If the token is not stored in the cache then it must be validated. Firstly a check is performed to make sure that the Assertion is signed, if it is not then it is rejected. The signature of the Assertion is then validated using the Crypto object retrieved from the STSPropertiesMBean passed in the TokenValidatorParameters. Finally, trust is verified in the certificate/public-key used to sign the Assertion. This is done using the Validator object that can be configured using setValidator. The default Validator is the WSS4J SignatureTrustValidator, which checks that the received certificate is known (or trusted) by the STS Crypto object.
Recall that a List of Strings can be set on the SAMLTokenValidator using the setSubjectConstraints method. These Strings correspond to regular expression constraints on the subject DN of a certificate that was used to sign an Assertion. This provides additional flexibility to validate a received SAML Assertion. For example, the Assertion could be signed by an entity that has a certificate issued by a particular CA, which in turn is trusted by the STS Crypto object. However, one might want to restrict the list of "valid" entities who can sign a SAML Assertion. This can be done by adding a list of regular expressions that match the Subject DN of all acceptable certificates that might be used to sign a valid SAML Assertion. This matching is done by the CertConstraintsParser.