Struct Polynomial 

pub struct Polynomial {
    pub points: Vec<PointInFiniteField>,
    pub threshold: usize,
}

Polynomial over GF(p) represented by its evaluation points.

Used for Lagrange interpolation in Shamir’s Secret Sharing. The polynomial passes through the stored points and can be evaluated at any x value using Lagrange interpolation.

Fields

points: Vec<PointInFiniteField>

threshold: usize

Implementations

impl Polynomial

pub fn new(points: Vec<PointInFiniteField>, threshold: Option<usize>) -> Self

Create a new polynomial from points with optional threshold.

If threshold is not specified, it defaults to the number of points.

pub fn from_private_key(key_bytes: &[u8], threshold: usize) -> Self

Create a polynomial from a private key for Shamir’s Secret Sharing.

The private key value is the y-intercept (x=0, y=key). Additional (threshold - 1) random points are generated.

pub fn value_at(&self, x: &BigNumber) -> BigNumber

Evaluate the polynomial at x using Lagrange interpolation.

Uses the stored points and Lagrange basis polynomials to compute the polynomial’s value at the given x coordinate. All arithmetic is performed mod p (secp256k1 field prime).