I'm rather new to EE, and I'm having a hard time finding some stuff in it. I started working on a legacy site that is pure EE template and for every validation it goes to a new page. I'm wanting to use jQuery/Ajax/EE for validation, but I can't find the function that would validate the data on submission. I also want to know what is EE using to hash the passwords so I can correctly hash before I send to the server. If anyone can provide a link or an answer I would be very grateful.
If I understand you correctly then you don't really need to know what function EE is using but simply submit your login form via Ajax to the URL it would normally submit to.
You might also want to look at these add-ons. Some of them cost a few dollars but they will probably cost less than the time you will spend on trying to create the same functionality.