That is my question, also. I’m still researching that.
Essentially all modern Catholic apologists: Hahn, Ray, Armstrong, Salza and, of course, Catholic Answers (ca. 1988) make the connection. But what was the source?
Lots of Protestants have seen it, too. Here’s just one:
“In Isa 22:22 the key of the house of David is promised to Eliakim. According to Paul, Jesus is the only foundation (1 Cor 3:11), and in Rev 1:18; 3:7, Jesus possesses the key of David and the keys of death and Hades. But in this passage [Matthew 16:19] Peter is made the foundation (cf. Eph 2:20, where the Christian apostles and prophets are the foundation and Christ is the cornerstone) and holds the keys.” --George Buttrick and others, eds., The Interpreter’s Bible, (New York: Abingdom, 1951), 453.
Willoughby C. Allen, in a still older commentary that interprets the “rock” of Matthew 16:18 as the “revealed truth” of the Messiahship of Christ, nevertheless writes in his The International Critical Commentary –
“The figure of the gates of Hades suggests the metaphor of the keys. There were keys of Hades, Rev 1:18; cf. 9:1; 20:1. The apocalyptic writer describes the risen Christ as having the keys of Hades, i.e. having power over it, power to enter it, and power to release from it, or to imprison in it. In the same way, ‘the kingdom of the heavens’ can be likened to a citadel with barred gates. He who held the keys would have power within it, power to admit, power to exclude. In Rev 3:7 this power is held by Christ Himself [quotes Rev 3:7]
…The words are modelled on Is 22:22, and express supreme authority. To hold the keys is to have absolute right, which can be contested by none…It would, therefore, be not unexpected if we found the Messiah or Son of Man described as having the keys of the kingdom of the heavens. This would imply that He was supreme within it. But it is surprising to find this power delegated to S. Peter…To S. Peter were to be given the keys of the kingdom. The kingdom is here, as elsewhere in this Gospel, the kingdom to be inaugurated when the Son of Man came upon the clouds of heaven. If S. Peter was to hold supreme authority within it, the other apostles were also to have places of rank…To ‘bind’ and to ‘loose’ in Jewish legal terminology are equivalent to ‘forbid’ and ‘allow,’ to ‘declare forbidden’ and to ‘declare allowed’…The terms, therefore, describe an authority of a legal nature. If he who has the keys has authority of an administrative nature, he who binds and looses exercises authority of a legislative character…Further, the position of v. 18, with its description of the Church as a fortress impregnable against the attacks of evil (the gates of Hades), suggest irresistibly that ‘the keys of the kingdom’ mean more than power to open merely, and imply rather authority within the kingdom. And this is confirmed by the ‘binding’ and ‘loosing’ which immediately follow…What were the keys thus given? Even if we identify the kingdom with the Church, it is not entirely satisfactory to suppose that the Lord simply foretold that S. Peter was to take a prominent part in the work of opening the door of faith to the Gentiles. His share in that work, though a great, was not an exclusive one…The motive must have been to emphasise the prominence of S. Peter in the Christan body as foretold and sanctioned by Christ Himself…They [the apostles] had left all to follow Christ; but when He sat on the throne of His glory they would sit on twelve thrones, judging the twelve tribes of Israel, 19:18. And amongst them Peter was pre-eminent. He was protos, 10:2.” (Allen, The International Critical Commentary orig 1909, 1985], page 176ff)
I’ll work on this and see how far back it goes because I want to know, too.