Obviously Christ is the head of the Church.
Who did he give the keys to the Kingdom to?
All the Apostles, and through them all - the church.
17. He has given, therefore, the keys to His Church, that whatsoever it should bind on earth might be bound in heaven, and whatsoever it should loose on earth might be loosed in heaven; that is to say, that whosoever in the Church should not believe that his sins are remitted, they should not be remitted to him; but that whosoever should believe and should repent, and turn from his sins, should be saved by the same faith and repentance on the ground of which he is received into the bosom of the Church. For he who does not believe that his sins can be pardoned, falls into despair, and becomes worse as if no greater good remained for him than to be evil, when he has ceased to have faith in the results of his own repentance.
Augustine City of God
Augustine notes that the keys are given to the whole church
"He has given, therefore, the keys to His Church, that whatsoever it should bind on earth might be bound in heaven, and whatsoever it should loose on earth might be, loosed in heaven"
"On Christian Doctrine"
Book I, Chapter 18.17
and again...
"...the keys that were given to the Church,"
A Treatise Concerning the Correction of the Donatists
Chapter 10.45
and
"How the Church? Why, to her it was said, "To thee I will give the keys of the kingdom of heaven, and whatsoever thou shall loose on earth shall be loosed in heaven, and whatsoever thou shall bind on earth shall be bound in heaven."
"Ten Homilies on the First Epistle of John"
Homily X.10
Cyprian
Cyprian acknowledges, of course, that Peter was the first to get the keys, but then adds
"Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity."
On the Unity of the Church Treatise I.4
John Cassian
But what are the other words which follow that saying of the Lord's, with which He commends Peter? "And I," said He, "say unto thee, that thou art Peter and upon this rock I will build My Church." Do you see how the saying of Peter is the faith of the Church? He then must of course be outside the Church, who does not hold the faith of the Church. "And to thee," saith the Lord, "I will give the keys of the kingdom of heaven." This faith deserved heaven: this faith received the keys of the heavenly kingdom. See what awaits you. You cannot enter the gate to which this key belongs, if you have denied the faith of this key. "And the gate," He adds, "of hell shall not prevail against thee." The gates of hell are the belief or rather the misbelief of heretics. For widely as hell is separated from heaven, so widely is he who denies from him who confessed that Christ is God. "Whatsoever," He proceeds, "thou shalt bind on earth, shalt be bound in heaven, and whatsoever thou shalt loose on earth, shalt be loosed also in heaven." The perfect faith of the Apostle somehow is given the power of Deity, that what it should bind or loose on earth, might be bound or loosed in heaven. For you then, who come against the Apostle's faith, as you see that already you are bound on earth, it only remains that you should know that you are bound also in heaven. But it would take too long to go into details which are so numerous as to make a long and wearisome story, even if they are related with brevity and conciseness."
"On the Incarnation of the Lord, Against Nestorius"
Book III
Chapter XIV "How the confession of the blessed Peter is the faith of the whole Church."
John Chrysostom
For the Son of thunder (John the Apostle), the beloved of Christ, the pillar of the Churches throughout the world, who holds the keys of heaven, who drank the cup of Christ, and was baptized with His baptism, who lay upon his Masters bosom, with much confidence, this man now comes forward to us now
Homilies on the Gospel of John, Homily 1.1
