Struct AuthenticatedDensePoly

pub struct AuthenticatedDensePoly<C: CurveGroup> {
    pub coeffs: Vec<AuthenticatedScalarResult<C>>,
}

An authenticated polynomial; i.e. a polynomial in which the coefficients are secret shared between parties

This is modeled after the ark_poly::DensePolynomial source

Fields

coeffs: Vec<AuthenticatedScalarResult<C>>

A vector of coefficients, the coefficient for x^i is stored at index i

Implementations

impl<C: CurveGroup> AuthenticatedDensePoly<C>

pub fn from_coeffs(coeffs: Vec<AuthenticatedScalarResult<C>>) -> Self

Constructor

pub fn zero(fabric: &MpcFabric<C>) -> Self

Allocate the zero polynomial (additive identity) in the given fabric

pub fn one(fabric: &MpcFabric<C>) -> Self

Allocate the one polynomial (multiplicative identity) in the given fabric

pub fn degree(&self) -> usize

Get the degree of the represented polynomial

pub fn random(d: usize, fabric: &MpcFabric<C>) -> Self

Sample a random polynomial of given degree

pub fn fabric(&self) -> &MpcFabric<C>

Get the fabric underlying the polynomial

pub fn eval(&self, x: &ScalarResult<C>) -> AuthenticatedScalarResult<C>

Evaluate the polynomial at a given point

TODO: Opt for a more efficient implementation that allocates fewer gates, i.e. by awaiting all results then creating the evaluation

pub fn open(&self) -> DensePolynomialResult<C>

Open the polynomial to the base type DensePolynomial

pub fn open_authenticated(&self) -> AuthenticatedDensePolyOpenResult<C>

Open the polynomial and authenticate the shares

impl<C: CurveGroup> AuthenticatedDensePoly<C>

Inversion and division helpers

pub fn mod_xn(&self, n: usize) -> Self

Reduce a given polynomial mod x^n

For a modulus of this form, this is equivalent to truncating the coefficients

pub fn rev(&self) -> Self

Reverse the coefficients of the polynomial and return a new polynomial

This is useful when implementing division between authenticated polynomials as per: https://iacr.org/archive/pkc2006/39580045/39580045.pdf Effectively, for a given polynomial a(x), the operation rev(a) returns the polynomial: rev(a)(x) = x^deg(a) * a(1/x) which is emulated by reversing the coefficients directly.

See the division docstring below for a more detailed explanation

pub fn random_polynomial(n: usize, fabric: &MpcFabric<C>) -> Self

Get a random, shared masking polynomial of degree n

pub fn mul_inverse_mod_t(&self, t: usize) -> Self

Compute the multiplicative inverse of a polynomial in the quotient ring F[x] / (x^t)

Uses an extension of the inverse method defined in: https://dl.acm.org/doi/pdf/10.1145/72981.72995

Trait Implementations

impl<C: CurveGroup> Add<&AuthenticatedDensePoly<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a AuthenticatedDensePoly<C>> for &'a DensePolynomial<C::ScalarField>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a AuthenticatedDensePoly<C>> for &'a DensePolynomialResult<C>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a AuthenticatedDensePoly<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a AuthenticatedDensePoly<C>> for DensePolynomial<C::ScalarField>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a AuthenticatedDensePoly<C>> for DensePolynomialResult<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<&DensePolynomial<<C as Group>::ScalarField>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &DensePolynomial<C::ScalarField>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a DensePolynomial<<C as Group>::ScalarField>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a DensePolynomial<C::ScalarField>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<&DensePolynomialResult<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &DensePolynomialResult<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<&'a DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: &'a DensePolynomialResult<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<AuthenticatedDensePoly<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<AuthenticatedDensePoly<C>> for &'a DensePolynomial<C::ScalarField>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<AuthenticatedDensePoly<C>> for &'a DensePolynomialResult<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<AuthenticatedDensePoly<C>> for DensePolynomial<C::ScalarField>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<AuthenticatedDensePoly<C>> for DensePolynomialResult<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<DensePolynomial<<C as Group>::ScalarField>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: DensePolynomial<C::ScalarField>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<DensePolynomial<<C as Group>::ScalarField>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: DensePolynomial<C::ScalarField>) -> Self::Output

Performs the + operation.

impl<'a, C: CurveGroup> Add<DensePolynomialResult<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add<DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the + operation.

impl<C: CurveGroup> Add for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the + operator.

fn add(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the + operation.

impl<C: Clone + CurveGroup> Clone for AuthenticatedDensePoly<C>

fn clone(&self) -> AuthenticatedDensePoly<C>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<C: Debug + CurveGroup> Debug for AuthenticatedDensePoly<C>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<C: Default + CurveGroup> Default for AuthenticatedDensePoly<C>

fn default() -> AuthenticatedDensePoly<C>

Returns the “default value” for a type.

impl<C: CurveGroup> Div<&AuthenticatedDensePoly<C>> for &AuthenticatedDensePoly<C>

Authenticated division, i.e. division in which the divisor is a secret shared polynomial

We follow the approach of: https://iacr.org/archive/pkc2006/39580045/39580045.pdf (Section 4)

To see why this method holds, consider the rev operation for a polynomial a(x): rev(a) = x^deg(a) * a(1/x) Note that this operation is equivalent to reversing the coefficients of a(x) For f(x) / g(x) where deg(f) = n, deg(g) = m, the objective of a division with remainder algorithm is to solve: f(x) = g(x)q(x) + r(x) for q(x), r(x) uniquely where deg(r) < deg(g).

We could solve for q(x) easily if: 1. We could “mod out” r(x) and 2. If g^{-1}(x) exists The rev operator provides a transformation that makes both of these true: rev(f) = rev(g) * rev(q) + x^{n - m + 1} * rev(r) Again, we have used the rev operator to reverse the coefficients of each polynomial so that the leading coefficients are those of r(x). Now we can “mod out” the highest terms to get: rev(f) = rev(g) * rev(q) mod x^{n - m + 1} And now that we are working in the quotient ring F[x] / (x^{n - m + 1}), we can be sure that rev(g)^{-1}(x) exists if its lowest degree coefficient (constant coefficient) is non-zero. For random (blinded) polynomials, this is true with probability 1 - 1/p.

So we: 1. apply the rev transformation, 2. mod out rev{r} and solve for rev(q) 3. undo the rev transformation to get q(x) 4. solve for r(x) = f(x) - q(x)g(x), though for floor division we skip this step

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: &AuthenticatedDensePoly<C>) -> Self::Output

Performs the / operation.

impl<'a, C: CurveGroup> Div<&'a AuthenticatedDensePoly<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the / operation.

impl<C: CurveGroup> Div<&DensePolynomialResult<C>> for &AuthenticatedDensePoly<C>

Given a public divisor b(x) and shared dividend a(x) = a_1(x) + a_2(x) for party shares a_1, a_2 We can divide each share locally to obtain a secret sharing of \floor{a(x) / b(x)}

To see this, consider that a_1(x) = q_1(x)b(x) + r_1(x) and a_2(x) = q_2(x)b(x) + r_2(x) where: - deg(q_1) = deg(a_1) - deg(b) - deg(q_2) = deg(a_2) - deg(b) - deg(r_1) < deg(b) - deg(r_2) < deg(b) The floor division operator for a(x), b(x) returns q(x) such that there exists r(x): deg(r) < deg(b) where a(x) = q(x)b(x) + r(x) Note that a_1(x) + a_2(x) = (q_1(x) + q_2(x))b(x) + r_1(x) + r_2(x), where of course deg(r_1 + r_2) < deg(b), so \floor{a(x) / b(x)} = q_1(x) + q_2(x); making q_1, q_2 additive secret shares of the result as desired

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: &DensePolynomialResult<C>) -> Self::Output

Performs the / operation.

impl<'a, C: CurveGroup> Div<&'a DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: &'a DensePolynomialResult<C>) -> Self::Output

Performs the / operation.

impl<'a, C: CurveGroup> Div<AuthenticatedDensePoly<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the / operation.

impl<'a, C: CurveGroup> Div<DensePolynomialResult<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the / operation.

impl<C: CurveGroup> Div<DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the / operation.

impl<C: CurveGroup> Div for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the / operator.

fn div(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the / operation.

impl<C: CurveGroup> Mul<&AuthenticatedDensePoly<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for &'a AuthenticatedScalarResult<C>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for &'a DensePolynomialResult<C>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for &'a ScalarResult<C>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for &'a Scalar<C>

lhs borrowed, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for AuthenticatedScalarResult<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for DensePolynomialResult<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for ScalarResult<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedDensePoly<C>> for Scalar<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<&AuthenticatedScalarResult<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &AuthenticatedScalarResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a AuthenticatedScalarResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a AuthenticatedScalarResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<&DensePolynomial<<C as Group>::ScalarField>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &DensePolynomial<C::ScalarField>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<&DensePolynomialResult<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &DensePolynomialResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a DensePolynomialResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<&ResultHandle<C, Scalar<C>>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &ScalarResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a ResultHandle<C, Scalar<C>>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a ScalarResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<&Scalar<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &Scalar<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<&'a Scalar<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'a Scalar<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for &'a AuthenticatedScalarResult<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for &'a DensePolynomialResult<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for &'a ScalarResult<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for &'a Scalar<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for AuthenticatedScalarResult<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for DensePolynomialResult<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for ScalarResult<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<AuthenticatedDensePoly<C>> for Scalar<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<AuthenticatedScalarResult<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedScalarResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<AuthenticatedScalarResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: AuthenticatedScalarResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<DensePolynomialResult<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<DensePolynomialResult<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: DensePolynomialResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<ResultHandle<C, Scalar<C>>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: ScalarResult<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<ResultHandle<C, Scalar<C>>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: ScalarResult<C>) -> Self::Output

Performs the * operation.

impl<'a, C: CurveGroup> Mul<Scalar<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Mul<Scalar<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the * operator.

fn mul(self, rhs: Scalar<C>) -> Self::Output

Performs the * operation.

impl<C: CurveGroup> Neg for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<C: CurveGroup> Neg for AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<C: CurveGroup> Sub<&AuthenticatedDensePoly<C>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: &AuthenticatedDensePoly<C>) -> Self::Output

Performs the - operation.

impl<'a, C: CurveGroup> Sub<&'a AuthenticatedDensePoly<C>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: &'a AuthenticatedDensePoly<C>) -> Self::Output

Performs the - operation.

impl<C: CurveGroup> Sub<&DensePolynomial<<C as Group>::ScalarField>> for &AuthenticatedDensePoly<C>

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: &DensePolynomial<C::ScalarField>) -> Self::Output

Performs the - operation.

impl<'a, C: CurveGroup> Sub<&'a DensePolynomial<<C as Group>::ScalarField>> for AuthenticatedDensePoly<C>

lhs owned, rhs borrowed

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: &'a DensePolynomial<C::ScalarField>) -> Self::Output

Performs the - operation.

impl<'a, C: CurveGroup> Sub<AuthenticatedDensePoly<C>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the - operation.

impl<'a, C: CurveGroup> Sub<DensePolynomial<<C as Group>::ScalarField>> for &'a AuthenticatedDensePoly<C>

lhs borrowed, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: DensePolynomial<C::ScalarField>) -> Self::Output

Performs the - operation.

impl<C: CurveGroup> Sub<DensePolynomial<<C as Group>::ScalarField>> for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: DensePolynomial<C::ScalarField>) -> Self::Output

Performs the - operation.

impl<C: CurveGroup> Sub for AuthenticatedDensePoly<C>

lhs owned, rhs owned

type Output = AuthenticatedDensePoly<C>

The resulting type after applying the - operator.

fn sub(self, rhs: AuthenticatedDensePoly<C>) -> Self::Output

Performs the - operation.