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

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

[−] Expand description

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[+]

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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[+]

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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[+]

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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[+]

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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[+]

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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[+]

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

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

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

This method tests for !=.

impl PartialOrd<Scalar> for Scalar[+]

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

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

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

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

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#[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.

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

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

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#[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.).

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type Output = Scalar

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

Returns a^b (mod l).

impl Shr<u8> for Scalar[+]

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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).