How does the Orthodox Church interpret Jesus' famous words to St. Peter the Holy Apostle?

Saints Peter and Paul Bulletin
July 22, 2001

St. Augustine (Homily X on John V. 1-3)
See what praises follow this faith.  'Thou art Peter, and upon this rock I will build this Church.'  What meaneth, 'Upon this rock I will build My Church'?  Upon this faith; upon this that has been said, 'Thou art the Christ, the Son of the Living God.  Upon this rock' saith He 'I will builfd My Church.'

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St. Ambrose ("On the Incarnation")
Faith is the foundation of the Church, for it was not of the person but of the faith of St. Peter that it was said that the gates of hell should not prevail against it;  it is the confession of faith that has vanquished hell.  Jesus Christ is the Rock.  He did not deny the grace of His name when He called him Peter, because he borrowed from the rock the constancy and solidity of hisfaith.  Endeavor then, thyself to be a rock -- thy rock is thy faith, and faith is the foundation of the Church.  If thou art a rock, thou shalt be in the Church, for the Church is built upon the rock."

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Chrysostom (Homily LIV on Matthew XIV:13)

"'And I way unto thee, Thou art Peter, and upon this rock I will build My Church', that is, on the faith of his confession."