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In RFC 6960 4.2.2.3. Basic Response the response components are defined. This list does not contain the OCSP Responders certificate. If the responder is a delegate, the requester does not have a copy of the responders certificate up-front. How can it be able to validate the response and check for id-kp-OCSPSigning in the OCSP response signer's certificate?

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Actually, the bullet list does not contain the certs. But directly underneath it is mentioned:

The responder MAY include certificates in the certs field of
BasicOCSPResponse that help the OCSP client verify the responder's
signature.

And in B.1. OCSP in ASN.1 - 1998 Syntax

BasicOCSPResponse ::= SEQUENCE {
  tbsResponseData          ResponseData,
  signatureAlgorithm       AlgorithmIdentifier,
  signature                BIT STRING,
  certs                [0] EXPLICIT SEQUENCE OF Certificate OPTIONAL }

Thus the answer to my question is: The client looks for a certificate in the certs list of the response that matches the ResponderID in either name or key hash:

o either the name of the responder or a hash of the responder's public key as the ResponderID;

Then it validates the chain to verify that the response was signed by a trusted or authorized responder.

I found it helpful to review the Verify existing OCSP Basic Response implementation in PKI.js

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