Simple math captcha for Rails Fixed version of http://blog.trikeapps.com/2010/12/20/secure-form-with-math-captcha.html Tested on Rails 3.2.13 and Ruby 2.0.0 P.S. don't forget to include math_captcha.rb to included paths.

controller.rb

require 'math_captcha'

class CarsController < ApplicationController

  # GET|POST /order
  def order
    @item = Item.find(params[:id])

    if request.get?
      @form = ModellessForm.new
      @captcha = MathCaptcha.new

      respond_with @item
    else
      @form = ModellessForm.new(params[:order_car_form])
      @captcha = MathCaptcha.decrypt(@form.captcha_secret)

      if @order_car_form.valid? and @captcha.correct?(@form.captcha)
      
      else
        unless @captcha.correct?(@form.captcha)
          @order_car_form.errors[:captcha] << I18n.t(:verification_failed, :scope => [:math_captcha, :errors])
        end
        @captcha = MathCaptcha.new

        respond_with @item
      end
    end
  end

end

math_captcha.rb

require 'ezcrypto'

class MathCaptcha
  CIPHER_KEY  = "your cipher key"
  CIPHER_SALT = "your cipher salt"
  NUMBERS = (1..100).to_a

  attr_reader :a, :b, :operator

  def initialize
    @a        = NUMBERS.sample
    @b        = NUMBERS.sample
    @operator = [:+, :-].sample
  end

  def initialize_from(secret)
    yml = YAML.load(key.decrypt64(secret))
    @a, @b, @operator = yml[:a], yml[:b], yml[:operator]
  end

  def correct?(value)
    result.to_i == value.to_i
  end

  def encrypt
    key.encrypt64 to_yaml
  end

  def self.decrypt(secret)
    result = new
    result.initialize_from secret
    result
  end

  def question
    "#{@a} #{@operator.to_s} #{@b} = ?"
  end

  def to_i
    result
  end

protected

  def to_yaml
    YAML::dump({
      :a        => @a,
      :b        => @b,
      :operator => @operator
    })
  end

private

  def key
    EzCrypto::Key.with_password CIPHER_KEY, CIPHER_SALT
  end

  def result
    @a.send(@operator, @b)
  end

end

model.rb

class ModellessForm
  include ActiveModel::Validations
  include ActiveModel::Conversion

  attr_accessor :captcha, :captcha_secret

  validates :captcha, :numericality => true,
                      :presence => true

  def initialize(attributes = {})
    attributes.each do |name, value|
      send("#{name}=", value)
    end
  end

  def persisted?
    false
  end
end

ru.yml

ru:
  math_captcha:
    errors:
      verification_failed: "неправильный ответ"

view.html.erb

<%# using Formtastic gem %>
<%= f.input :captcha, :as => :string, :required => false, :label => @captcha.question, :input_html => { :value => '' } %>
<%= f.input :captcha_secret, :as => :hidden, :input_html => { :value => @captcha.encrypt } %>