Gods standard of righteousness is and always has been the moral Law, the Ten Commandments. The problem for fallen man is that he can't keep that Law of his own ability. Jesus told the Jews in John 7:19,
"Did not Moses give you the law, and yet none of you keepeth the law? Why go ye about to kill me?"
Man can't save himself by keeping the Laws of God on his own, he needs a Saviour!
At first thought it would seem unreasonable for God to demand that man keep His Law when man can't of his own accord. If man is honest with himself he will admit and know he cannot keep the Law on his own. This brings us to God's plan for man, justification by faith in Jesus Christ.
There are three parts of the Law of Moses, the moral Law -- the Ten Commandments, the civil Law, and the sacrificial Law. The apostle Paul tells us "the Law was our schoolmaster that points us to Christ."
Gal. 3:24-25,
"Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
But after that faith is come, we are no longer under a schoolmaster."
The sacrificial system of the Law is what pointed to Christ, the great sacrifice for mans sins that he can be justified by faith in the sight of God. Those under the Law of Moses were saved NOT by their ability to keep the Law, but by faith in the coming Messiah through the sacrifice of an animal that represented Christ.
This sacrifice began in the Garden of Eden when Adam and Eve fell and was present throughout the entirety of the Old Testament. With Christ hidden in type and shadows in the Old Testament through this sacrifice, He is revealed to us by the Apostles in the New Covenant through the Holy Spirit.
John the Baptist told us, "Behold the Lamb of God that takes away the sin of the world." John is speaking here of the Great Sacrifice that Christ made for man to be justified by faith in Christ's death and resurrection, not by his own merits in keeping the Law, which man cannot do anyway but by faith in Christ.
This brings us to how man keeps the Law in the sight of God! Jesus told us in Matt. 5:17,
"Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil."
Christ kept the Law in every aspect for us, He fulfilled the Law which we could not do on our own. Paul tells us why Christ did this for us.
Rom. 8:3-4,
"For what the law could not do, in that it was weak through the flesh, God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit."
Man cannot keep the righteousness of the Law on his own, so Christ fulfilled the Law for us, in that, by faith in His sacrifice the Holy Spirit will fulfill the righteousness of the Law in us. This is done by faith in Christ and denying the ability of our flesh to do it ourselves.