wNAF static method

WNAF wNAF(BigInt n)

Implementation

static WNAF wNAF(BigInt n) {
  // w-ary non-adjacent form (wNAF) method.
  // Compared to other point mult methods,
  if (Gpows.isEmpty) {
    Gpows.addAll(Utilities.precompute());
  }
  final comp = Gpows.map((e) => e.copy()).toList();
  // negate
  Point neg(bool cnd, Point p) {
    final n = p.negate();
    return cnd ? n : p;
  }

  // f must be G, or could become I in the end
  Point p = Point.I.copy();
  Point f = Point.G.copy();

  // W=8 17 windows
  final int windows = 1 + 256 ~/ W;
  // W=8 128 window size
  final wsize = 1 << (W - 1);
  // W=8 will create mask 0b11111111
  final mask = BigInt.from(1 << W) - BigInt.one;
  // W=8 256
  final int maxNum = 1 << W;
  // W=8 8
  final shiftBy = BigInt.from(W);
  for (var w = 0; w < windows; w++) {
    final int off = w * wsize;
    // extract W bits.
    int wbits = (n & mask).toInt();
    // shift number by W bits.
    n >>= shiftBy.toInt();
    // split if bits > max: +224 => 256-32
    if (wbits > wsize) {
      wbits -= maxNum;
      n += BigInt.one;
    }
    // offsets, evaluate both
    final int off1 = off;
    final int off2 = off + (wbits.abs()) - 1;
    final bool cnd1 = w % 2 != 0;
    final bool cnd2 = wbits < 0;
    // conditions, evaluate both
    if (wbits == 0) {
      // bits are 0: add garbage to fake point
      f = f.add(neg(cnd1, comp[off1]));
    } else {
      // ^ can't add off2, off2 = I
      // bits are 1: add to result point
      p = p.add(neg(cnd2, comp[off2]));
    }
  } // return both real and fake points for JIT
  return WNAF._(p, f);
}