I think the specific dependency on Rails 3.2.12 on authentify gem is the reason of conflict.
Solution 1: Direct fix
The most intuitive solution would be changing this hard dependency. Say, revise the gemspec as rails, '> 3.2'
.
However, your authentify gem itself may not be ready for Rails 4 yet. So using this would be a bit aggressive.
Solution 2: Use git brach
The better alternative is to add a branch in authentify gem say "rails-4", then change the gemspec as above.
Then you need to specify this git branch in Gemfile.
If you use Github to host this gem
gem 'authentify', git: 'git://github.com/username/authentify', branch: 'rails-4'
If you are not going to opensource this gem, you can still use local path. But you need to setup Bundle to recognize it.
$ bundle config local.authentify ~/Work/git/authentify
Then set it in Gemfile
# gem 'authentify', :github => 'authentify/authentify', :branch => 'master'
I commented out the last line of code because I just copied it from Bundle doc but not verified that before. You can check the doc and experiment by yourself. http://bundler.io/v1.2/git.html