Jerome ties the idea of Christ and the confession with "Christ the Rock" (though not explicitly here).
Chrysostom:
That is, On this faith and confession I will build my Church. Herein shewing that many should believe what Peter had confessed, and raising his understanding, and making him His shepherd.
Augustine
I have said in a certain place of the Apostle Peter, that it was on him, as on a rock, that the Church was built. but I know that since that I have often explained these words of the Lord, “Thou art Peter, and on this rock will I build my Church,” as meaning upon Him whom Peter had confessed in the words, “Thou art Christ, the Son of the living God;: and so that Peter, taking his name from this rock, would represent the Church, which is built upon this rock. For it is not said to him, Thou art the rock, but, “Thou art Peter.” But the rock was Christ, [1 Cor 10:4] whom because Simon thus confessed, as the whole Church confesses Him, he was named Peter. Let the reader choose whether of these two opinions seems to him the more probable.
Origen
Wherefore if we, by the revelation of our Father who is in heaven, shall confess that Jesus Christ is the Son of God, having also our conversation in heaven, to us also shall be said, “Thou art Peter;” for every one is a Rock who is an imitator of Christ. But against whomsoever the gates of hell prevail, he is neither to be called a rock upon which Christ builds His Church; neither a Church, or part of the Church, which Christ builds upon a rock.
More Jerome (which I found intresting):
Bishops and Presbyters, not understanding this passage, assume to themselves something of the lofty pretensions of the Pharisees, and suppose that they may either condemn the innocent, or absolve the guilty; whereas what will be enquired into before the Lord will be not the sentence of the Priests, but the life of him that is being judged.
We read in Leviticus of the lepers, how they are commanded to shew themselves to the Priests; and if they have the leprosy, then they are made unclean by the Priest; not that the Priest makes them leprous and unclean, but that the Priest has knowledge of what is leprosy and what is not leprosy, and can discern who is clean, and who is unclean. In the same way then as there the Priest makes the leper unclean, here the Bishop or Presbyter binds or looses not those who are without sin, or guilt, but in discharge of his function when he has heard the varieties of their sins, he knows who is to be bound, and who loosed.
Chrysostom again:
“And I say unto thee, Thou art Peter, and upon this rock will I build my Church;” Matt. xvi. 18. that is, on the faith of his confession. Hereby He signifies that many were now on the point of believing, and raises his spirit, and makes him a shepherd. “And the gates of hell shall not prevail against it.” “And if not against it, much more not against me. So be not troubled because thou art shortly to hear that I shall be betrayed and crucified.” (Bold mine)
Gregory VII., in an inscription he sent with a crown to the emperor Rudolph
Petra [i.e., Christ] dedit Petro [i.e., to the apostle], Petrus [the pope] diadema Rudolpho
Origen:
And perhaps that which Simon Peter an swered and said, "Thou art the Christ, the Son of the living God," if we say it as Peter, not by flesh and blood revealing it unto us, but by the light from the Father in heaven shining in our heart, we too become as Peter, being pronounced blessed as he was, because that the grounds on which he was pronounced blessed apply also to us, by reason of the fact that flesh and blood have not revealed to us with regard to Jesus that He is Christ, the Son of the living God, but the Father in heaven, from the very heavens, that our citizenship may be in heaven, revealing to us the revelation which carries up to heaven those who take away every veil from the heart, and receive "the spirit of the wisdom and revelation" of God. And if we too have said like Peter, "Thou art the Christ, the Son of the living God," not as if flesh and blood had revealed it unto us, but by light from the Father in heaven having shone in our heart, we become a Peter, and to us there might be said by the Word, "Thou art Peter," etc. For a rock is every disciple of Christ of whom those drank who drank of the spiritual rock which followed them, and upon every such rock is built every word of the church, add the polity in accordance with it; for in each of the perfect, who have the combination of words and deeds and thoughts which fill up the blessedness, is the church built by God.
But if you suppose that upon that one Peter only the whole church is built by God, what would you say about John the son of thunder or each one of the Apostles? Shall we otherwise dare to say, that against Peter in particular the gates of Hades shall not prevail, but that they shall prevail against the other Apostles and the perfect? Does not the saying previously made, "The gates of Hades shall not prevail against it," hold in regard to all and in the case of each of them? And also the saying, "Upon this rock I will build My church"? Are the keys of the kingdom of heaven given by the Lord to Peter only, and will no other of the blessed receive them? But if this promise, "I will give unto thee the keys of the kingdom of heaven," be common to the others, how shall not all the things previously spoken of, and the things which are subjoined as having been addressed to Peter, be common to them? For in this place these words seem to be addressed as to Peter only, "Whatsoever thou shalt bind on earth shall be bound in heaven," etc; but in the Gospel of John the Saviour having given the Holy Spirit unto the disciples by breathing upon them said, "Receive ye the Holy Spirit," etc.
Many then will say to the Saviour, "Thou art the Christ, the Son of the living God;" but not all who say this will say it to Him, as not at all having learned it by the revelation of flesh and blood but by the Father in heaven Himself taking away the veil that lay upon their heart, in order that after this "with unveiled face reflecting as a mirror the glory of the Lord" they may speak through the Spirit of God saying concerning Him, "Lord Jesus," and to Him, "Thou art the Christ, the Son of the living God." And if any one says this to Him, not by flesh and blood revealing it unto Him but through the Father in heaven, he will obtain the things that were spoken according to the letter of the Gospel to that Peter, but, as the spirit of the Gospel teaches, to every one who becomes such as that Peter was. For all bear the surname of "rock" who are the imitators of Christ, that is, of the spiritual rock which followed those who are being saved, that they may drink from it the spiritual draught. But these bear the surname of the rock just as Christ does.
Finally, Cyprian, Augustine and Jerome say that the keys were given to the church,not just to Peter. But that's just the beginning of the discussion.
Wow! Nice!
First, I have no argument with the distinction, petros vs. petra. (Although it is interesting that in the Aramaic, the word kipa is used for both -- thus the Greek transliteration Cephas, but I digress). I have heard a lot of Protestant ministers say "pebble" versus "boulder" as being the distinction, but I like the disctinction made by Thayer, drawing the image of petros being a boulder (rock) and petra being rocky crag or ledge (e.g., the Rock of Gibralter). It sort of appeals to me as being like our cliche, "A chip off the old block."
As to the discussion of binding and loosing, please refer to Matthew 18:18. Jesus gave that authority to all the apostles (and from thence, the bishops).
Your quote from Origen is interesting, as I haven't seen it before. Could you please provide a citation and perhaps a hotlink? (I tried locating it from a text search and was unable to do so)
What I have seen in Origen regarding the topic is in the Commentary on Matthew, Book XIII, 31:
But to me it seems that, to the case of him who after being thrice admonished was adjudged to be as the Gentile and the publican, it is fitly subjoined, "Verily, I say unto you,"--namely, to those who have judged any one to be as the Gentile and the publican,--"and what things soever ye shall bind on the earth," etc.; for with justice has he, who has thrice admonished and not been heard, bound him who is judged to be as a Gentile and a publican; wherefore, when such an one is bound and condemned by one of this character, he remains bound, as no one of those in heaven overturns the judgment of the man who bound him. And, in like manner, he who was admonished once for all, and did things worthy of being gained, having been set free by the admonition of the man who gained him, and no longer bound by the cords of his own sins, for which he was admonished, shall be adjudged to have been set free by those in heaven. Only, it seems to be indicated that the things, which above were granted to Peter alone, are here given to all who give the three admonitions to all that have sinned; so that, if they be not heard, they will bind on earth him who is judged to be as a Gentile and a publican, as such an one has been bound in heaven. But since it was necessary, even if something in common had been said in the case of Peter and those who had thrice admonished the brethren, that Peter should have some element superior to those who thrice admonished, in the case of Peter, this saying "I will give to thee the keys of the kingdom of the heavens," has been specially set before the words, "And what things soever ye shall bind on earth," etc. And, indeed, if we were to attend carefully to the evangelical writings, we would also find here, and in relation to those things which seem to be common to Peter and those who have thrice admonished the brethren, a great difference and a pre-eminence in the things said to Peter, compared with the second class. For it is no small difference that Peter received the keys not of one heaven but of more, and in order that whatsoever things he binds on the earth may be bound not in one heaven but in them all, as compared with the many who bind on earth and loose on earth, so that these things are bound and loosed not in the heavens, as in the case of Peter, but in one only; for they do not reach so high a stage, with power as Peter to bind and loose in all the heavens. The better, therefore, is the binder, so much more blessed is he who has been loosed, so that in every part of the heavens his loosing has been accomplished