Class: FROST::Polynomial

Inherits:
Object
  • Object
show all
Defined in:
lib/frost/polynomial.rb

Overview

Polynomial class.

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(coefficients, group) ⇒ Polynomial

Generate polynomial. The first is the constant term, followed by the coefficients in descending order of order.

Parameters:

  • coefficients (Array) —

    Coefficients of polynomial.

  • group (ECDSA::Group)

Raises:

  • (ArgumentError) 


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# File 'lib/frost/polynomial.rb', line 12

def initialize(coefficients, group)
  raise ArgumentError, "coefficients must be an Array." unless coefficients.is_a?(Array)
  raise ArgumentError, "group must be ECDSA::Group." unless group.is_a?(ECDSA::Group)
  raise ArgumentError, "Two or more coefficients are required." if coefficients.length < 2

  @coefficients = coefficients
  @group = group
end

Instance Attribute Details

#coefficients ⇒ Object (readonly)

Returns the value of attribute coefficients.



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# File 'lib/frost/polynomial.rb', line 5

def coefficients
  @coefficients
end

#group ⇒ Object (readonly)

Returns the value of attribute group.



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# File 'lib/frost/polynomial.rb', line 6

def group
  @group
end

Class Method Details

.derive_interpolating_value(x_coordinates, xi, group, x: nil) ⇒ Integer

Generates the lagrange coefficient for the i’th participant. The Lagrange polynomial for a set of points (xj, yj) for 0 <= j <= k is ∑_i=0^k yi.ℓi(x), where ℓi(x) is the Lagrange basis polynomial: ℓi(x) = ∏_j≠i (x - xj) / (xi - xj). This computes ℓj(x) for the set of points ‘xs` and for the j corresponding to the given xj.

Parameters:

  • x_coordinates (Array) —

    The list of x-coordinates.

  • xi (Integer) —

    an x-coordinate contained in x_coordinates.

  • group (ECDSA::Group) —

    Elliptic curve group.

  • x (Integer) (defaults to: nil) —

    (Optional) if x is nil, it uses 0 for it (since Identifiers can’t be 0).

Returns:

  • (Integer) —

    The lagrange coefficient.

Raises:

  • (ArgumentError) 


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# File 'lib/frost/polynomial.rb', line 87

def self.derive_interpolating_value(x_coordinates, xi, group, x: nil)
  raise ArgumentError, "xi is not included in x_coordinates." unless x_coordinates.include?(xi)
  raise ArgumentError, "Duplicate values in x_coordinates." if (x_coordinates.length - x_coordinates.uniq.length) > 0
  raise ArgumentError, "group must be ECDSA::Group." unless group.is_a?(ECDSA::Group)
  raise ArgumentError, "x must be Integer." if x && !x.is_a?(Integer)

  field = ECDSA::PrimeField.new(group.order)
  numerator = 1
  denominator = 1

  x_coordinates.each do |xj|
    next if xi == xj
    if x
      numerator *= (x - xj)
      denominator *= (xi - xj)
    else
      numerator *= xj
      denominator *= (xj - xi)
    end
  end

  field.mod(numerator * field.inverse(denominator))
end

.from_secret(secret, degree, group) ⇒ FROST::Polynomial

Generate random polynomial using secret as constant term.

Parameters:

  • secret (Integer|FROST::SigningKey) —

    Secret value as constant term.

  • degree (Integer) —

    Degree of polynomial.

Returns:

Raises:

  • (ArgumentError) 


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# File 'lib/frost/polynomial.rb', line 25

def self.from_secret(secret, degree, group)
  secret = secret.scalar if secret.is_a?(FROST::SigningKey)
  raise ArgumentError, "secret must be Integer." unless secret.is_a?(Integer)
  raise ArgumentError, "degree must be Integer." unless degree.is_a?(Integer)
  raise ArgumentError, "degree must be greater than or equal to 1." if degree < 1
  coeffs = degree.times.map {SecureRandom.random_number(group.order - 1)}
  Polynomial.new(coeffs.prepend(secret), group)
end

Instance Method Details

#gen_commitments ⇒ Array

Generate coefficient commitments

Returns:

  • (Array) —

    A list of coefficient commitment (ECDSA::Point).



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# File 'lib/frost/polynomial.rb', line 54

def gen_commitments
  coefficients.map{|c| group.generator * c }
end

#gen_proof_of_knowledge(identifier) ⇒ FROST::Signature

Generate proof of knowledge for secret.

Parameters:

  • identifier (Integer) —

    Identifier of the owner of this polynomial.

Returns:



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# File 'lib/frost/polynomial.rb', line 61

def gen_proof_of_knowledge(identifier)
  FROST::DKG.gen_proof_of_knowledge(identifier, self)
end

#gen_share(identifier) ⇒ FROST::SecretShare

Generate secret share.

Parameters:

  • identifier (Integer) —

    Identifier for evaluating polynomials.

Returns:

Raises:

  • (ArgumentError) 


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# File 'lib/frost/polynomial.rb', line 37

def gen_share(identifier)
  raise ArgumentError, "identifiers must be Integer." unless identifier.is_a?(Integer)

  return SecretShare.new(identifier, 0, group) if coefficients.empty?
  return SecretShare.new(identifier, coefficients.last, group) if identifier == 0

  # Calculate using Horner's method.
  last = coefficients.last
  (coefficients.length - 2).step(0, -1) do |i|
    tmp = last * identifier
    last = (tmp + coefficients[i]) % group.order
  end
  SecretShare.new(identifier, last, group)
end

#secret ⇒ Integer

Get secret value in this polynomial.

Returns:

  • (Integer) —

    secret



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# File 'lib/frost/polynomial.rb', line 67

def secret
  coefficients.first
end

#verification_point ⇒ ECDSA::Point

Get point to correspond to secret in this polynomial.

Returns:

  • (ECDSA::Point) —

    secret point



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# File 'lib/frost/polynomial.rb', line 73

def verification_point
  group.generator * secret
end