Struct dusk_jubjub::Fr
source · pub struct Fr(/* private fields */);
Expand description
Represents an element of the scalar field $\mathbb{F}_r$ of the Jubjub elliptic curve construction.
Implementations§
source§impl Fr
impl Fr
sourcepub fn hash_to_scalar(input: &[u8]) -> Self
pub fn hash_to_scalar(input: &[u8]) -> Self
Creates a Fr
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 = 0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
p = 6554484396890773809930967563523245729705921265872317281365359162392183254199
l = 2
s^l = (2^256)^2 = 2^512
s = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
r' = 2045593080716281616348203381729468609728209645786990242449482205581148743408809
m' = 2244478849891746936202736009816130624903096691796347063256129649283183245105
sourcepub fn reduce(&self) -> Self
pub fn reduce(&self) -> Self
Reduces bit representation of numbers, such that they can be evaluated in terms of the least significant bit.
sourcepub fn mod_2_pow_k(&self, k: u8) -> u8
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.
sourcepub fn mods_2_pow_k(&self, w: u8) -> i8
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.
sourcepub fn compute_windowed_naf(&self, width: u8) -> [i8; 256]
pub fn compute_windowed_naf(&self, width: u8) -> [i8; 256]
Computes the windowed-non-adjacent form for a given an element in the JubJub Scalar field.
The wnaf of a scalar is its breakdown: scalar = sum_i{wnaf[i]*2^i} where for all i: -2^{w-1} < wnaf[i] < 2^{w-1} and wnaf[i] * wnaf[i+1] = 0
source§impl Fr
impl Fr
sourcepub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fr>
pub fn from_bytes(bytes: &[u8; 32]) -> CtOption<Fr>
Attempts to convert a little-endian byte representation of
a field element into an element of Fr
, failing if the input
is not canonical (is not smaller than r).
sourcepub fn to_bytes(&self) -> [u8; 32]
pub fn to_bytes(&self) -> [u8; 32]
Converts an element of Fr
into a byte representation in
little-endian byte order.
sourcepub fn from_bytes_wide(bytes: &[u8; 64]) -> Fr
pub fn from_bytes_wide(bytes: &[u8; 64]) -> Fr
Converts a 512-bit little endian integer into an element of Fr by reducing modulo r.
sourcepub const fn from_raw(val: [u64; 4]) -> Self
pub const fn from_raw(val: [u64; 4]) -> Self
Converts from an integer represented in little endian
into its (congruent) Fr
representation.
sourcepub fn pow(&self, by: &[u64; 4]) -> Self
pub fn pow(&self, by: &[u64; 4]) -> Self
Exponentiates self
by by
, where by
is a
little-endian order integer exponent.
sourcepub fn pow_vartime(&self, by: &[u64; 4]) -> Self
pub fn pow_vartime(&self, by: &[u64; 4]) -> Self
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.
Trait Implementations§
source§impl<'b> AddAssign<&'b Fr> for Fr
impl<'b> AddAssign<&'b Fr> for Fr
source§fn add_assign(&mut self, rhs: &'b Fr)
fn add_assign(&mut self, rhs: &'b Fr)
+=
operation. Read moresource§impl AddAssign for Fr
impl AddAssign for Fr
source§fn add_assign(&mut self, rhs: Fr)
fn add_assign(&mut self, rhs: Fr)
+=
operation. Read moresource§impl ConditionallySelectable for Fr
impl ConditionallySelectable for Fr
source§impl ConstantTimeEq for Fr
impl ConstantTimeEq for Fr
source§impl Field for Fr
impl Field for Fr
source§fn random(rng: impl RngCore) -> Self
fn random(rng: impl RngCore) -> Self
source§fn invert(&self) -> CtOption<Self>
fn invert(&self) -> CtOption<Self>
source§fn sqrt(&self) -> CtOption<Self>
fn sqrt(&self) -> CtOption<Self>
source§fn is_zero_vartime(&self) -> bool
fn is_zero_vartime(&self) -> bool
source§impl<'a, 'b> Mul<&'b Fr> for &'a AffineNielsPoint
impl<'a, 'b> Mul<&'b Fr> for &'a AffineNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a, 'b> Mul<&'b Fr> for &'a AffinePoint
impl<'a, 'b> Mul<&'b Fr> for &'a AffinePoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a, 'b> Mul<&'b Fr> for &'a ExtendedNielsPoint
impl<'a, 'b> Mul<&'b Fr> for &'a ExtendedNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a, 'b> Mul<&'b Fr> for &'a ExtendedPoint
impl<'a, 'b> Mul<&'b Fr> for &'a ExtendedPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a, 'b> Mul<&'b Fr> for &'a SubgroupPoint
impl<'a, 'b> Mul<&'b Fr> for &'a SubgroupPoint
§type Output = SubgroupPoint
type Output = SubgroupPoint
*
operator.source§impl<'b> Mul<&'b Fr> for AffineNielsPoint
impl<'b> Mul<&'b Fr> for AffineNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'b> Mul<&'b Fr> for AffinePoint
impl<'b> Mul<&'b Fr> for AffinePoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'b> Mul<&'b Fr> for ExtendedNielsPoint
impl<'b> Mul<&'b Fr> for ExtendedNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'b> Mul<&'b Fr> for ExtendedPoint
impl<'b> Mul<&'b Fr> for ExtendedPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'b> Mul<&'b Fr> for SubgroupPoint
impl<'b> Mul<&'b Fr> for SubgroupPoint
§type Output = SubgroupPoint
type Output = SubgroupPoint
*
operator.source§impl<'a> Mul<Fr> for &'a AffineNielsPoint
impl<'a> Mul<Fr> for &'a AffineNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a> Mul<Fr> for &'a AffinePoint
impl<'a> Mul<Fr> for &'a AffinePoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a> Mul<Fr> for &'a ExtendedNielsPoint
impl<'a> Mul<Fr> for &'a ExtendedNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a> Mul<Fr> for &'a ExtendedPoint
impl<'a> Mul<Fr> for &'a ExtendedPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl<'a> Mul<Fr> for &'a SubgroupPoint
impl<'a> Mul<Fr> for &'a SubgroupPoint
§type Output = SubgroupPoint
type Output = SubgroupPoint
*
operator.source§impl Mul<Fr> for AffineNielsPoint
impl Mul<Fr> for AffineNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl Mul<Fr> for AffinePoint
impl Mul<Fr> for AffinePoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl Mul<Fr> for ExtendedNielsPoint
impl Mul<Fr> for ExtendedNielsPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl Mul<Fr> for ExtendedPoint
impl Mul<Fr> for ExtendedPoint
§type Output = ExtendedPoint
type Output = ExtendedPoint
*
operator.source§impl Mul<Fr> for SubgroupPoint
impl Mul<Fr> for SubgroupPoint
§type Output = SubgroupPoint
type Output = SubgroupPoint
*
operator.source§impl<'b> MulAssign<&'b Fr> for ExtendedPoint
impl<'b> MulAssign<&'b Fr> for ExtendedPoint
source§fn mul_assign(&mut self, rhs: &'b Fr)
fn mul_assign(&mut self, rhs: &'b Fr)
*=
operation. Read moresource§impl<'b> MulAssign<&'b Fr> for Fr
impl<'b> MulAssign<&'b Fr> for Fr
source§fn mul_assign(&mut self, rhs: &'b Fr)
fn mul_assign(&mut self, rhs: &'b Fr)
*=
operation. Read moresource§impl<'b> MulAssign<&'b Fr> for SubgroupPoint
impl<'b> MulAssign<&'b Fr> for SubgroupPoint
source§fn mul_assign(&mut self, rhs: &'b Fr)
fn mul_assign(&mut self, rhs: &'b Fr)
*=
operation. Read moresource§impl MulAssign<Fr> for ExtendedPoint
impl MulAssign<Fr> for ExtendedPoint
source§fn mul_assign(&mut self, rhs: Fr)
fn mul_assign(&mut self, rhs: Fr)
*=
operation. Read moresource§impl MulAssign<Fr> for SubgroupPoint
impl MulAssign<Fr> for SubgroupPoint
source§fn mul_assign(&mut self, rhs: Fr)
fn mul_assign(&mut self, rhs: Fr)
*=
operation. Read moresource§impl MulAssign for Fr
impl MulAssign for Fr
source§fn mul_assign(&mut self, rhs: Fr)
fn mul_assign(&mut self, rhs: Fr)
*=
operation. Read moresource§impl Ord for Fr
impl Ord for Fr
source§impl PartialEq for Fr
impl PartialEq for Fr
source§impl PartialOrd for Fr
impl PartialOrd for Fr
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 Fr
impl PrimeField for Fr
§type Repr = [u8; 32]
type Repr = [u8; 32]
source§fn from_repr(r: Self::Repr) -> CtOption<Self>
fn from_repr(r: Self::Repr) -> CtOption<Self>
source§fn to_repr(&self) -> Self::Repr
fn to_repr(&self) -> Self::Repr
source§const MODULUS: &'static str = "0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7"
const MODULUS: &'static str = "0x0e7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7"
source§const CAPACITY: u32 = 251u32
const CAPACITY: u32 = 251u32
source§const MULTIPLICATIVE_GENERATOR: Self = GENERATOR
const MULTIPLICATIVE_GENERATOR: Self = GENERATOR
modulus - 1
order. This element must also be
a quadratic nonresidue. Read moresource§const ROOT_OF_UNITY: Self = ROOT_OF_UNITY
const ROOT_OF_UNITY: Self = ROOT_OF_UNITY
2^s
root of unity. Read moresource§const ROOT_OF_UNITY_INV: Self = ROOT_OF_UNITY_INV
const ROOT_OF_UNITY_INV: Self = 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 PrimeFieldBits for Fr
impl PrimeFieldBits for Fr
source§fn to_le_bits(&self) -> FieldBits<Self::ReprBits>
fn to_le_bits(&self) -> FieldBits<Self::ReprBits>
source§fn char_le_bits() -> FieldBits<Self::ReprBits>
fn char_le_bits() -> FieldBits<Self::ReprBits>
source§impl Serializable<32> for Fr
impl Serializable<32> for Fr
source§fn from_bytes(bytes: &[u8; 32]) -> Result<Self, Self::Error>
fn from_bytes(bytes: &[u8; 32]) -> Result<Self, Self::Error>
Attempts to convert a little-endian byte representation of
a field element into an element of Fr
, failing if the input
is not canonical (is not smaller than r).
source§impl<'b> SubAssign<&'b Fr> for Fr
impl<'b> SubAssign<&'b Fr> for Fr
source§fn sub_assign(&mut self, rhs: &'b Fr)
fn sub_assign(&mut self, rhs: &'b Fr)
-=
operation. Read moresource§impl SubAssign for Fr
impl SubAssign for Fr
source§fn sub_assign(&mut self, rhs: Fr)
fn sub_assign(&mut self, rhs: Fr)
-=
operation. Read moreimpl Copy for Fr
impl Eq for Fr
Auto Trait Implementations§
impl Freeze for Fr
impl RefUnwindSafe for Fr
impl Send for Fr
impl Sync for Fr
impl Unpin for Fr
impl UnwindSafe for Fr
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>,
impl<T, const N: usize> DeserializableSlice<N> for Twhere
T: Serializable<N>,
source§impl<T> FmtForward for T
impl<T> FmtForward for T
source§fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
self
to use its Binary
implementation when Debug
-formatted.source§fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
self
to use its Display
implementation when
Debug
-formatted.source§fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
self
to use its LowerExp
implementation when
Debug
-formatted.source§fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
self
to use its LowerHex
implementation when
Debug
-formatted.source§fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,
fn fmt_octal(self) -> FmtOctal<Self>where
Self: Octal,
self
to use its Octal
implementation when Debug
-formatted.source§fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
self
to use its Pointer
implementation when
Debug
-formatted.source§fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
self
to use its UpperExp
implementation when
Debug
-formatted.source§fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
self
to use its UpperHex
implementation when
Debug
-formatted.source§impl<T, const N: usize> ParseHexStr<N> for Twhere
T: Serializable<N>,
impl<T, const N: usize> ParseHexStr<N> for Twhere
T: Serializable<N>,
source§impl<T> Pipe for Twhere
T: ?Sized,
impl<T> Pipe for Twhere
T: ?Sized,
source§fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
source§fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,
fn pipe_ref<'a, R>(&'a self, func: impl FnOnce(&'a Self) -> R) -> Rwhere
R: 'a,
self
and passes that borrow into the pipe function. Read moresource§fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,
fn pipe_ref_mut<'a, R>(&'a mut self, func: impl FnOnce(&'a mut Self) -> R) -> Rwhere
R: 'a,
self
and passes that borrow into the pipe function. Read moresource§fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> R
source§fn pipe_borrow_mut<'a, B, R>(
&'a mut self,
func: impl FnOnce(&'a mut B) -> R
) -> R
fn pipe_borrow_mut<'a, B, R>( &'a mut self, func: impl FnOnce(&'a mut B) -> R ) -> R
source§fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> R
self
, then passes self.as_ref()
into the pipe function.source§fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> R
self
, then passes self.as_mut()
into the pipe
function.source§fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> R
self
, then passes self.deref()
into the pipe function.source§impl<T> Tap for T
impl<T> Tap for T
source§fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Self
Borrow<B>
of a value. Read moresource§fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Self
BorrowMut<B>
of a value. Read moresource§fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Self
AsRef<R>
view of a value. Read moresource§fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Self
AsMut<R>
view of a value. Read moresource§fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Self
Deref::Target
of a value. Read moresource§fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Self
Deref::Target
of a value. Read moresource§fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self
fn tap_dbg(self, func: impl FnOnce(&Self)) -> Self
.tap()
only in debug builds, and is erased in release builds.source§fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self
fn tap_mut_dbg(self, func: impl FnOnce(&mut Self)) -> Self
.tap_mut()
only in debug builds, and is erased in release
builds.source§fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Self
.tap_borrow()
only in debug builds, and is erased in release
builds.source§fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Self
.tap_borrow_mut()
only in debug builds, and is erased in release
builds.source§fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
fn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Self
.tap_ref()
only in debug builds, and is erased in release
builds.source§fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
fn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Self
.tap_ref_mut()
only in debug builds, and is erased in release
builds.source§fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
fn tap_deref_dbg<T>(self, func: impl FnOnce(&T)) -> Self
.tap_deref()
only in debug builds, and is erased in release
builds.