mapToPoint static method

Implementation

static EDPoint mapToPoint(BigInt r0) {
  final sqrtM1 = BigInt.parse(
    '19681161376707505956807079304988542015446066515923890162744021073123829784752',
  );

  /// The square of -1 in the Ristretto255 curve field.
  final minusOneSq = BigInt.parse(
    '40440834346308536858101042469323190826248399146238708352240133220865137265952',
  );

  /// The value 1 - d^2 in the Ristretto255 curve field.
  final oneMinusDSq = BigInt.parse(
    '1159843021668779879193775521855586647937357759715417654439879720876111806838',
  );

  /// The value (a*d) - 1 in the Ristretto255 curve field.
  final sqrtAdMinusOne = BigInt.parse(
    '25063068953384623474111414158702152701244531502492656460079210482610430750235',
  );
  final curveD = Curves.generatorED25519.curve.d;
  final primeP = Curves.curveEd25519.p;

  final rSquared = positiveMod(sqrtM1 * r0 * r0, primeP);
  final numeratorS = positiveMod(
    (rSquared + BigInt.one) * oneMinusDSq,
    primeP,
  );

  var c = BigInt.from(-1);

  final D = positiveMod(
    (c - curveD * rSquared) * positiveMod(rSquared + curveD, primeP),
    primeP,
  );

  final uvRatio = sqrtUV(numeratorS, D);

  final useSecondRoot = uvRatio.$1;
  BigInt sValue = uvRatio.$2;

  BigInt sComputed = positiveMod(sValue * r0, primeP);

  if (!isOdd(sComputed, primeP)) {
    sComputed = positiveMod(-sComputed, primeP);
  }

  if (!useSecondRoot) {
    sValue = sComputed;
  }

  if (!useSecondRoot) {
    c = rSquared;
  }

  final ntValue = positiveMod(
    c * (rSquared - BigInt.one) * minusOneSq - D,
    primeP,
  );

  final sSquared = sValue * sValue;
  final w0 = positiveMod((sValue + sValue) * D, primeP);
  final w1 = positiveMod(ntValue * sqrtAdMinusOne, primeP);
  final w2 = positiveMod(BigInt.one - sSquared, primeP);
  final w3 = positiveMod(BigInt.one + sSquared, primeP);

  return EDPoint(
    curve: Curves.curveEd25519,
    x: positiveMod(w0 * w3, primeP),
    y: positiveMod(w2 * w1, primeP),
    z: positiveMod(w1 * w3, primeP),
    t: positiveMod(w0 * w2, primeP),
  );
}