Struct dusk_jubjub::Fq
source · pub struct Fq(pub [u64; 4]);
Expand description
Represents an element of the scalar field $\mathbb{F}_q$ of the BLS12-381 elliptic curve construction.
Tuple Fields§
§0: [u64; 4]
Implementations§
source§impl Scalar
impl Scalar
sourcepub const fn internal_repr(&self) -> &[u64; 4]
pub const fn internal_repr(&self) -> &[u64; 4]
Returns the internal representation of the Scalar.
sourcepub fn to_bits(&self) -> [u8; 256]
pub fn to_bits(&self) -> [u8; 256]
Returns the bit representation of the given Scalar
as
an array of 256 bits represented as u8
.
sourcepub fn reduce(&self) -> Scalar
pub fn reduce(&self) -> Scalar
Reduces the scalar and returns it multiplied by the montgomery radix.
sourcepub fn pow_of_2(by: u64) -> Scalar
pub fn pow_of_2(by: u64) -> Scalar
Computes 2^X
where X is a u64
without the need to generate
an array in the stack as pow
& pow_vartime
require.
sourcepub fn hash_to_scalar(input: &[u8]) -> Scalar
pub fn hash_to_scalar(input: &[u8]) -> Scalar
Creates a Scalar
from arbitrary bytes by hashing the input with
BLAKE2b into a 512-bits number, and then converting the number into its
Scalar
representation by reducing it by the modulo.
By treating the output of the BLAKE2b hash as a random oracle, this implementation follows the first conversion of https://hackmd.io/zV6qe1_oSU-kYU6Tt7pO7Q with concrete numbers:
p = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
p = 52435875175126190479447740508185965837690552500527637822603658699938581184513
s = 2^512
s = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
r = 255699135089535202043525422716183576215815630510683217819334674386498370757523
m = 3294906474794265442129797520630710739278575682199800681788903916070560242797
source§impl Scalar
impl Scalar
sourcepub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Scalar>
pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Scalar>
Attempts to convert a little-endian byte representation of a scalar into a Scalar, failing if the input is not canonical.
sourcepub fn to_bytes(&self) -> [u8; 32]
pub fn to_bytes(&self) -> [u8; 32]
Converts an element of Scalar into a byte representation in little-endian byte order.
sourcepub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar
pub fn from_bytes_wide(bytes: &[u8; 64]) -> Scalar
Converts a 512-bit little endian integer into
a Scalar
by reducing by the modulus.
sourcepub const fn from_raw(val: [u64; 4]) -> Scalar
pub const fn from_raw(val: [u64; 4]) -> Scalar
Converts from an integer represented in little endian
into its (congruent) Scalar
representation.
sourcepub fn pow(&self, by: &[u64; 4]) -> Scalar
pub fn pow(&self, by: &[u64; 4]) -> Scalar
Exponentiates self
by by
, where by
is a
little-endian order integer exponent.
sourcepub fn pow_vartime(&self, by: &[u64; 4]) -> Scalar
pub fn pow_vartime(&self, by: &[u64; 4]) -> Scalar
Exponentiates self
by by
, where by
is a
little-endian order integer exponent.
This operation is variable time with respect to the exponent. If the exponent is fixed, this operation is effectively constant time.
sourcepub fn invert(&self) -> Option<Scalar>
pub fn invert(&self) -> Option<Scalar>
Computes the multiplicative inverse of this element, failing if the element is zero.
Trait Implementations§
source§impl<'b> AddAssign<&'b Scalar> for Scalar
impl<'b> AddAssign<&'b Scalar> for Scalar
source§fn add_assign(&mut self, rhs: &'b Scalar)
fn add_assign(&mut self, rhs: &'b Scalar)
+=
operation. Read moresource§impl AddAssign for Scalar
impl AddAssign for Scalar
source§fn add_assign(&mut self, rhs: Scalar)
fn add_assign(&mut self, rhs: Scalar)
+=
operation. Read moresource§impl ConditionallySelectable for Scalar
impl ConditionallySelectable for Scalar
source§impl ConstantTimeEq for Scalar
impl ConstantTimeEq for Scalar
source§impl Field for Scalar
impl Field for Scalar
source§fn random(rng: impl RngCore) -> Scalar
fn random(rng: impl RngCore) -> Scalar
source§fn invert(&self) -> CtOption<Scalar>
fn invert(&self) -> CtOption<Scalar>
source§fn sqrt(&self) -> CtOption<Scalar>
fn sqrt(&self) -> CtOption<Scalar>
source§fn is_zero_vartime(&self) -> bool
fn is_zero_vartime(&self) -> bool
source§impl<'b> MulAssign<&'b Scalar> for Scalar
impl<'b> MulAssign<&'b Scalar> for Scalar
source§fn mul_assign(&mut self, rhs: &'b Scalar)
fn mul_assign(&mut self, rhs: &'b Scalar)
*=
operation. Read moresource§impl MulAssign for Scalar
impl MulAssign for Scalar
source§fn mul_assign(&mut self, rhs: Scalar)
fn mul_assign(&mut self, rhs: Scalar)
*=
operation. Read moresource§impl Ord for Scalar
impl Ord for Scalar
source§impl PartialEq for Scalar
impl PartialEq for Scalar
source§impl PartialOrd for Scalar
impl PartialOrd for Scalar
1.0.0 · source§fn le(&self, other: &Rhs) -> bool
fn le(&self, other: &Rhs) -> bool
self
and other
) and is used by the <=
operator. Read moresource§impl PrimeField for Scalar
impl PrimeField for Scalar
§type Repr = [u8; 32]
type Repr = [u8; 32]
source§fn from_repr(r: <Scalar as PrimeField>::Repr) -> CtOption<Scalar>
fn from_repr(r: <Scalar as PrimeField>::Repr) -> CtOption<Scalar>
source§fn to_repr(&self) -> <Scalar as PrimeField>::Repr
fn to_repr(&self) -> <Scalar as PrimeField>::Repr
source§const MODULUS: &'static str = "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"
const MODULUS: &'static str = "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"
source§const CAPACITY: u32 = 254u32
const CAPACITY: u32 = 254u32
source§const MULTIPLICATIVE_GENERATOR: Scalar = GENERATOR
const MULTIPLICATIVE_GENERATOR: Scalar = GENERATOR
modulus - 1
order. This element must also be
a quadratic nonresidue. Read moresource§const ROOT_OF_UNITY: Scalar = ROOT_OF_UNITY
const ROOT_OF_UNITY: Scalar = ROOT_OF_UNITY
2^s
root of unity. Read moresource§const ROOT_OF_UNITY_INV: Scalar = ROOT_OF_UNITY_INV
const ROOT_OF_UNITY_INV: Scalar = ROOT_OF_UNITY_INV
Self::ROOT_OF_UNITY
.source§fn from_str_vartime(s: &str) -> Option<Self>
fn from_str_vartime(s: &str) -> Option<Self>
source§impl Serializable<32> for Scalar
impl Serializable<32> for Scalar
source§fn to_bytes(&self) -> [u8; 32]
fn to_bytes(&self) -> [u8; 32]
Converts an element of Scalar
into a byte representation in
little-endian byte order.
source§fn from_bytes(
buf: &[u8; 32]
) -> Result<Scalar, <Scalar as Serializable<32>>::Error>
fn from_bytes( buf: &[u8; 32] ) -> Result<Scalar, <Scalar as Serializable<32>>::Error>
Attempts to convert a little-endian byte representation of
a scalar into a Scalar
, failing if the input is not canonical.
source§impl<'b> SubAssign<&'b Scalar> for Scalar
impl<'b> SubAssign<&'b Scalar> for Scalar
source§fn sub_assign(&mut self, rhs: &'b Scalar)
fn sub_assign(&mut self, rhs: &'b Scalar)
-=
operation. Read moresource§impl SubAssign for Scalar
impl SubAssign for Scalar
source§fn sub_assign(&mut self, rhs: Scalar)
fn sub_assign(&mut self, rhs: Scalar)
-=
operation. Read moreimpl Copy for Scalar
impl Eq for Scalar
Auto Trait Implementations§
impl Freeze for Scalar
impl RefUnwindSafe for Scalar
impl Send for Scalar
impl Sync for Scalar
impl Unpin for Scalar
impl UnwindSafe for Scalar
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> ConditionallyNegatable for T
impl<T> ConditionallyNegatable for T
source§fn conditional_negate(&mut self, choice: Choice)
fn conditional_negate(&mut self, choice: Choice)
source§impl<T, const N: usize> DeserializableSlice<N> for Twhere
T: Serializable<N>,
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source§impl<T> FmtForward for T
impl<T> FmtForward for T
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Self: Binary,
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Self: Binary,
self
to use its Binary
implementation when Debug
-formatted.source§fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
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Self: Display,
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to use its Display
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Debug
-formatted.source§fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
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Debug
-formatted.source§fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
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Self: LowerHex,
self
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Debug
-formatted.source§fn fmt_octal(self) -> FmtOctal<Self>where
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