Short answer: check OAUTH, and manage caches of credentials in each microservice that needs to access other microservices. By "manage" I mean, be careful with security. Specially, mind who can access those credentials and let the network topology be your friend. Create a DMZ layer and other internal layers reflecting the dependency graph of your microservices.
Long answer, keep reading. Your question is a good one because there is no simple silver bullet to do what you need although your problem is quite recurrent.
As with everything related with microservices that I saw so far, nothing is really new. Whenever you need to have a distributed system doing things on behalf of a certain user, you need distributed credentials to enable such solution. This is true since mainframe times. There is no way to violate that.
Auto SSH is, in a sense, such a thing. Perhaps it may sound like a glorified way to describe something simple, but in the end, it enables processes in one machine to use services in another machine.
In the Grid world, the Globus Toolkit, for instance, bases its distributed security using the following:
- X.509 certificates;
- MyProxy - manages a repository of credentials and helps you define a chain of certificate authorities up to finding the root one, which should be trusted by default;
- An extension of OpenSSH, which is the de facto standard SSH implementation for Linux distributions.
OAUTH is perhaps what you need. It is a way provide authorization with extra restrictions. For instance, imagine that a certain user has read and write permission on a certain service. When you issue an OAUTH authorization you do not necessarily give full user powers to the third party. You may only give read access.
CORS, mentioned in another answer, is useful when the end client (typically a web browser) needs single-sign-on across web sites. But it seems that your problem is closer to a cluster in which you have many microservices that are managed by you. Nevertheless, you can take advantage of solutions developed by the Grid field to ensure security in a cluster distributed across sites (for high availability reasons, for instance).
Complete security is something unattainable. So all this is of no use if credentials are valid forever or if you do not take enough care to keep them secret to whatever received them. For such purpose, I would recommend partitioning your network using layers. Each layer with a different degree of secrecy and exposure to the outside world.
If you do not want the burden to have the required infrastructure to allow for OAUTH, you can either use basic HTTP or create your own tokens.
When using basic HTTP authentication, the client needs to send credentials on each request, therefore eliminating the need to keep session state on the server side for the purpose of authorization.
If you want to create your own mechanism, then change your login requests such that a token is returned as the response to a successful login. Subsequent requests having the same token will act as the basic HTTP authentication with the advantage that this takes place at the application level (in contrast with the framework or app server level in basic HTTP authentication).