Struct Poly 

pub struct Poly { /* private fields */ }

A univariate polynomial in the prime field.

Polynomials are used for secret sharing in threshold cryptography. A polynomial of degree t can be used to create n shares such that any t + 1 shares can reconstruct the secret (the polynomial’s value at 0).

Example

use threshold_pairing::poly::Poly;

// Create a random polynomial of degree 2
let mut rng = rand::thread_rng();
let poly = Poly::random(2, &mut rng);

// Evaluate the polynomial at different points
let y1 = poly.evaluate(1u64);
let y2 = poly.evaluate(2u64);

// Get the corresponding public commitment
let commitment = poly.commitment();
assert_eq!(poly.degree(), commitment.degree());

Security

The polynomial coefficients are zeroized on drop to prevent secret leakage.

Implementations

impl Poly

pub fn random<R: RngCore>(degree: usize, rng: &mut R) -> Self

Creates a random polynomial.

Panics

Panics if the degree is too large for the coefficients to fit into a Vec.

pub fn try_random<R: RngCore>(degree: usize, rng: &mut R) -> Result<Self>

Creates a random polynomial. This constructor is identical to the Poly::random() constructor in every way except that this constructor will return an Err where try_random would return an error.

pub fn zero() -> Self

Returns the polynomial with constant value 0.

pub fn is_zero(&self) -> bool

Returns true if the polynomial is the constant value 0.

pub fn one() -> Self

Returns the polynomial with constant value 1.

pub fn constant(c: Scalar) -> Self

Returns the polynomial with constant value c.

pub fn identity() -> Self

Returns the identity function, i.e. the polynomial “x”.

pub fn monomial(degree: usize) -> Self

Returns the (monic) monomial: x.pow(degree).

pub fn interpolate<T, U, I>(samples_repr: I) -> Self

where I: IntoIterator<Item = (T, U)>, T: IntoScalar, U: IntoScalar,

Returns the unique polynomial f of degree samples.len() - 1 with the given values (x, f(x)).

pub fn degree(&self) -> usize

Returns the degree.

pub fn evaluate<T: IntoScalar>(&self, i: T) -> Scalar

Returns the value at the point i.

pub fn commitment(&self) -> Commitment

Returns the corresponding commitment.

Trait Implementations

impl<B: Borrow<Poly>> Add<B> for &Poly

type Output = Poly

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Poly

Performs the + operation.

impl<B: Borrow<Poly>> Add<B> for Poly

type Output = Poly

The resulting type after applying the + operator.

fn add(self, rhs: B) -> Poly

Performs the + operation.

impl Add<Scalar> for Poly

type Output = Poly

The resulting type after applying the + operator.

fn add(self, rhs: Scalar) -> Self::Output

Performs the + operation.

impl Add<u64> for Poly

type Output = Poly

The resulting type after applying the + operator.

fn add(self, rhs: u64) -> Self::Output

Performs the + operation.

impl<B: Borrow<Poly>> AddAssign<B> for Poly

fn add_assign(&mut self, rhs: B)

Performs the += operation.

impl Clone for Poly

fn clone(&self) -> Poly

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Poly

A debug statement where the coeff vector of prime field elements has been redacted.

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for Poly

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Drop for Poly

fn drop(&mut self)

Executes the destructor for this type.

impl From<Poly> for SecretKeySet

fn from(poly: Poly) -> SecretKeySet

Converts to this type from the input type.

impl From<Vec<Scalar>> for Poly

Creates a new Poly instance from a vector of prime field elements representing the coefficients of the polynomial.

fn from(coeff: Vec<Scalar>) -> Self

Converts to this type from the input type.

impl<'a> Mul<&'a Scalar> for &'a Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<&Scalar> for Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl<B: Borrow<Poly>> Mul<B> for &Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl<B: Borrow<Poly>> Mul<B> for Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: B) -> Self::Output

Performs the * operation.

impl Mul<Scalar> for &Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Scalar> for Poly

type Output = Poly

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<u64> for Poly

type Output = Poly

The resulting type after applying the * operator.

fn mul(self, rhs: u64) -> Self::Output

Performs the * operation.

impl<B: Borrow<Self>> MulAssign<B> for Poly

fn mul_assign(&mut self, rhs: B)

Performs the *= operation.

impl MulAssign<Scalar> for Poly

fn mul_assign(&mut self, rhs: Scalar)

Performs the *= operation.

impl PartialEq for Poly

fn eq(&self, other: &Poly) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for Poly

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<B: Borrow<Poly>> Sub<B> for &Poly

type Output = Poly

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Poly

Performs the - operation.

impl<B: Borrow<Poly>> Sub<B> for Poly

type Output = Poly

The resulting type after applying the - operator.

fn sub(self, rhs: B) -> Poly

Performs the - operation.

impl Sub<Scalar> for Poly

type Output = Poly

The resulting type after applying the - operator.

fn sub(self, rhs: Scalar) -> Self::Output

Performs the - operation.

impl Sub<u64> for Poly

type Output = Poly

The resulting type after applying the - operator.

fn sub(self, rhs: u64) -> Self::Output

Performs the - operation.

impl<B: Borrow<Poly>> SubAssign<B> for Poly

fn sub_assign(&mut self, rhs: B)

Performs the -= operation.

impl Zeroize for Poly

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl Eq for Poly

impl StructuralPartialEq for Poly