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When I looked the digital signature properties of LSASS.EXE, I am presented with this:

Which states Serial Number 33 00 00 ... 00 CC. Fair enough.

When I looked the attached digital certificate properties, what I see is: same.

Which has the exact serial number presented in SIGNATURE. Why is this? Is the serial number part of certificate or signature?

Further, the thumb-print of certificate is mentioned as:

Diff.

Which is a different one.

So, what does uniquely identify a signature - a thumbprint or a serial number?

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None of them. A digital signature does not have a recognizable identifier.

You are seeing in the two forms the serial number of the certificate. The serial number is a unique identifier assigned by the Certificate Authority to the certificate and the thumbprint is a hash of the certificate data.

A signature contains a message digest of the signed data (you can see it in form), signed with the private key of the sender. A digital signature has no a identifier but you can know:

  • the identity of the signatory, because the public key contained in the referenced certificate match with the private key

  • That the message has not been altered, because it will break the signature

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