/*! OpenPGP.js v5.8.0 - 2023-08-14 - 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'
      ],
      [
        'e5037de0afc1d8d43d8348414bbf4103043ec8f575bfdc432953cc8d2037fa2d',
        '4571534baa94d3b5f9f98d09fb990bddbd5f5b03ec481f10e0e5dc841d755bda'
      ],
      [
        'e06372b0f4a207adf5ea905e8f1771b4e7e8dbd1c6a6c5b725866a0ae4fce725',
        '7a908974bce18cfe12a27bb2ad5a488cd7484a7787104870b27034f94eee31dd'
      ],
      [
        '213c7a715cd5d45358d0bbf9dc0ce02204b10bdde2a3f58540ad6908d0559754',
        '4b6dad0b5ae462507013ad06245ba190bb4850f5f36a7eeddff2c27534b458f2'
      ],
      [
        '4e7c272a7af4b34e8dbb9352a5419a87e2838c70adc62cddf0cc3a3b08fbd53c',
        '17749c766c9d0b18e16fd09f6def681b530b9614bff7dd33e0b3941817dcaae6'
      ],
      [
        'fea74e3dbe778b1b10f238ad61686aa5c76e3db2be43057632427e2840fb27b6',
        '6e0568db9b0b13297cf674deccb6af93126b596b973f7b77701d3db7f23cb96f'
      ],
      [
        '76e64113f677cf0e10a2570d599968d31544e179b760432952c02a4417bdde39',
        'c90ddf8dee4e95cf577066d70681f0d35e2a33d2b56d2032b4b1752d1901ac01'
      ],
      [
        'c738c56b03b2abe1e8281baa743f8f9a8f7cc643df26cbee3ab150242bcbb891',
        '893fb578951ad2537f718f2eacbfbbbb82314eef7880cfe917e735d9699a84c3'
      ],
      [
        'd895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b',
        'febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f'
      ],
      [
        'b8da94032a957518eb0f6433571e8761ceffc73693e84edd49150a564f676e03',
        '2804dfa44805a1e4d7c99cc9762808b092cc584d95ff3b511488e4e74efdf6e7'
      ],
      [
        'e80fea14441fb33a7d8adab9475d7fab2019effb5156a792f1a11778e3c0df5d',
        'eed1de7f638e00771e89768ca3ca94472d155e80af322ea9fcb4291b6ac9ec78'
      ],
      [
        'a301697bdfcd704313ba48e51d567543f2a182031efd6915ddc07bbcc4e16070',
        '7370f91cfb67e4f5081809fa25d40f9b1735dbf7c0a11a130c0d1a041e177ea1'
      ],
      [
        '90ad85b389d6b936463f9d0512678de208cc330b11307fffab7ac63e3fb04ed4',
        'e507a3620a38261affdcbd9427222b839aefabe1582894d991d4d48cb6ef150'
      ],
      [
        '8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da',
        '662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82'
      ],
      [
        'e4f3fb0176af85d65ff99ff9198c36091f48e86503681e3e6686fd5053231e11',
        '1e63633ad0ef4f1c1661a6d0ea02b7286cc7e74ec951d1c9822c38576feb73bc'
      ],
      [
        '8c00fa9b18ebf331eb961537a45a4266c7034f2f0d4e1d0716fb6eae20eae29e',
        'efa47267fea521a1a9dc343a3736c974c2fadafa81e36c54e7d2a4c66702414b'
      ],
      [
        'e7a26ce69dd4829f3e10cec0a9e98ed3143d084f308b92c0997fddfc60cb3e41',
        '2a758e300fa7984b471b006a1aafbb18d0a6b2c0420e83e20e8a9421cf2cfd51'
      ],
      [
        'b6459e0ee3662ec8d23540c223bcbdc571cbcb967d79424f3cf29eb3de6b80ef',
        '67c876d06f3e06de1dadf16e5661db3c4b3ae6d48e35b2ff30bf0b61a71ba45'
      ],
      [
        'd68a80c8280bb840793234aa118f06231d6f1fc67e73c5a5deda0f5b496943e8',
        'db8ba9fff4b586d00c4b1f9177b0e28b5b0e7b8f7845295a294c84266b133120'
      ],
      [
        '324aed7df65c804252dc0270907a30b09612aeb973449cea4095980fc28d3d5d',
        '648a365774b61f2ff130c0c35aec1f4f19213b0c7e332843967224af96ab7c84'
      ],
      [
        '4df9c14919cde61f6d51dfdbe5fee5dceec4143ba8d1ca888e8bd373fd054c96',
        '35ec51092d8728050974c23a1d85d4b5d506cdc288490192ebac06cad10d5d'
      ],
      [
        '9c3919a84a474870faed8a9c1cc66021523489054d7f0308cbfc99c8ac1f98cd',
        'ddb84f0f4a4ddd57584f044bf260e641905326f76c64c8e6be7e5e03d4fc599d'
      ],
      [
        '6057170b1dd12fdf8de05f281d8e06bb91e1493a8b91d4cc5a21382120a959e5',
        '9a1af0b26a6a4807add9a2daf71df262465152bc3ee24c65e899be932385a2a8'
      ],
      [
        'a576df8e23a08411421439a4518da31880cef0fba7d4df12b1a6973eecb94266',
        '40a6bf20e76640b2c92b97afe58cd82c432e10a7f514d9f3ee8be11ae1b28ec8'
      ],
      [
        '7778a78c28dec3e30a05fe9629de8c38bb30d1f5cf9a3a208f763889be58ad71',
        '34626d9ab5a5b22ff7098e12f2ff580087b38411ff24ac563b513fc1fd9f43ac'
      ],
      [
        '928955ee637a84463729fd30e7afd2ed5f96274e5ad7e5cb09eda9c06d903ac',
        'c25621003d3f42a827b78a13093a95eeac3d26efa8a8d83fc5180e935bcd091f'
      ],
      [
        '85d0fef3ec6db109399064f3a0e3b2855645b4a907ad354527aae75163d82751',
        '1f03648413a38c0be29d496e582cf5663e8751e96877331582c237a24eb1f962'
      ],
      [
        'ff2b0dce97eece97c1c9b6041798b85dfdfb6d8882da20308f5404824526087e',
        '493d13fef524ba188af4c4dc54d07936c7b7ed6fb90e2ceb2c951e01f0c29907'
      ],
      [
        '827fbbe4b1e880ea9ed2b2e6301b212b57f1ee148cd6dd28780e5e2cf856e241',
        'c60f9c923c727b0b71bef2c67d1d12687ff7a63186903166d605b68baec293ec'
      ],
      [
        'eaa649f21f51bdbae7be4ae34ce6e5217a58fdce7f47f9aa7f3b58fa2120e2b3',
        'be3279ed5bbbb03ac69a80f89879aa5a01a6b965f13f7e59d47a5305ba5ad93d'
      ],
      [
        'e4a42d43c5cf169d9391df6decf42ee541b6d8f0c9a137401e23632dda34d24f',
        '4d9f92e716d1c73526fc99ccfb8ad34ce886eedfa8d8e4f13a7f7131deba9414'
      ],
      [
        '1ec80fef360cbdd954160fadab352b6b92b53576a88fea4947173b9d4300bf19',
        'aeefe93756b5340d2f3a4958a7abbf5e0146e77f6295a07b671cdc1cc107cefd'
      ],
      [
        '146a778c04670c2f91b00af4680dfa8bce3490717d58ba889ddb5928366642be',
        'b318e0ec3354028add669827f9d4b2870aaa971d2f7e5ed1d0b297483d83efd0'
      ],
      [
        'fa50c0f61d22e5f07e3acebb1aa07b128d0012209a28b9776d76a8793180eef9',
        '6b84c6922397eba9b72cd2872281a68a5e683293a57a213b38cd8d7d3f4f2811'
      ],
      [
        'da1d61d0ca721a11b1a5bf6b7d88e8421a288ab5d5bba5220e53d32b5f067ec2',
        '8157f55a7c99306c79c0766161c91e2966a73899d279b48a655fba0f1ad836f1'
      ],
      [
        'a8e282ff0c9706907215ff98e8fd416615311de0446f1e062a73b0610d064e13',
        '7f97355b8db81c09abfb7f3c5b2515888b679a3e50dd6bd6cef7c73111f4cc0c'
      ],
      [
        '174a53b9c9a285872d39e56e6913cab15d59b1fa512508c022f382de8319497c',
        'ccc9dc37abfc9c1657b4155f2c47f9e6646b3a1d8cb9854383da13ac079afa73'
      ],
      [
        '959396981943785c3d3e57edf5018cdbe039e730e4918b3d884fdff09475b7ba',
        '2e7e552888c331dd8ba0386a4b9cd6849c653f64c8709385e9b8abf87524f2fd'
      ],
      [
        'd2a63a50ae401e56d645a1153b109a8fcca0a43d561fba2dbb51340c9d82b151',
        'e82d86fb6443fcb7565aee58b2948220a70f750af484ca52d4142174dcf89405'
      ],
      [
        '64587e2335471eb890ee7896d7cfdc866bacbdbd3839317b3436f9b45617e073',
        'd99fcdd5bf6902e2ae96dd6447c299a185b90a39133aeab358299e5e9faf6589'
      ],
      [
        '8481bde0e4e4d885b3a546d3e549de042f0aa6cea250e7fd358d6c86dd45e458',
        '38ee7b8cba5404dd84a25bf39cecb2ca900a79c42b262e556d64b1b59779057e'
      ],
      [
        '13464a57a78102aa62b6979ae817f4637ffcfed3c4b1ce30bcd6303f6caf666b',
        '69be159004614580ef7e433453ccb0ca48f300a81d0942e13f495a907f6ecc27'
      ],
      [
        'bc4a9df5b713fe2e9aef430bcc1dc97a0cd9ccede2f28588cada3a0d2d83f366',
        'd3a81ca6e785c06383937adf4b798caa6e8a9fbfa547b16d758d666581f33c1'
      ],
      [
        '8c28a97bf8298bc0d23d8c749452a32e694b65e30a9472a3954ab30fe5324caa',
        '40a30463a3305193378fedf31f7cc0eb7ae784f0451cb9459e71dc73cbef9482'
      ],
      [
        '8ea9666139527a8c1dd94ce4f071fd23c8b350c5a4bb33748c4ba111faccae0',
        '620efabbc8ee2782e24e7c0cfb95c5d735b783be9cf0f8e955af34a30e62b945'
      ],
      [
        'dd3625faef5ba06074669716bbd3788d89bdde815959968092f76cc4eb9a9787',
        '7a188fa3520e30d461da2501045731ca941461982883395937f68d00c644a573'
      ],
      [
        'f710d79d9eb962297e4f6232b40e8f7feb2bc63814614d692c12de752408221e',
        'ea98e67232d3b3295d3b535532115ccac8612c721851617526ae47a9c77bfc82'
      ]
    ]
  },
  naf: {
    wnd: 7,
    points: [
      [
        'f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9',
        '388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672'
      ],
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        '8fd64a14c06b589c26b947ae2bcf6bfa0149ef0be14ed4d80f448a01c43b1c6d'
      ],
      [
        'b4f9eaea09b6917619f6ea6a4eb5464efddb58fd45b1ebefcdc1a01d08b47986',
        '39e5c9925b5a54b07433a4f18c61726f8bb131c012ca542eb24a8ac07200682a'
      ],
      [
        'd4263dfc3d2df923a0179a48966d30ce84e2515afc3dccc1b77907792ebcc60e',
        '62dfaf07a0f78feb30e30d6295853ce189e127760ad6cf7fae164e122a208d54'
      ],
      [
        '48457524820fa65a4f8d35eb6930857c0032acc0a4a2de422233eeda897612c4',
        '25a748ab367979d98733c38a1fa1c2e7dc6cc07db2d60a9ae7a76aaa49bd0f77'
      ],
      [
        'dfeeef1881101f2cb11644f3a2afdfc2045e19919152923f367a1767c11cceda',
        'ecfb7056cf1de042f9420bab396793c0c390bde74b4bbdff16a83ae09a9a7517'
      ],
      [
        '6d7ef6b17543f8373c573f44e1f389835d89bcbc6062ced36c82df83b8fae859',
        'cd450ec335438986dfefa10c57fea9bcc521a0959b2d80bbf74b190dca712d10'
      ],
      [
        'e75605d59102a5a2684500d3b991f2e3f3c88b93225547035af25af66e04541f',
        'f5c54754a8f71ee540b9b48728473e314f729ac5308b06938360990e2bfad125'
      ],
      [
        'eb98660f4c4dfaa06a2be453d5020bc99a0c2e60abe388457dd43fefb1ed620c',
        '6cb9a8876d9cb8520609af3add26cd20a0a7cd8a9411131ce85f44100099223e'
      ],
      [
        '13e87b027d8514d35939f2e6892b19922154596941888336dc3563e3b8dba942',
        'fef5a3c68059a6dec5d624114bf1e91aac2b9da568d6abeb2570d55646b8adf1'
      ],
      [
        'ee163026e9fd6fe017c38f06a5be6fc125424b371ce2708e7bf4491691e5764a',
        '1acb250f255dd61c43d94ccc670d0f58f49ae3fa15b96623e5430da0ad6c62b2'
      ],
      [
        'b268f5ef9ad51e4d78de3a750c2dc89b1e626d43505867999932e5db33af3d80',
        '5f310d4b3c99b9ebb19f77d41c1dee018cf0d34fd4191614003e945a1216e423'
      ],
      [
        'ff07f3118a9df035e9fad85eb6c7bfe42b02f01ca99ceea3bf7ffdba93c4750d',
        '438136d603e858a3a5c440c38eccbaddc1d2942114e2eddd4740d098ced1f0d8'
      ],
      [
        '8d8b9855c7c052a34146fd20ffb658bea4b9f69e0d825ebec16e8c3ce2b526a1',
        'cdb559eedc2d79f926baf44fb84ea4d44bcf50fee51d7ceb30e2e7f463036758'
      ],
      [
        '52db0b5384dfbf05bfa9d472d7ae26dfe4b851ceca91b1eba54263180da32b63',
        'c3b997d050ee5d423ebaf66a6db9f57b3180c902875679de924b69d84a7b375'
      ],
      [
        'e62f9490d3d51da6395efd24e80919cc7d0f29c3f3fa48c6fff543becbd43352',
        '6d89ad7ba4876b0b22c2ca280c682862f342c8591f1daf5170e07bfd9ccafa7d'
      ],
      [
        '7f30ea2476b399b4957509c88f77d0191afa2ff5cb7b14fd6d8e7d65aaab1193',
        'ca5ef7d4b231c94c3b15389a5f6311e9daff7bb67b103e9880ef4bff637acaec'
      ],
      [
        '5098ff1e1d9f14fb46a210fada6c903fef0fb7b4a1dd1d9ac60a0361800b7a00',
        '9731141d81fc8f8084d37c6e7542006b3ee1b40d60dfe5362a5b132fd17ddc0'
      ],
      [
        '32b78c7de9ee512a72895be6b9cbefa6e2f3c4ccce445c96b9f2c81e2778ad58',
        'ee1849f513df71e32efc3896ee28260c73bb80547ae2275ba497237794c8753c'
      ],
      [
        'e2cb74fddc8e9fbcd076eef2a7c72b0ce37d50f08269dfc074b581550547a4f7',
        'd3aa2ed71c9dd2247a62df062736eb0baddea9e36122d2be8641abcb005cc4a4'
      ],
      [
        '8438447566d4d7bedadc299496ab357426009a35f235cb141be0d99cd10ae3a8',
        'c4e1020916980a4da5d01ac5e6ad330734ef0d7906631c4f2390426b2edd791f'
      ],
      [
        '4162d488b89402039b584c6fc6c308870587d9c46f660b878ab65c82c711d67e',
        '67163e903236289f776f22c25fb8a3afc1732f2b84b4e95dbda47ae5a0852649'
      ],
      [
        '3fad3fa84caf0f34f0f89bfd2dcf54fc175d767aec3e50684f3ba4a4bf5f683d',
        'cd1bc7cb6cc407bb2f0ca647c718a730cf71872e7d0d2a53fa20efcdfe61826'
      ],
      [
        '674f2600a3007a00568c1a7ce05d0816c1fb84bf1370798f1c69532faeb1a86b',
        '299d21f9413f33b3edf43b257004580b70db57da0b182259e09eecc69e0d38a5'
      ],
      [
        'd32f4da54ade74abb81b815ad1fb3b263d82d6c692714bcff87d29bd5ee9f08f',
        'f9429e738b8e53b968e99016c059707782e14f4535359d582fc416910b3eea87'
      ],
      [
        '30e4e670435385556e593657135845d36fbb6931f72b08cb1ed954f1e3ce3ff6',
        '462f9bce619898638499350113bbc9b10a878d35da70740dc695a559eb88db7b'
      ],
      [
        'be2062003c51cc3004682904330e4dee7f3dcd10b01e580bf1971b04d4cad297',
        '62188bc49d61e5428573d48a74e1c655b1c61090905682a0d5558ed72dccb9bc'
      ],
      [
        '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 };