.redIAdd(c8);
        nx = f.redISub(d).redISub(d);
        ny = e.redMul(d.redISub(nx)).redISub(c8);
        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;
    if (this.zOne) {
        var xx = this.x.redSqr();
        var yy = this.y.redSqr();
        var yyyy = yy.redSqr();
        var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
        s = s.redIAdd(s);
        var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);
        var t = m.redSqr().redISub(s).redISub(s);
        nx = t;
        var yyyy8 = yyyy.redIAdd(yyyy);
        yyyy8 = yyyy8.redIAdd(yyyy8);
        yyyy8 = yyyy8.redIAdd(yyyy8);
        ny = m.redMul(s.redISub(t)).redISub(yyyy8);
        nz = this.y.redAdd(this.y);
    }
    else {
        var delta = this.z.redSqr();
        var gamma = this.y.redSqr();
        var beta = this.x.redMul(gamma);
        var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));
        alpha = alpha.redAdd(alpha).redIAdd(alpha);
        var beta4 = beta.redIAdd(beta);
        beta4 = beta4.redIAdd(beta4);
        var beta8 = beta4.redAdd(beta4);
        nx = alpha.redSqr().redISub(beta8);
        nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);
        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;
    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);
    var xx = this.x.redSqr();
    var yy = this.y.redSqr();
    var zz = this.z.redSqr();
    var yyyy = yy.redSqr();
    var m = xx.redAdd(xx).redIAdd(xx);
    var mm = m.redSqr();
    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);
    var ee = e.redSqr();
    var t = yyyy.redIAdd(yyyy);
    t = t.redIAdd(t);
    t = t.redIAdd(t);
    t = t.redIAdd(t);
    var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);
    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);
    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);
    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;
    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;
    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() {
    return this.z.cmpn(0) === 0;
};
//# sourceMappingURL=short.js.map