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Class BSV::Primitives::Polynomial

Inherits: Object

A polynomial defined by a set of points, evaluated using Lagrange interpolation.

Used in Shamir's Secret Sharing Scheme to split and reconstruct a secret. All arithmetic is performed in the finite field GF(P) where P is the secp256k1 field prime.

The secret is encoded as the y-value at x=0. Given threshold distinct points the polynomial can be evaluated at any x by Lagrange interpolation.

@example Construct shares from a private key 

poly   = Polynomial.from_private_key(key, threshold: 2)
share1 = poly.value_at(OpenSSL::BN.new('1'))
share0 = poly.value_at(OpenSSL::BN.new('0'))  # recovers the secret

Constants

P

Not documented.

Attributes

points [R]

  • @return [Array] the defining points of the polynomial

threshold [R]

  • @return [Integer] the minimum number of shares needed to reconstruct the secret

Public Class Methods

from_private_key(key, threshold:)

Build a polynomial whose y-intercept (secret) is the private key scalar.

The first point is (0, key_scalar). The remaining threshold-1 points have random coordinates in [0, P), providing the random coefficients of the underlying polynomial. - @param key [PrivateKey] the private key to split - @param threshold [Integer] the reconstruction threshold (minimum 2) - @return [Polynomial]

Public Instance Methods

initialize(points, threshold = nil)

  • @param points [Array] defining points
  • @param threshold [Integer] reconstruction threshold (defaults to points.length)
  • @return [Polynomial] a new instance of Polynomial

value_at(x)

Evaluate the polynomial at x using Lagrange interpolation mod P. - @param x [OpenSSL::BN] the x value at which to evaluate - @return [OpenSSL::BN] the y value, in [0, P)