openpgp/dist/lightweight/elliptic.mjs

OpenPGP.js is a Javascript implementation of the OpenPGP protocol. This is defined in RFC 4880.

/*! OpenPGP.js v5.11.2 - 2024-06-19 - 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/aut