1. An assertion signed by the SAML authority supports:
– Assertion integrity.
– Authentication of the SAML authority to a SAML relying party.
– If the signature is based on the SAML authority’s public-private key pair, then it also provides for non-repudiation of origin.
2. A SAML protocol request or response message signed by the message originator supports:
– Message integrity.
– Authentication of message origin to a destination.
– If the signature is based on the originator's public-private key pair, then it also provides for non-repudiation of origin.
The  talks about only signing the Assertion - and  talks about signing the request as well as the response message which also carries the Assertion.
A digital signature is not always required in SAML. For example, it may not be required in the following situations:
- In some circumstances signatures may be “inherited," such as when an unsigned assertion gains protection from a signature on the containing protocol response message. "Inherited" signatures should be used with care when the contained object (such as the assertion) is intended to have non-transitory lifetime. The reason is that the entire context must be retained to allow validation, exposing the XML content and adding potentially unnecessary overhead.
- The SAML relying party or SAML requester may have obtained an assertion or protocol message from the SAML authority or SAML responder directly (with no intermediaries) through a secured channel, with the SAML authority or SAML responder having authenticated to the relying party or SAML responder by some means other than a digital signature.
It is recommended that, in all other contexts, digital signatures be used for assertions and request and response messages. Specifically:
- A SAML assertion obtained by a SAML relying party from an entity other than the SAML authority SHOULD be signed by the SAML authority.
- A SAML protocol message arriving at a destination from an entity other than the originating site SHOULD be signed by the origin site.
XML Signatures are intended to be the primary SAML signature mechanism.
Unless a profile specifies an alternative signature mechanism, enveloped XML Digital Signatures MUST be used if signing. This is bit different from the signature pattern recommended in WS-Security specification.
WS-Security specification says..
"Because of the mutability of some SOAP headers, producers SHOULD NOT use the Enveloped Signature Transform defined in XML Signature. Instead, messages SHOULD explicitly include the elements to be signed. Similarly, producers SHOULD NOT use the Enveloping Signature defined in XML Signature".
Although this contrasts with what is recommended in SAML specification - WS-Security doesn't have nothing to with SAML. SAML becomes a token type for WS-Security and SAML specification has the full control to define it's own recommendation for signing.
Why SAML specification recommends enveloped signature?
With enveloped signature, the signature element will be inside the element been signed it self - which is the Assertion element.
Enveloped signature is useful when we have a signed XML document that we wish to insert into other XML documents. Which is the case with SAML Assertion. There you get the SAML Assertion from the issuer and include it in to a request to the service provider.
SAML implementations also SHOULD use Exclusive Canonicalization [Excl-C14N], with or without comments, both in the
Exclusive Canonicalization tries to figure out what namespaces you are actually using and just copies those. Specifically, it copies the ones that are "visibly used", which means the ones that are a part of the XML syntax. However, it does not look into attribute values or element content, so the namespace declarations required to process these are not copied. For example if you had an attribute like xx:foo="yy:bar" it would copy the declaration for xx, but not yy. It also does not copy the xml: attributes that are declared outside the scope of the signature.
Exclusive Canonicalization allows you to create a list of the namespaces that must be declared, so that it will pick up the declarations for the ones that are not visibly used.
Exclusive Canonicalization is useful when you have a signed XML document that you wish to insert into other XML documents - as in a signed SAML assertion which might be inserted as a XML Token in the security header of various SOAP messages. The Issuer who signs the assertion will be aware of the namespaces being used and able to construct the list. The use of Exclusive Canonicalization will insure the signature verifies correctly every time.
In contrast, the Inclusive Canonicalization copies all the declarations that are currently in force, even if they are defined outside of the scope of the signature. It also copies any xml: attributes that are in force, such as xml:lang or xml:base. This guarantees that all the declarations you might make use of will be unambigiously specified. The problem with this is that if the signed XML is moved into another XML document which has other declarations, the Inclusive Canonicalization will copy them and the signature will be invalid. This can even happen if you simply add an attribute in a different namespace to the surrounding context.