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Terminology
•Subject (principal) - the user; the entity being authenticated.  The subject could be a human, but could also be some other kind of entity, such as a company or a computer.
–Note: I will use "subject" and "user" interchangeably.
•Asserting party (SAML authority) - a system entity that makes SAML assertions.
–Also called the Identity Provider (IdP).
•Relying party (SAML requestor) - a system entity that uses the received assertions.
–Also called the Service Provider (SP).