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
k256::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 shr_vartime(&self, shift: usize) -> Scalar
pub fn shr_vartime(&self, shift: usize) -> Scalar
Right shifts the scalar.
Note: not constant-time with respect to the shift
parameter.
sourcepub fn generate_biased(rng: impl CryptoRng + RngCore) -> Self
pub fn generate_biased(rng: impl CryptoRng + RngCore) -> Self
Returns a (nearly) uniformly-random scalar, generated in constant time.
sourcepub fn generate_vartime(rng: impl RngCore) -> Self
pub fn generate_vartime(rng: impl RngCore) -> Self
Returns a uniformly-random scalar, generated using rejection sampling.
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)
Performs the +=
operation. Read more
sourceimpl AddAssign<Scalar> for Scalar
impl AddAssign<Scalar> for Scalar
sourcefn add_assign(&mut self, rhs: Scalar)
fn add_assign(&mut self, rhs: Scalar)
Performs the +=
operation. Read more
sourceimpl ConditionallySelectable for Scalar
impl ConditionallySelectable for Scalar
sourceimpl ConstantTimeEq for Scalar
impl ConstantTimeEq for Scalar
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
Returns an element chosen uniformly at random using a user-provided RNG.
sourcefn invert(&self) -> CtOption<Self>
fn invert(&self) -> CtOption<Self>
Computes the multiplicative inverse of this element, failing if the element is zero. Read more
fn is_zero_vartime(&self) -> bool
fn is_zero_vartime(&self) -> bool
Returns true iff this element is zero. Read more
fn cube(&self) -> Self
fn cube(&self) -> Self
Cubes this element.
sourceimpl From<&'_ Scalar> for ScalarCore<Secp256k1>
impl From<&'_ Scalar> for ScalarCore<Secp256k1>
sourcefn from(scalar: &Scalar) -> ScalarCore<Secp256k1>
fn from(scalar: &Scalar) -> ScalarCore<Secp256k1>
Converts to this type from the input type.
sourceimpl From<&'_ Scalar> for FieldBytes
impl From<&'_ Scalar> for FieldBytes
sourceimpl From<&'_ ScalarCore<Secp256k1>> for Scalar
impl From<&'_ ScalarCore<Secp256k1>> for Scalar
sourcefn from(scalar: &ScalarCore<Secp256k1>) -> Scalar
fn from(scalar: &ScalarCore<Secp256k1>) -> Scalar
Converts to this type from the input type.
sourceimpl From<Scalar> for ScalarCore<Secp256k1>
impl From<Scalar> for ScalarCore<Secp256k1>
sourcefn from(scalar: Scalar) -> ScalarCore<Secp256k1>
fn from(scalar: Scalar) -> ScalarCore<Secp256k1>
Converts to this type from the input type.
sourceimpl From<Scalar> for FieldBytes
impl From<Scalar> for FieldBytes
sourceimpl From<ScalarCore<Secp256k1>> for Scalar
impl From<ScalarCore<Secp256k1>> for Scalar
sourcefn from(scalar: ScalarCore<Secp256k1>) -> Scalar
fn from(scalar: ScalarCore<Secp256k1>) -> Scalar
Converts to this type from the input type.
sourceimpl Mul<&'_ Scalar> for AffinePoint
impl Mul<&'_ Scalar> for AffinePoint
type Output = ProjectivePoint
type Output = ProjectivePoint
The resulting type after applying the *
operator.
sourcefn mul(self, scalar: &Scalar) -> ProjectivePoint
fn mul(self, scalar: &Scalar) -> ProjectivePoint
Performs the *
operation. Read more
sourceimpl Mul<&'_ Scalar> for &ProjectivePoint
impl Mul<&'_ Scalar> for &ProjectivePoint
type Output = ProjectivePoint
type Output = ProjectivePoint
The resulting type after applying the *
operator.
sourcefn mul(self, other: &Scalar) -> ProjectivePoint
fn mul(self, other: &Scalar) -> ProjectivePoint
Performs the *
operation. Read more
sourceimpl Mul<&'_ Scalar> for ProjectivePoint
impl Mul<&'_ Scalar> for ProjectivePoint
type Output = ProjectivePoint
type Output = ProjectivePoint
The resulting type after applying the *
operator.
sourcefn mul(self, other: &Scalar) -> ProjectivePoint
fn mul(self, other: &Scalar) -> ProjectivePoint
Performs the *
operation. Read more
sourceimpl Mul<Scalar> for AffinePoint
impl Mul<Scalar> for AffinePoint
type Output = ProjectivePoint
type Output = ProjectivePoint
The resulting type after applying the *
operator.
sourcefn mul(self, scalar: Scalar) -> ProjectivePoint
fn mul(self, scalar: Scalar) -> ProjectivePoint
Performs the *
operation. Read more
sourceimpl Mul<Scalar> for ProjectivePoint
impl Mul<Scalar> for ProjectivePoint
type Output = ProjectivePoint
type Output = ProjectivePoint
The resulting type after applying the *
operator.
sourcefn mul(self, other: Scalar) -> ProjectivePoint
fn mul(self, other: Scalar) -> ProjectivePoint
Performs the *
operation. Read more
sourceimpl MulAssign<&'_ Scalar> for ProjectivePoint
impl MulAssign<&'_ Scalar> for ProjectivePoint
sourcefn mul_assign(&mut self, rhs: &Scalar)
fn mul_assign(&mut self, rhs: &Scalar)
Performs the *=
operation. Read more
sourceimpl MulAssign<&'_ Scalar> for Scalar
impl MulAssign<&'_ Scalar> for Scalar
sourcefn mul_assign(&mut self, rhs: &Scalar)
fn mul_assign(&mut self, rhs: &Scalar)
Performs the *=
operation. Read more
sourceimpl MulAssign<Scalar> for ProjectivePoint
impl MulAssign<Scalar> for ProjectivePoint
sourcefn mul_assign(&mut self, rhs: Scalar)
fn mul_assign(&mut self, rhs: Scalar)
Performs the *=
operation. Read more
sourceimpl MulAssign<Scalar> for Scalar
impl MulAssign<Scalar> for Scalar
sourcefn mul_assign(&mut self, rhs: Scalar)
fn mul_assign(&mut self, rhs: Scalar)
Performs the *=
operation. Read more
sourceimpl 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, <<Secp256k1 as Curve>::UInt as ArrayEncoding>::ByteSize>
type Repr = GenericArray<u8, <<Secp256k1 as Curve>::UInt as ArrayEncoding>::ByteSize>
The prime field can be converted back and forth into this binary representation. Read more
sourceconst CAPACITY: u32 = 255u32
const CAPACITY: u32 = 255u32
How many bits of information can be reliably stored in the field element. Read more
sourceconst S: u32 = 6u32
const S: u32 = 6u32
An integer s
satisfying the equation 2^s * t = modulus - 1
with t
odd. Read more
sourcefn to_repr(&self) -> FieldBytes
fn to_repr(&self) -> FieldBytes
Converts an element of the prime field into the standard byte representation for this field. Read more
sourcefn multiplicative_generator() -> Self
fn multiplicative_generator() -> Self
Returns a fixed multiplicative generator of modulus - 1
order. This element must
also be a quadratic nonresidue. Read more
sourcefn root_of_unity() -> Self
fn root_of_unity() -> Self
Returns the 2^s
root of unity. Read more
fn from_str_vartime(s: &str) -> Option<Self>
fn from_str_vartime(s: &str) -> Option<Self>
Interpret a string of numbers as a (congruent) prime field element. Does not accept unnecessary leading zeroes or a blank string. Read more
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
fn from_repr_vartime(repr: Self::Repr) -> Option<Self>
Attempts to convert a byte representation of a field element into an element of this prime field, failing if the input is not canonical (is not smaller than the field’s modulus). Read more
sourceimpl Reduce<UInt<{_: usize}>> for Scalar
impl Reduce<UInt<{_: usize}>> for Scalar
sourcefn from_uint_reduced(w: U256) -> Self
fn from_uint_reduced(w: U256) -> Self
Perform a modular reduction, returning a field element.
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
Interpret the given byte array as a big endian integer and perform a modular reduction. Read more
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
Interpret the given byte array as a little endian integer and perform a modular reduction. Read more
sourcefn from_be_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_be_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
Interpret a digest as a big endian integer and perform a modular reduction. Read more
sourcefn from_le_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_le_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
Interpret a digest as a little endian integer and perform a modular reduction. Read more
sourceimpl Reduce<UInt<{_: usize}>> for Scalar
impl Reduce<UInt<{_: usize}>> for Scalar
sourcefn from_uint_reduced(w: U512) -> Self
fn from_uint_reduced(w: U512) -> Self
Perform a modular reduction, returning a field element.
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
Interpret the given byte array as a big endian integer and perform a modular reduction. Read more
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
Interpret the given byte array as a little endian integer and perform a modular reduction. Read more
sourcefn from_be_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_be_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
Interpret a digest as a big endian integer and perform a modular reduction. Read more
sourcefn from_le_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
fn from_le_digest_reduced<D>(digest: D) -> Self where
D: FixedOutput<OutputSize = <UInt as ArrayEncoding>::ByteSize>,
Interpret a digest as a little endian integer and perform a modular reduction. Read more
sourceimpl ReduceNonZero<UInt<{_: usize}>> for Scalar
impl ReduceNonZero<UInt<{_: usize}>> for Scalar
sourcefn from_uint_reduced_nonzero(w: U256) -> Self
fn from_uint_reduced_nonzero(w: U256) -> Self
Perform a modular reduction, returning a field element.
sourceimpl ReduceNonZero<UInt<{_: usize}>> for Scalar
impl ReduceNonZero<UInt<{_: usize}>> for Scalar
sourcefn from_uint_reduced_nonzero(w: U512) -> Self
fn from_uint_reduced_nonzero(w: U512) -> Self
Perform a modular reduction, returning a field element.
sourceimpl SignPrimitive<Secp256k1> for Scalar
Available on crate feature ecdsa-core
only.
impl SignPrimitive<Secp256k1> for Scalar
ecdsa-core
only.sourcefn try_sign_prehashed<K>(
&self,
ephemeral_scalar: K,
z: FieldBytes
) -> Result<(Signature, Option<RecoveryId>), Error> where
K: Borrow<Scalar> + Invert<Output = CtOption<Scalar>>,
fn try_sign_prehashed<K>(
&self,
ephemeral_scalar: K,
z: FieldBytes
) -> Result<(Signature, Option<RecoveryId>), Error> where
K: Borrow<Scalar> + Invert<Output = CtOption<Scalar>>,
Try to sign the prehashed message. Read more
sourcefn try_sign_prehashed_rfc6979<D>(
&self,
z: GenericArray<u8, <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
ad: &[u8]
) -> Result<(Signature<C>, Option<RecoveryId>), Error> where
Self: From<ScalarCore<C>>,
D: CoreProxy + FixedOutput<OutputSize = <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
<C as Curve>::UInt: for<'a> From<&'a Self>,
<D as CoreProxy>::Core: BlockSizeUser,
<D as CoreProxy>::Core: BufferKindUser,
<D as CoreProxy>::Core: Clone,
<D as CoreProxy>::Core: Default,
<D as CoreProxy>::Core: FixedOutputCore,
<D as CoreProxy>::Core: HashMarker,
<D as CoreProxy>::Core: OutputSizeUser,
<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize: IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>,
<<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize as IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>>::Output: NonZero,
<<D as CoreProxy>::Core as BufferKindUser>::BufferKind == Eager,
<<D as CoreProxy>::Core as OutputSizeUser>::OutputSize == <D as OutputSizeUser>::OutputSize,
fn try_sign_prehashed_rfc6979<D>(
&self,
z: GenericArray<u8, <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
ad: &[u8]
) -> Result<(Signature<C>, Option<RecoveryId>), Error> where
Self: From<ScalarCore<C>>,
D: CoreProxy + FixedOutput<OutputSize = <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
<C as Curve>::UInt: for<'a> From<&'a Self>,
<D as CoreProxy>::Core: BlockSizeUser,
<D as CoreProxy>::Core: BufferKindUser,
<D as CoreProxy>::Core: Clone,
<D as CoreProxy>::Core: Default,
<D as CoreProxy>::Core: FixedOutputCore,
<D as CoreProxy>::Core: HashMarker,
<D as CoreProxy>::Core: OutputSizeUser,
<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize: IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>,
<<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize as IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>>::Output: NonZero,
<<D as CoreProxy>::Core as BufferKindUser>::BufferKind == Eager,
<<D as CoreProxy>::Core as OutputSizeUser>::OutputSize == <D as OutputSizeUser>::OutputSize,
sourcefn try_sign_digest_rfc6979<D>(
&self,
msg_digest: D,
ad: &[u8]
) -> Result<(Signature<C>, Option<RecoveryId>), Error> where
Self: From<ScalarCore<C>>,
D: CoreProxy + FixedOutput<OutputSize = <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
<C as Curve>::UInt: for<'a> From<&'a Self>,
<D as CoreProxy>::Core: BlockSizeUser,
<D as CoreProxy>::Core: BufferKindUser,
<D as CoreProxy>::Core: Clone,
<D as CoreProxy>::Core: Default,
<D as CoreProxy>::Core: FixedOutputCore,
<D as CoreProxy>::Core: HashMarker,
<D as CoreProxy>::Core: OutputSizeUser,
<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize: IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>,
<<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize as IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>>::Output: NonZero,
<<D as CoreProxy>::Core as BufferKindUser>::BufferKind == Eager,
<<D as CoreProxy>::Core as OutputSizeUser>::OutputSize == <D as OutputSizeUser>::OutputSize,
fn try_sign_digest_rfc6979<D>(
&self,
msg_digest: D,
ad: &[u8]
) -> Result<(Signature<C>, Option<RecoveryId>), Error> where
Self: From<ScalarCore<C>>,
D: CoreProxy + FixedOutput<OutputSize = <<C as Curve>::UInt as ArrayEncoding>::ByteSize>,
<C as Curve>::UInt: for<'a> From<&'a Self>,
<D as CoreProxy>::Core: BlockSizeUser,
<D as CoreProxy>::Core: BufferKindUser,
<D as CoreProxy>::Core: Clone,
<D as CoreProxy>::Core: Default,
<D as CoreProxy>::Core: FixedOutputCore,
<D as CoreProxy>::Core: HashMarker,
<D as CoreProxy>::Core: OutputSizeUser,
<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize: IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>,
<<<D as CoreProxy>::Core as BlockSizeUser>::BlockSize as IsLess<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UInt<UTerm, B1>, B0>, B0>, B0>, B0>, B0>, B0>, B0>, B0>>>::Output: NonZero,
<<D as CoreProxy>::Core as BufferKindUser>::BufferKind == Eager,
<<D as CoreProxy>::Core as OutputSizeUser>::OutputSize == <D as OutputSizeUser>::OutputSize,
sourceimpl SubAssign<&'_ Scalar> for Scalar
impl SubAssign<&'_ Scalar> for Scalar
sourcefn sub_assign(&mut self, rhs: &Scalar)
fn sub_assign(&mut self, rhs: &Scalar)
Performs the -=
operation. Read more
sourceimpl SubAssign<Scalar> for Scalar
impl SubAssign<Scalar> for Scalar
sourcefn sub_assign(&mut self, rhs: Scalar)
fn sub_assign(&mut self, rhs: Scalar)
Performs the -=
operation. Read more
impl 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 T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more
sourceimpl<T> ConditionallyNegatable for T where
T: ConditionallySelectable,
&'a T: for<'a> Neg,
<&'a T as Neg>::Output == T,
impl<T> ConditionallyNegatable for T where
T: ConditionallySelectable,
&'a T: for<'a> Neg,
<&'a T as Neg>::Output == T,
sourcefn conditional_negate(&mut self, choice: Choice)
fn conditional_negate(&mut self, choice: Choice)
Negate self
if choice == Choice(1)
; otherwise, leave it
unchanged. Read more
sourceimpl<T> ToOwned for T where
T: Clone,
impl<T> ToOwned for T where
T: Clone,
type Owned = T
type Owned = T
The resulting type after obtaining ownership.
sourcefn clone_into(&self, target: &mut T)
fn clone_into(&self, target: &mut T)
toowned_clone_into
)Uses borrowed data to replace owned data, usually by cloning. Read more