射影座標を使ったスカラー倍算サンプル

projective_point.rb

require 'ecdsa'

class ProjectivePoint

  attr_reader :x
  attr_reader :y
  attr_reader :z
  attr_reader :field

  def initialize(x, y ,z)
    @x =x
    @y = y
    @z = z
    @field = ECDSA::Group::Secp256k1.field
  end

  # Convert coordinate from affine
  def self.from_affine(x, y)
    new(x, y, 1)
  end

  def self.infinity
    new(0, 1, 0)
  end

  def infinity?
    x == 0 && z == 0
  end

  def add(other)
    return other if infinity?
    t0 = field.mod(y * other.z)
    t1 = field.mod(other.y * z)
    u0 = field.mod(x * other.z)
    u1 = field.mod(other.x * z)
    return double if u0 == u1 && t0 == t1
    t = field.mod(t0 - t1)
    u = field.mod(u0 - u1)
    u2 = field.mod(u * u)
    v = field.mod(z * other.z)
    w = field.mod(t * t* v - u2 * (u0 + u1))
    u3 = field.mod(u * u2)
    new_x = field.mod(u * w)
    new_y = field.mod(t * (u0 * u2 - w) - t0 * u3)
    new_z = field.mod(u3 * v)
    ProjectivePoint.new(new_x, new_y, new_z)
  end

  def double
    w = field.mod(3 * x**2)
    s = field.mod(y * z)
    b = field.mod(s * x * y)
    h = field.mod(w**2 - 8 * b)
    new_x = field.mod(2 * h * s)
    new_y = field.mod(w * (4 * b - h) - 8 * y**2 * s**2)
    new_z = field.mod(8 * s**3)
    ProjectivePoint.new(new_x, new_y, new_z)
  end

  def to_affine
    ECDSA::Point.new(ECDSA::Group::Secp256k1, field.mod(x * field.inverse(z)), field.mod(y * field.inverse(z)))
  end

  def multiply_by_scalar(x)
    q = ProjectivePoint.infinity
    v = self
    i = x
    while i > 0
      q = q.add(v) if i.odd?
      v = v.double
      i >>= 1
    end
    q
  end

end