/// Reduce a 64 byte / 512 bit scalar mod l
public static UnpackedScalar from_bytes_wide(byte[] bytes)
{
var words = new ulong[8];
for (int i = 0; i < 8; i++)
{
for (int j = 0; j < 8; j++)
{
words[i] |= ((ulong)bytes[(i * 8) + j]) << (j * 8);
}
}
var mask = (((ulong)1) << 52) - 1;
var lo = UnpackedScalar.zero();
var hi = UnpackedScalar.zero();
var los = lo.value.Span;
var his = hi.value.Span;
los[0] = words[0] & mask;
los[1] = ((words[0] >> 52) | (words[1] << 12)) & mask;
los[2] = ((words[1] >> 40) | (words[2] << 24)) & mask;
los[3] = ((words[2] >> 28) | (words[3] << 36)) & mask;
los[4] = ((words[3] >> 16) | (words[4] << 48)) & mask;
his[0] = (words[4] >> 4) & mask;
his[1] = ((words[4] >> 56) | (words[5] << 8)) & mask;
his[2] = ((words[5] >> 44) | (words[6] << 20)) & mask;
his[3] = ((words[6] >> 32) | (words[7] << 32)) & mask;
his[4] = words[7] >> 20;
lo = UnpackedScalar.montgomery_mul(lo, Constant.R); // (lo * R) / R = lo
hi = UnpackedScalar.montgomery_mul(hi, Constant.RR); // (hi * R^2) / R = hi * R
return(UnpackedScalar.add(hi, lo));
}
///// Given a slice of nonzero (possibly secret) `Scalar`s,
///// compute their inverses in a batch.
/////
///// # Return
/////
///// Each element of `inputs` is replaced by its inverse.
/////
///// The product of all inverses is returned.
/////
///// # Warning
/////
///// All input `Scalars` **MUST** be nonzero. If you cannot
///// *prove* that this is the case, you **SHOULD NOT USE THIS
///// FUNCTION**.
/////
///// # Example
/////
///// ```
///// # extern crate curve25519_dalek;
///// # use curve25519_dalek::scalar::Scalar;
///// # fn main() {
///// let mut scalars = [
///// Scalar::from(3u64),
///// Scalar::from(5u64),
///// Scalar::from(7u64),
///// Scalar::from(11u64),
///// ];
/////
///// let allinv = Scalar::batch_invert(&mut scalars);
/////
///// assert_eq!(allinv, Scalar::from(3*5*7*11u64).invert());
///// assert_eq!(scalars[0], Scalar::from(3u64).invert());
///// assert_eq!(scalars[1], Scalar::from(5u64).invert());
///// assert_eq!(scalars[2], Scalar::from(7u64).invert());
///// assert_eq!(scalars[3], Scalar::from(11u64).invert());
///// # }
///// ```
public static Scalar batch_invert(Scalar[] inputs)
{
// This code is essentially identical to the FieldElement
// implementation, and is documented there. Unfortunately,
// it's not easy to write it generically, since here we want
// to use `UnpackedScalar`s internally, and `Scalar`s
// externally, but there's no corresponding distinction for
// field elements.
//use clear_on_drop::ClearOnDrop;
//use clear_on_drop::clear::ZeroSafe;
// Mark UnpackedScalars as zeroable.
//unsafe impl ZeroSafe for UnpackedScalar {}
var n = inputs.Length;
var one = Scalar.one().unpack().to_montgomery();
// Wrap the scratch storage in a ClearOnDrop to wipe it when
// we pass out of scope.
Span <Scalar> scratch_vec = new Scalar[n];
scratch_vec.Fill(Scalar.one());
// Keep an accumulator of all of the previous products
var acc = Scalar.one().unpack().to_montgomery();
// Pass through the input vector, recording the previous
// products in the scratch space
for (int i = 0; i < n; i++)
{
var input = scratch_vec[n];
//scratch = acc;
// Avoid unnecessary Montgomery multiplication in second pass by
// keeping inputs in Montgomery form
var tmp = input.unpack().to_montgomery();
input = tmp.pack();
acc = UnpackedScalar.montgomery_mul(acc, tmp);
}
// acc is nonzero iff all inputs are nonzero
Debug.Assert(acc.pack() != zero());
// Compute the inverse of all products
acc = acc.montgomery_invert().from_montgomery();
// We need to return the product of all inverses later
var ret = acc.pack();
// Pass through the vector backwards to compute the inverses
// in place
for (int i = 0; i < n; i++)
{
var scratch = scratch_vec[n];
var input = inputs[n];
var tmp = UnpackedScalar.montgomery_mul(acc, input.unpack());
input = UnpackedScalar.montgomery_mul(acc, scratch.unpack()).pack();
acc = tmp;
}
return(ret);
}
/// Puts a Scalar64 in to Montgomery form, i.e. computes `a*R (mod l)`
public UnpackedScalar to_montgomery()
{
return(UnpackedScalar.montgomery_mul(this, Constant.RR));
}