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Consider this scenario:

  • Alice sends a message signed under her public key to Bob.
  • Bob has never exchanged a keys with Alice.
  • Alice's key is signed by a certain X.
  • X's key is signed by Y, an entity that Bob trusts.

Is Alice's key valid or not for Bob?

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  • $\begingroup$ Please someone correct me if I'm wrong, but I think this is in fact how CAs work: A root CA (Y in your example) signs the key of a subordinate CA (X in your example), which now can issue certificates. In some sense, Y is authorizing X to do this, so if Y is trusted X should be trusted as well. $\endgroup$ – Daniel Feb 4 '18 at 14:37
  • $\begingroup$ This sounds a lot like PGP's web of trust (en.wikipedia.org/wiki/Web_of_trust) $\endgroup$ – Eugene Styer Feb 4 '18 at 18:28
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    $\begingroup$ Isn't this something for security.SE? In any case, I think the definition of "to trust" is indeed underspecified. X.509 Certificates get signed for a specific usage (i.e., allowed to sign other certs, allowed for HTTPS, ...). In PGP, trust "fades out" after a few hops, and has also multiple levels. $\endgroup$ – Ruben De Smet Feb 5 '18 at 10:12
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This very much depends on what you mean by

Bob trusts Y.

If Y is a root CA and Bob "trusts" them to do their job properly, then yes he would trust Alice's key. This is because the job of a root CA is exactly discerning whether a subordinate CA (in this case X) should be trusted to in turn do their job: I.e., check people's identity and sign their public keys if and only if they can be certain beyond reasonable doubt that the person presenting the public key is in possession of the corresponding secret key and that they are the entity they claim to be.

If on the other hand Y is just some random friend ob Bob, whom he trusts in the sense that they are sure that the key they is theirs and they probably genuinely believe whatever it is they signed with that key, then no, this is no basis to trust Alice's key. In fact in general Bob has no way of telling in what context and why Y ever signed X's key.

Which means that we lack the necessary information to answer the question, because the statement "Bob trusts Y." is underspecified.

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we trust Y so the X's key is good! But we can not deduce a trust in X. The latter can sign anything and claim that it is the Alice's key.

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