What is X.509 and how does one use it?

What is X.509?

How 开发者_如何学编程does one use it in REST web service for authentication?

X.509

As stated above in comments your question is too bread. I assume that you mean authetication using SSL with Client Authentication. But may be you mean something else...

Anyway, Basically you need to configure SSL with Client Authentication. Most servlet containers (like Tomcat) or Web Servers (like Apache) can do it for you.

Here's guide how to configure SSL in Tomcat. Pay attention that clientAuth should be true,