Shibboleth is primarily built on the SAML standard as defined by the OASIS SSTC working group. Shibboleth also has formal profile and conformance documents that define additional constraints on top of the base standard.
Specifications & Architecture:
- Shibboleth Technical Overview
- Shibboleth Protocol Specification
- Shibboleth Conformance Specification
- SAML 1.1 Assertions, bindings, etc.
In addition to these standards, note that within specific communities of use, additional profiles may be defined to further constrain options, define attributes, etc.