Fred, Jesus would build upon what God revealed to Peter.. Thou art the Christ, the Son of the living God.
And Christ said: And I will give unto thee the keys of the kingdom of heaven: The keys to heaven are that which opens the door to heaven, and can not be open by man... Christ The Anointed One
Peter's authority was exercised in Act 2 in Israel and in Acts 10 among the Gentiles. The Holy Spirit was the leader and directed Peter in every case. (God hath shewed me)
His disciples were endued with power from God. Noting that they would be witnesses of Christ (Luke 24:48)
Luke 24:49 And, behold, I send the promise of my Father upon you: but tarry ye in the city of Jerusalem, until ye be endued with power from on high.