pub struct Scalar(_);
arithmetic
only.Expand description
Scalars are elements in the finite field modulo n.
Trait impls
Much of the important functionality of scalars is provided by traits from
the ff
crate, which is re-exported as
p256::elliptic_curve::ff
:
Field
- represents elements of finite fields and provides:Field::random
- generate a random scalardouble
,square
, andinvert
operations- Bounds for
Add
,Sub
,Mul
, andNeg
(as well as*Assign
equivalents) - Bounds for
ConditionallySelectable
from thesubtle
crate
PrimeField
- represents elements of prime fields and provides:from_repr
/to_repr
for converting field elements from/to big integers.multiplicative_generator
androot_of_unity
constants.
PrimeFieldBits
- operations over field elements represented as bits (requiresbits
feature)
Please see the documentation for the relevant traits for more information.
serde
support
When the serde
feature of this crate is enabled, the Serialize
and
Deserialize
traits are impl’d for this type.
The serialization is a fixed-width big endian encoding. When used with textual formats, the binary data is encoded as hexadecimal.
Implementations
sourceimpl Scalar
impl Scalar
sourcepub fn to_bytes(&self) -> FieldBytes
pub fn to_bytes(&self) -> FieldBytes
Returns the SEC1 encoding of this scalar.
sourcepub fn invert(&self) -> CtOption<Self>
pub fn invert(&self) -> CtOption<Self>
Returns the multiplicative inverse of self, if self is non-zero
sourcepub fn invert_vartime(&self) -> CtOption<Self>
pub fn invert_vartime(&self) -> CtOption<Self>
Faster inversion using Stein’s algorithm
Trait Implementations
sourceimpl AddAssign<&Scalar> for Scalar
impl AddAssign<&Scalar> for Scalar
sourcefn add_assign(&mut self, rhs: &Scalar)
fn add_assign(&mut self, rhs: &Scalar)
+=
operation. Read moresourceimpl AddAssign<Scalar> for Scalar
impl AddAssign<Scalar> for Scalar
sourcefn add_assign(&mut self, rhs: Scalar)
fn add_assign(&mut self, rhs: Scalar)
+=
operation. Read moresourceimpl Borrow<Scalar> for BlindedScalar
impl Borrow<Scalar> for BlindedScalar
sourceimpl ConditionallySelectable for Scalar
impl ConditionallySelectable for Scalar
sourcefn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self
fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self
sourcefn conditional_assign(&mut self, other: &Self, choice: Choice)
fn conditional_assign(&mut self, other: &Self, choice: Choice)
sourceimpl ConstantTimeEq for Scalar
impl ConstantTimeEq for Scalar
sourceimpl<'de> Deserialize<'de> for Scalar
Available on crate feature serde
only.
impl<'de> Deserialize<'de> for Scalar
serde
only.sourcefn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
sourceimpl Field for Scalar
impl Field for Scalar
sourcefn sqrt(&self) -> CtOption<Self>
fn sqrt(&self) -> CtOption<Self>
Tonelli-Shank’s algorithm for q mod 16 = 1 https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
sourcefn random(rng: impl RngCore) -> Self
fn random(rng: impl RngCore) -> Self
sourcefn invert(&self) -> CtOption<Self>
fn invert(&self) -> CtOption<Self>
fn is_zero_vartime(&self) -> bool
fn is_zero_vartime(&self) -> bool
fn cube(&self) -> Self
fn cube(&self) -> Self
fn pow_vartime<S>(&self, exp: S) -> Selfwhere
S: AsRef<[u64]>,
fn pow_vartime<S>(&self, exp: S) -> Selfwhere
S: AsRef<[u64]>,
sourceimpl From<&Scalar> for FieldBytes
impl From<&Scalar> for FieldBytes
sourceimpl From<&Scalar> for ScalarBits
Available on crate feature bits
only.
impl From<&Scalar> for ScalarBits
bits
only.sourcefn from(scalar: &Scalar) -> ScalarBits
fn from(scalar: &Scalar) -> ScalarBits
sourceimpl From<&Scalar> for ScalarCore<NistP256>
impl From<&Scalar> for ScalarCore<NistP256>
sourcefn from(scalar: &Scalar) -> ScalarCore<NistP256>
fn from(scalar: &Scalar) -> ScalarCore<NistP256>
sourceimpl From<&ScalarCore<NistP256>> for Scalar
impl From<&ScalarCore<NistP256>> for Scalar
sourcefn from(scalar: &ScalarCore<NistP256>) -> Scalar
fn from(scalar: &ScalarCore<NistP256>) -> Scalar
sourceimpl From<Scalar> for FieldBytes
impl From<Scalar> for FieldBytes
sourceimpl From<Scalar> for ScalarCore<NistP256>
impl From<Scalar> for ScalarCore<NistP256>
sourcefn from(scalar: Scalar) -> ScalarCore<NistP256>
fn from(scalar: Scalar) -> ScalarCore<NistP256>
sourceimpl From<ScalarCore<NistP256>> for Scalar
impl From<ScalarCore<NistP256>> for Scalar
sourcefn from(scalar: ScalarCore<NistP256>) -> Scalar
fn from(scalar: ScalarCore<NistP256>) -> Scalar
sourceimpl MulAssign<&Scalar> for Scalar
impl MulAssign<&Scalar> for Scalar
sourcefn mul_assign(&mut self, rhs: &Scalar)
fn mul_assign(&mut self, rhs: &Scalar)
*=
operation. Read moresourceimpl MulAssign<Scalar> for Scalar
impl MulAssign<Scalar> for Scalar
sourcefn mul_assign(&mut self, rhs: Scalar)
fn mul_assign(&mut self, rhs: Scalar)
*=
operation. Read moresourceimpl Ord for Scalar
impl Ord for Scalar
1.21.0 · sourcefn max(self, other: Self) -> Selfwhere
Self: Sized,
fn max(self, other: Self) -> Selfwhere
Self: Sized,
1.21.0 · sourcefn min(self, other: Self) -> Selfwhere
Self: Sized,
fn min(self, other: Self) -> Selfwhere
Self: Sized,
1.50.0 · sourcefn clamp(self, min: Self, max: Self) -> Selfwhere
Self: Sized + PartialOrd<Self>,
fn clamp(self, min: Self, max: Self) -> Selfwhere
Self: Sized + PartialOrd<Self>,
sourceimpl PartialOrd<Scalar> for Scalar
impl PartialOrd<Scalar> for Scalar
sourcefn partial_cmp(&self, other: &Self) -> Option<Ordering>
fn partial_cmp(&self, other: &Self) -> Option<Ordering>
1.0.0 · sourcefn le(&self, other: &Rhs) -> bool
fn le(&self, other: &Rhs) -> bool
self
and other
) and is used by the <=
operator. Read moresourceimpl PrimeField for Scalar
impl PrimeField for Scalar
sourcefn from_repr(bytes: FieldBytes) -> CtOption<Self>
fn from_repr(bytes: FieldBytes) -> CtOption<Self>
Attempts to parse the given byte array as an SEC1-encoded scalar.
Returns None if the byte array does not contain a big-endian integer in the range [0, p).
type Repr = GenericArray<u8, <<NistP256 as Curve>::UInt as ArrayEncoding>::ByteSize>
type Repr = GenericArray<u8, <<NistP256 as Curve>::UInt as ArrayEncoding>::ByteSize>
sourceconst CAPACITY: u32 = 255u32
const CAPACITY: u32 = 255u32
sourcefn to_repr(&self) -> FieldBytes
fn to_repr(&self) -> FieldBytes
sourcefn multiplicative_generator() -> Self
fn multiplicative_generator() -> Self
modulus - 1
order. This element must
also be a quadratic nonresidue. Read moresourcefn root_of_unity() -> Self
fn root_of_unity() -> Self
2^s
root of unity. Read morefn from_str_vartime(s: &str) -> Option<Self>
fn from_str_vartime(s: &str) -> Option<Self>
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
sourceimpl PrimeFieldBits for Scalar
Available on crate feature bits
only.
impl PrimeFieldBits for Scalar
bits
only.sourcefn to_le_bits(&self) -> ScalarBits
fn to_le_bits(&self) -> ScalarBits
sourcefn char_le_bits() -> ScalarBits
fn char_le_bits() -> ScalarBits
sourceimpl Reduce<UInt<_>> for Scalar
impl Reduce<UInt<_>> for Scalar
sourcefn from_uint_reduced(w: U256) -> Self
fn from_uint_reduced(w: U256) -> Self
sourcefn from_be_bytes_reduced(
bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self
fn from_be_bytes_reduced(
bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self
sourcefn from_le_bytes_reduced(
bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self
fn from_le_bytes_reduced(
bytes: GenericArray<u8, <UInt as ArrayEncoding>::ByteSize>
) -> Self
sourcefn from_be_digest_reduced<D>(digest: D) -> Selfwhere
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_be_digest_reduced<D>(digest: D) -> Selfwhere
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
sourcefn from_le_digest_reduced<D>(digest: D) -> Selfwhere
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_le_digest_reduced<D>(digest: D) -> Selfwhere
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
sourceimpl ReduceNonZero<UInt<_>> for Scalar
impl ReduceNonZero<UInt<_>> for Scalar
sourcefn from_uint_reduced_nonzero(w: U256) -> Self
fn from_uint_reduced_nonzero(w: U256) -> Self
sourceimpl SignPrimitive<NistP256> for Scalar
Available on crate feature ecdsa-core
only.
impl SignPrimitive<NistP256> for Scalar
ecdsa-core
only.sourceimpl SubAssign<&Scalar> for Scalar
impl SubAssign<&Scalar> for Scalar
sourcefn sub_assign(&mut self, rhs: &Scalar)
fn sub_assign(&mut self, rhs: &Scalar)
-=
operation. Read moresourceimpl SubAssign<Scalar> for Scalar
impl SubAssign<Scalar> for Scalar
sourcefn sub_assign(&mut self, rhs: Scalar)
fn sub_assign(&mut self, rhs: Scalar)
-=
operation. Read moreimpl Copy for Scalar
impl DefaultIsZeroes for Scalar
impl Eq for Scalar
Auto Trait Implementations
impl RefUnwindSafe for Scalar
impl Send for Scalar
impl Sync for Scalar
impl Unpin for Scalar
impl UnwindSafe for Scalar
Blanket Implementations
sourceimpl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
sourceimpl<T> ConditionallyNegatable for Twhere
T: ConditionallySelectable,
&'a T: for<'a> Neg<Output = T>,
impl<T> ConditionallyNegatable for Twhere
T: ConditionallySelectable,
&'a T: for<'a> Neg<Output = T>,
sourcefn conditional_negate(&mut self, choice: Choice)
fn conditional_negate(&mut self, choice: Choice)
impl<T> FmtForward for T
impl<T> FmtForward for T
fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
fn fmt_binary(self) -> FmtBinary<Self>where
Self: Binary,
fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
fn fmt_display(self) -> FmtDisplay<Self>where
Self: Display,
fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
fn fmt_lower_exp(self) -> FmtLowerExp<Self>where
Self: LowerExp,
fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
fn fmt_lower_hex(self) -> FmtLowerHex<Self>where
Self: LowerHex,
fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
fn fmt_pointer(self) -> FmtPointer<Self>where
Self: Pointer,
fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
fn fmt_upper_exp(self) -> FmtUpperExp<Self>where
Self: UpperExp,
fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
fn fmt_upper_hex(self) -> FmtUpperHex<Self>where
Self: UpperHex,
fn fmt_list(self) -> FmtList<Self>where
&'a Self: for<'a> IntoIterator,
fn fmt_list(self) -> FmtList<Self>where
&'a Self: for<'a> IntoIterator,
impl<T> Pipe for Twhere
T: ?Sized,
impl<T> Pipe for Twhere
T: ?Sized,
fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
fn pipe<R>(self, func: impl FnOnce(Self) -> R) -> Rwhere
Self: Sized,
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 morefn 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 morefn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> Rwhere
Self: Borrow<B>,
B: 'a + ?Sized,
R: 'a,
fn pipe_borrow<'a, B, R>(&'a self, func: impl FnOnce(&'a B) -> R) -> Rwhere
Self: Borrow<B>,
B: 'a + ?Sized,
R: 'a,
fn pipe_borrow_mut<'a, B, R>(
&'a mut self,
func: impl FnOnce(&'a mut B) -> R
) -> Rwhere
Self: BorrowMut<B>,
B: 'a + ?Sized,
R: 'a,
fn pipe_borrow_mut<'a, B, R>(
&'a mut self,
func: impl FnOnce(&'a mut B) -> R
) -> Rwhere
Self: BorrowMut<B>,
B: 'a + ?Sized,
R: 'a,
fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> Rwhere
Self: AsRef<U>,
U: 'a + ?Sized,
R: 'a,
fn pipe_as_ref<'a, U, R>(&'a self, func: impl FnOnce(&'a U) -> R) -> Rwhere
Self: AsRef<U>,
U: 'a + ?Sized,
R: 'a,
self
, then passes self.as_ref()
into the pipe function.fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> Rwhere
Self: AsMut<U>,
U: 'a + ?Sized,
R: 'a,
fn pipe_as_mut<'a, U, R>(&'a mut self, func: impl FnOnce(&'a mut U) -> R) -> Rwhere
Self: AsMut<U>,
U: 'a + ?Sized,
R: 'a,
fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> Rwhere
Self: Deref<Target = T>,
T: 'a + ?Sized,
R: 'a,
fn pipe_deref<'a, T, R>(&'a self, func: impl FnOnce(&'a T) -> R) -> Rwhere
Self: Deref<Target = T>,
T: 'a + ?Sized,
R: 'a,
self
, then passes self.deref()
into the pipe function.impl<T> Tap for T
impl<T> Tap for T
fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow<B>,
B: ?Sized,
fn tap_borrow<B>(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow<B>,
B: ?Sized,
Borrow<B>
of a value. Read morefn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,
fn tap_borrow_mut<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,
BorrowMut<B>
of a value. Read morefn tap_ref<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,
fn tap_ref<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,
AsRef<R>
view of a value. Read morefn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,
fn tap_ref_mut<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,
AsMut<R>
view of a value. Read morefn tap_deref<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
T: ?Sized,
fn tap_deref<T>(self, func: impl FnOnce(&T)) -> Selfwhere
Self: Deref<Target = T>,
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Deref::Target
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Self: DerefMut<Target = T> + Deref,
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fn tap_deref_mut<T>(self, func: impl FnOnce(&mut T)) -> Selfwhere
Self: DerefMut<Target = T> + Deref,
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of a value. Read morefn 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.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
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Self: Borrow<B>,
B: ?Sized,
fn tap_borrow_dbg<B>(self, func: impl FnOnce(&B)) -> Selfwhere
Self: Borrow<B>,
B: ?Sized,
.tap_borrow()
only in debug builds, and is erased in release
builds. Read morefn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,
fn tap_borrow_mut_dbg<B>(self, func: impl FnOnce(&mut B)) -> Selfwhere
Self: BorrowMut<B>,
B: ?Sized,
.tap_borrow_mut()
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builds. Read morefn tap_ref_dbg<R>(self, func: impl FnOnce(&R)) -> Selfwhere
Self: AsRef<R>,
R: ?Sized,
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Self: AsRef<R>,
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only in debug builds, and is erased in release
builds. Read morefn tap_ref_mut_dbg<R>(self, func: impl FnOnce(&mut R)) -> Selfwhere
Self: AsMut<R>,
R: ?Sized,
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Self: AsMut<R>,
R: ?Sized,
.tap_ref_mut()
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