Is Christ's church built on Peter or all living stones of truth?

Answer Request:
Is Christ's Church built on Peter or all living stones of truth? Did God reveal the truth to Peter that Jesus is The Rock?

The Greek word translated "church" in the New Testament is ekklesia. A literal translation of ekklesia would be "a called-out assembly". Thus, when God calls one out, to separate them, it is for a purpose. In other words, there is a specific function that this entity should fulfil. For example, God separated the nation of Israel for a purpose. Israel can be identified as an ekklesia, (or church in modern English).

Deut.7:6 For thou art an holy people unto the Lord thy God: the Lord thy God hath chosen thee to be a special people unto himself, above all people that are upon the face of the earth.

Num.23:9 For from the top of the rocks I see him, and from the hills I behold him: lo, the people [Israel] shall dwell alone, and shall not be reckoned among the nations.

The function that Israel was to fulfil was to represent God in this world. Israel was called to be a light to the Gentiles, to shine forth the righteousness of God to the Gentiles through the law, and they were chosen to bring forth the Redeemer of mankind.

Isaiah 60:3 And the Gentiles shall come to thy light, and kings to the brightness of thy rising.

Acts 26:23 That Christ should suffer, and that he should be the first that should rise from the dead, and should shew light unto the people, and to the Gentiles. 

Proverbs 6:23 For the commandment is a lamp; and the law is light; 

Galatians 4:4 But when the fulness of the time was come, God sent forth his Son, made [born] of a woman, made [born] under the law, 5 To redeem them that were under the law [Israel] ...

Having established the meaning of the word, "church", let's get back to the question.

Matt.16:13 When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, Whom do men say that I the Son of man am? ... 16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God. ... 18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.

The Lord Jesus would establish His new covenant church, (the Jewish church, those under the law and who belong to the Kingdom program), upon the confession that Peter gave; that Jesus was the Christ, the Messiah, the Son of God. Christ is the Rock upon which this church would be built, but it was based on that faith confession that Jesus was their Messiah, the Son of God. The Jewish church started with a blazing 'bang' in the early part of Acts, but we must recognize that this program was put into hiatus due to the unbelief of the nation of Israel. Due to the blinding of Israel, (Rom.11:7; Rom.11:25), God would start a new ekklesia, an assembly of people called, "The Body of Christ".

1 Corinthians 12:27 Now ye are the body of Christ, and members in particular.

This church is not built on the law and principles of the Kingdom church, but it has a brand-new foundation, based on the mystery doctrine that Paul teaches us in the books of Romans to Philemon. The principles that we abide by are based on the grace of God through the death, burial, and resurrection of Jesus Christ. Paul tells us the following,

1 Corinthians 3:9 For we are labourers together with God: ye are God's husbandry, ye are God's building. 10 According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. 11 For other foundation can no man lay than that is laid, which is Jesus Christ.

2 Corinthians 5:15 And that he died for all, that they which live should not henceforth live unto themselves, but unto him which died for them, and rose again. 16 Wherefore henceforth know we no man after the flesh: yea, though we have known Christ after the flesh, yet now henceforth know we him no more. 17 Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.

Paul, by the instruction and authority of the risen Christ, was given the task to build a new foundation; a foundation different to what Jesus built for the Jewish church. Paul says that even though we knew Christ according to the flesh (His earthly ministry to Israel), yet now, in this grace age, we do not know Christ in that way anymore. We do not subject ourselves to the principles of law but are a brand-new creature who walk by faith and not sight. We walk not by laws written in stone, but by the Spirit of Life who resides within us. We walk in, and by, the Spirit. This is a spiritual foundation and one that is very different to the Jewish church.

So, to summarize, there are two assemblies of people. The Jewish church built on the foundation of the law and the prophets, and the Body of Christ, built upon a spiritual foundation of grace. Both foundations rest upon Christ, as Christ is the fulfillment of the law and the prophets in the Kingdom program, and Christ is the very essence of grace that God showers on us through the cross in the Mystery (Grace) program. 

What is the function of these two churches? What is the purpose of both these individual bodies? Well, the Jewish church will ultimately fill the earth (their inheritance) with the glory of Christ, and the Body of Christ will ultimately fill the heavens (their inheritance) with the glory of Christ. With these two churches (assemblies of people), established in their respective places in heaven and in earth, it will thus bringing God's great plan of salvation to fulfillment through His Son, Jesus Christ, and bring the whole creation back into the glories in which it was originally created,

Col.1:19 For it pleased the Father that in Him [Christ] all the fullness should dwell, 20 and by Him [Christ] to reconcile all things to Himself [Father], by Him [Christ], whether things on earth or things in heaven,…

Eph.1:9 having made known to us the mystery of His will, according to His good pleasure which He purposed in Himself, 10 that in the dispensation of the fullness of the times He might gather together in one all things in Christ, both which are in heaven and which are on earth —in Him.

1 Cor.15:28 And when all things shall be subdued unto him, then shall the Son also himself be subject unto Him that put all things under him, that God may be all in all.