setWideBytes method
This file contains additional functionality that is not included in the upstream crypto/ed25519/edwards25519/field package.
SetWideBytes sets v to x, where x is a 64-byte little-endian encoding, which is reduced modulo the field order. If x is not of the right length, SetWideBytes returns nil and an error, and the receiver is unchanged.
SetWideBytes is not necessary to select a uniformly distributed value, and is only provided for compatibility: SetBytes can be used instead as the chance of bias is less than 2⁻²⁵⁰.
Implementation
void setWideBytes(Uint8List x) {
if (x.length != 64) {
throw ArgumentError('edwards25519: invalid SetWideBytes input size');
}
// Split the 64 bytes into two elements, and extract the most significant
// bit of each, which is ignored by SetBytes.
final lo = Element.feZero()..setBytes(x.sublist(0, 32));
final loMSB = (x[31] >> 7).toBigInt;
final hi = Element.feZero()..setBytes(x.sublist(32));
final hiMSB = (x[63] >> 7).toBigInt;
// The output we want is
//
// v = lo + loMSB * 2²⁵⁵ + hi * 2²⁵⁶ + hiMSB * 2⁵¹¹
//
// which applying the reduction identity comes out to
//
// v = lo + loMSB * 19 + hi * 2 * 19 + hiMSB * 2 * 19²
//
// l0 will be the sum of a 52 bits value (lo.l0), plus a 5 bits value
// (loMSB * 19), a 6 bits value (hi.l0 * 2 * 19), and a 10 bits value
// (hiMSB * 2 * 19²), so it fits in a uint64.
l0 = lo.l0 +
(loMSB * bigInt19) +
(hi.l0 * BigInt.two * bigInt19) +
(hiMSB * BigInt.two * bigInt19 * bigInt19);
l1 = lo.l1 + (hi.l1 * BigInt.two * bigInt19);
l2 = lo.l2 + (hi.l2 * BigInt.two * bigInt19);
l3 = lo.l3 + (hi.l3 * BigInt.two * bigInt19);
l4 = lo.l4 + (hi.l4 * BigInt.two * bigInt19);
carryPropagateGeneric();
}