Struct Scalar 

pub struct Scalar(pub [u64; 5]);

A scalar in the ECgFp5 curve’s scalar field, stored in non-Montgomery form as five 64-bit little-endian limbs.

Canonical instances (< n) round-trip through every public operation. The arithmetic primitives add / sub / mul require canonical inputs; from_le_bytes_reduce handles the wider input range produced by hashing.

Tuple Fields

0: [u64; 5]

Implementations

impl Scalar

pub const ZERO: Self

Additive identity.

pub const ONE: Self

Multiplicative identity.

pub const fn from_limbs(limbs: [u64; 5]) -> Self

Build a scalar from five raw 64-bit limbs without any reduction.

The caller is responsible for ensuring the value is canonical when it will subsequently feed the modular Add, Sub, Neg or Mul operators.

pub const fn to_limbs(self) -> [u64; 5]

Return the underlying limbs in little-endian order.

pub fn is_canonical(self) -> bool

Test whether this scalar is canonical (self < n).

pub const fn is_zero(self) -> bool

Test whether the scalar is zero.

pub fn to_le_bytes(self) -> [u8; 40]

Canonical 40-byte little-endian encoding (5 x 8-byte limbs).

pub fn from_le_bytes_reduce(bytes: [u8; 40]) -> Self

Decode 40 little-endian bytes, reducing modulo n if the encoded value exceeds the canonical range. Mirrors the upstream Lighter helper.

pub const fn select(c: u64, a0: Self, a1: Self) -> Self

Branch-free constant-time select: returns a0 when c == 0 and a1 when c == u64::MAX.

pub fn add_inner(self, rhs: Self) -> Self

Raw 320-bit addition with no modular reduction.

pub fn sub_inner(self, rhs: Self) -> (Self, u64)

Raw 320-bit subtraction with no modular reduction. Returns the difference and an 0 / u64::MAX mask indicating whether the operation borrowed beyond the top limb.

pub fn monty_mul(self, rhs: Self) -> Self

Montgomery multiplication (self * rhs) / 2^320 mod n.

self MUST be canonical. rhs may exceed n provided it fits in 320 bits, mirroring the upstream behaviour used to lift values into Montgomery form via the R2 constant.

pub fn from_fp5(e: Fp5) -> Self

Build a scalar from an Fp5 element via reduction modulo n.

Concatenates the five canonical 64-bit limbs of e into a 320-bit little-endian integer and reduces, matching the upstream behaviour of FromGfp5. Used by the Schnorr binding to derive a scalar from a Poseidon2 digest.

pub fn split_to_4_bit_limbs(self) -> [u8; 80]

Split the canonical scalar value into 80 little-endian 4-bit nibbles.

Iteration order is least-significant nibble first.

pub fn recode_signed(self, ss: &mut [i32], w: u32)

Recode the scalar into signed digits for a width-w window.

ss is filled with (2^w + 1)-range signed values (lying in -(2^(w-1)) ..= 2^(w-1) after carry propagation) so that sum(ss[i] * 2^(w*i)) == self mod 2^(w * len). When w * len >= 320, the recoding spans the entire scalar and the top digit is non-negative.

w MUST satisfy 2 <= w <= 10. This helper is variable-time and is only suitable for non-secret window selection.

Trait Implementations

impl Add for Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl AddAssign for Scalar

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Scalar

impl Debug for Scalar

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Scalar

fn default() -> Self

Returns the “default value” for a type.

impl Eq for Scalar

impl Hash for Scalar

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Mul for Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl Mul<Point> for Scalar

type Output = Point

The resulting type after applying the * operator.

fn mul(self, rhs: Point) -> Point

Performs the * operation.

impl Mul<Scalar> for Point

type Output = Point

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar) -> Self

Performs the * operation.

impl MulAssign for Scalar

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Scalar

fn eq(&self, other: &Scalar) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for Scalar

impl Sub for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl SubAssign for Scalar

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.