It's always best to let Bible answer Bible. Take a look at the Rock in the rest of the Bible:
Consequently, you are no longer foreigners and aliens, but fellow citizens with God's people and members of God's household, with CHRIST JESUS HIMSELF as the chief cornerstone. (Ephesians 2:19-20)
Jesus Christ HIMSELF is the stone, or rock, of Matthew 16:18 and parallel verses. Please take a look at some of the Scriptures the disciples, and all Jews, knew:
Genesis 49:24 -- But his bow remained steady,
his strong arms stayed limber,
bacause of the hand of the Mighty One of Jacob,
because of the Shepherd the Rock of Israel,
because of your father's God, who helps you...
Deuteronomy 32:3-4 -- I will proclaim the name of the LORD,
Oh, praise the greatness of our God!
He is the Rock, his works are perfect, and all his ways are just.
Deuteronomy 32:15 -- Jeshurun grew fat and kicked;
filled with food, he became heavy and sleek.
He abandoned the God who made him
and rejected the Rock his Savior.
Deuteronomy 32:18 -- You deserted the Rock, who fathered you;
you forgot the God who gave you birth.
Deuteronomy 32:30 -- How could one man chase a thousand,
or two put ten thousand to flight,
unless their Rock had sold them,
unless the LORD had given them up?
For their rock is not like our Rock,
even as our enemies concede.
Those verses are from the Torah -- the first five books of our Old Testament, which are referred to by Christ and all Jews as The Law. It is very clear in The Law who the Rock is.
Continued on the next post -- it was too long for this one --