楕円曲線上の法の有限体で足し算とかけ算

ECC_point.rb

module ECC
  class ECC_Point

    def initialize(x, y)
      @x = reduce(x, MOD)
      @y = reduce(y, MOD)
    end
    
    def zero?
      (@x == 0 && @y == 0)
    end

    def validPoint?
      EC_func::l(@y) % MOD == EC_func::r(@x) % MOD
    end

    def multipl(k)
      bin = reduce(k, ORD).to_s(2)
      rev = bin.reverse
      res = (rev[0].chr == '1') ? self : ECC::ECC_Point.new(0, 0)
      w = [self]
      (1..(rev.size-1)).each do |i|
        w[i] = w[i-1].add(w[i-1])
        res = res.add(w[i]) if rev[i].chr == '1'
      end
      res
    end

    def to_s
      "#{@x}, #{@y}"
    end

    def rev(n)
      raise "bud input" if n % MOD == 0
      r = [MOD, reduce(n, MOD)]
      q = [0, 0]
      x = [1, 0]
      y = [0, 1]
      (2..99).each do |i|
        r[i] = r[i-2] % r[i-1]
        return reduce( y[i-1] , MOD) if r[i] == 0 
        q[i] = ( r[i-2] - r[i] ) / r[i-1]
        x[i] = x[i-2] - q[i] * x[i-1]
        y[i] = y[i-2] - q[i] * y[i-1]
      end
      raise 'loop too short'
    end

    def add(other)
      return self if other.zero?
      return other if zero?
      raise "something wrong" if @x == other.x && @y != other.y

      if @x == other.x && @y == other.y
        return ECC::ECC_Point.new(0, 0) if (@y * 2) % MOD == 0
        l = EC_func.dif_r(@x) * rev(EC_func.dif_l(@y))
      else
        l = (other.y - @y) * rev(other.x - @x)
      end
      tx = (l % MOD)**2 - @x - other.x
      ECC::ECC_Point.new(reduce(tx, MOD), reduce(l * (@x-tx) - @y, MOD))
    end

    def reduce(n, mod)
      return n % mod if n >= 0
      return ((n.abs/mod).ceil * mod + n) % mod
    end

    attr_reader:x
    attr_reader:y

  end
end