Struct zerocaf::backend::u64::scalar::Scalar

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

The Scalar struct represents an Scalar over the modulo 2^249 + 14490550575682688738086195780655237219 as 5 52-bit limbs represented in radix 2^52.

Methods

impl Scalar

pub const fn zero() -> Scalar

Return a Scalar with value = 0.

pub const fn one() -> Scalar

Return a Scalar with value = 1.

pub const fn minus_one() -> Scalar

Return a Scalar with value = -1 (mod l).

pub fn is_even(self) -> bool

Evaluate if a Scalar is even or not.

pub fn into_bits(&self) -> [u8; 256]

Returns the bit representation of the given Scalar as an array of 256 bits represented as u8.

pub fn compute_NAF(&self) -> [i8; 256]

Compute the Non-Adjacent Form of a given Scalar.

pub fn compute_window_NAF(&self, width: u8) -> [i8; 256]

Compute the Windowed-Non-Adjacent Form of a given Scalar.

Inputs

• width => Represents the window-width i.e. width = 2^width.

pub fn mod_2_pow_k(&self, k: u8) -> u8

Compute the result from Scalar (mod 2^k).

Panics

If the given k is > 32 (5 bits) as the value gets greater than the limb.

pub fn mods_2_pow_k(&self, w: u8) -> i8

Compute the result from Scalar (mods k).

Panics

If the given k > 32 (5 bits) || k == 0 as the value gets greater than the limb.

pub fn from_bytes(bytes: &[u8; 32]) -> Scalar

Unpack a 32 byte / 256 bit Scalar into 5 52-bit limbs.

pub fn from_bytes_wide(_bytes: &[u8; 64]) -> Scalar

Reduce a 64 byte / 512 bit scalar mod l

pub fn to_bytes(&self) -> [u8; 32]

Pack the limbs of this Scalar into 32 bytes

pub fn two_pow_k(exp: u64) -> Scalar

Given a k: u64, compute 2^k giving the resulting result as a Scalar.

See that the input must be between the range => 0..250.

Panics

If the input is greater than the Sub-group order.

pub fn half_without_mod(self) -> Scalar

Returns the half of an EVEN Scalar.

This function performs almost 4x faster than the Half implementation but SHOULD be used carefully.

Panics

When the Scalar provided is not even.

Trait Implementations

impl<'a, 'b> Add<&'b Scalar> for &'a Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, b: &'b Scalar) -> Scalar

Compute a + b (mod l).

impl Add<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the + operator.

fn add(self, b: Scalar) -> Scalar

Compute a + b (mod l).

impl Clone for Scalar

fn clone(&self) -> Scalar

Returns a copy 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 From<i8> for Scalar

fn from(_inp: i8) -> Scalar

Performs the conversion.

impl From<u128> for Scalar

fn from(_inp: u128) -> Scalar

Performs the conversion.

impl From<u16> for Scalar

fn from(_inp: u16) -> Scalar

Performs the conversion.

impl From<u32> for Scalar

fn from(_inp: u32) -> Scalar

Performs the conversion.

impl From<u64> for Scalar

fn from(_inp: u64) -> Scalar

Performs the conversion.

impl From<u8> for Scalar

fn from(_inp: u8) -> Scalar

Performs the conversion.

impl<'a> Half for &'a Scalar

type Output = Scalar

fn half(self) -> Scalar

Give the half of the Scalar value (mod l).

impl Identity for Scalar

fn identity() -> Scalar

Returns the Identity element for Scalar which equals 1 (mod l).

impl Index<usize> for Scalar

type Output = u64

The returned type after indexing.

fn index(&self, _index: usize) -> &u64

Performs the indexing (container[index]) operation.

impl IndexMut<usize> for Scalar

fn index_mut(&mut self, _index: usize) -> &mut u64

Performs the mutable indexing (container[index]) operation.

impl<'a, 'b> Mul<&'a Scalar> for &'b Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, b: &'a Scalar) -> Scalar

This Mul implementation returns a double precision result. The result of the standard mul is stored on a [u128; 9].

Then, we apply the Montgomery Reduction function to perform the modulo and the reduction to the Scalar format: [u64; 5].

impl<'a, 'b> Mul<&'a Scalar> for &'b ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'a Scalar) -> ProjectivePoint

Scalar multiplication: compute Scalar * self. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl<'a, 'b> Mul<&'b Scalar> for &'a EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> EdwardsPoint

Scalar multiplication: compute self * Scalar. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl<'a, 'b> Mul<&'b Scalar> for &'a RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, scalar: &'b Scalar) -> RistrettoPoint

Scalar multiplication: compute self * Scalar. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl Mul<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the * operator.

fn mul(self, b: Scalar) -> Scalar

This Mul implementation returns a double precision result. The result of the standard mul is stored on a [u128; 9].

Then, we apply the Montgomery Reduction function to perform the modulo and the reduction to the Scalar format: [u64; 5].

impl Mul<Scalar> for EdwardsPoint

type Output = EdwardsPoint

The resulting type after applying the * operator.

fn mul(self, scalar: Scalar) -> EdwardsPoint

Scalar multiplication: compute Scalar * self. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl Mul<Scalar> for ProjectivePoint

type Output = ProjectivePoint

The resulting type after applying the * operator.

fn mul(self, scalar: Scalar) -> ProjectivePoint

Scalar multiplication: compute Scalar * self. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl Mul<Scalar> for RistrettoPoint

type Output = RistrettoPoint

The resulting type after applying the * operator.

fn mul(self, scalar: Scalar) -> RistrettoPoint

Scalar multiplication: compute self * Scalar. This implementation uses the algorithm: add_and_doubling which is the standard one for this operations and also adds less constraints on R1CS.

Hankerson, Darrel; Vanstone, Scott; Menezes, Alfred (2004). Guide to Elliptic Curve Cryptography. Springer Professional Computing. New York: Springer-Verlag.

impl<'a> Neg for &'a Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the negate operation over the sub-group modulo l.

impl Neg for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn neg(self) -> Scalar

Performs the negate operation over the sub-group modulo l.

impl Ord for Scalar

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

🔬 This is a nightly-only experimental API. (clamp)

Restrict a value to a certain interval.

impl PartialEq<Scalar> for Scalar

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<Scalar> for Scalar

fn partial_cmp(&self, other: &Scalar) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

#[must_use] fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

#[must_use] fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

#[must_use] fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

#[must_use] fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, 'b> Pow<&'b Scalar> for &'a Scalar

Performs the op: a^b (mod l).

Exponentiation by squaring classical algorithm implementation for Scalar.

Schneier, Bruce (1996). Applied Cryptography: Protocols, Algorithms, and Source Code in C, Second Edition (2nd ed.).

type Output = Scalar

fn pow(self, exp: &'b Scalar) -> Scalar

Returns a^b (mod l).

impl Shr<u8> for Scalar

type Output = Scalar

The resulting type after applying the >> operator.

fn shr(self, _rhs: u8) -> Scalar

Performs the >> operation.

impl<'a> Square for &'a Scalar

type Output = Scalar

fn square(self) -> Scalar

This Square implementation returns a double precision result. The result of the standard mul is stored on a [u128; 9].

Then, we apply the Montgomery Reduction function to perform the modulo and the reduction to the Scalar format: [u64; 5].

impl<'a, 'b> Sub<&'b Scalar> for &'a Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, b: &'b Scalar) -> Scalar

Compute a - b (mod l).

impl Sub<Scalar> for Scalar

type Output = Scalar

The resulting type after applying the - operator.

fn sub(self, b: Scalar) -> Scalar

Compute a - b (mod l).