I am reading a paper about key exchange and trying to understand the protocol described in Figure 4 on page 6 in the above paper. I understand the majority of the notation but am having a hard time understanding steps 7 and 11.
It states that PE (device 1) signs some data using its own private key in step 7, and later PV (device 2) verifies this data. How does PV verify the data if it had been signed with PE's private key? Wouldn't it need to be signed with PV's public key, so PV could verify the content with its own private key?
I just do not understand why the signed data is useful to PV.
Sorry if this is a novice question and thanks for any clarifications.