Licensing system for client side code web application

I have a client-side web application running on SharePoint Site Collection, each site collection has it's own unique id. I want to use a licensing process to lock the app to a site collection.

This is the challenge-response process I'm trying to implement:

• User prompted to generate challenge code
• challenge code is site_collection_id processed through some function
• User emails me challenge code
• Encrypt challenge code with a private key
• The encrypted result is considered the license key which I send to user
• User saves license key into the application

Validation Process:

• On app load, retrieve license key
• Decrypt license key using a public key stored in app
• The result is the challenge code the user had sent before
• Take that challenge code revert it back to a site collection id
• Retrieve the site collection id app is currently running on
• Compare the two to determine if license key is valid

Does this make sense? The one thing I'm not sure about is the public/private key stuff and if there's a way to do this in JavaScript.

I know it's impossible to 100% secure client-side applications. I'm just looking for something to prevent someone from easily distributing the application