Further understanding of the role of righteousness is given in Ephesians 6. There it speaks about the armor of God that was given to us to fight the spiritual war:

Ephesians 6:13 
"Therefore put on the full armor of God, so that when the day of evil comes you may be able to withstand, and having done all to stand."

I would like to point out two things in this verse. First, the armor is of GOD. It is NOT an armor that you constructed. Rather, it is an armor that has been constructed by GOD. Second, it is YOU that put on that armor. God will not put it on for you. God made it available. Now you have to put it on. These two things are important for correct understanding of the next verse. There it states:

Ephesians 6:14 
"Stand firm then, with the belt of truth buckled around you waist, with the breastplate of righteousness in place....."

It is this second piece of the armor, the breastplate of righteousness, on which we will concentrate our attention here. The various parts of the armor, as they are described in verses 14-17, have not been given a name by chance. God has a reason for everything He says. So, we must ask ourselves what is the job that a breastplate is designed to do? I believe that most of us know the answer: in an armor the breastplate protects the breast. As you know, the heart, a vital instrument for our lives, is located in the left side of the breast. Therefore, one of the most important jobs of the breastplate is to protect the heart. Biblically, the word heart means the inner part of the mind; the inner being of a man. What is in our heart determines what we are. As Proverbs 4:23 tells us:

"Above all else guard your heart; for out of it are the issues of life"

The Word of God calls us to guard our hearts more than anything else and when it says heart the actual reference is to the inner part of our minds. Indeed, what is in the inner part of our minds, what is in our heart, determines "the issues of life". No wonder therefore, that it is exactly this part at which Satan aims his darts. If his darts manage to pierce the heart i.e. the inner part of our being, then this is exactly what he wants. One of the weapons that Satan frequently uses to fire his darts into the heart of sincere and devoted Christians is none other than condemnation. Condemnation is one of his best weapons since it makes the heart, the inner part of our beings, ill. It is a powerful weapon of Satan to corrupt our fellowship with God. I John describes the effects of this disease which affects many Christians.

1 John 3:21 
"Beloved, if our hearts do not condemn us, we have confidence before God."

Pay careful attention to that "if". Note also that the reference is to the heart. Condemnation is a serious disease that affects the heart, the inner being of a man. When there is condemnation in our hearts then there is no confidence before God and if there is no confidence before God, then I really question of the fellowship that we are able to have with God. The will of God is to "rejoice in the Lord always" (Philippians 4:4). It is however impossible to rejoice in Him when you do not have confidence before Him. Nevertheless, Satan will not manage to bring condemnation into our lives IF (and only if) we use the armor of God for our defense. So the question is what is the piece of the armor of God that protects the heart? Ephesians 6:14 tells us:

"Stand firm then, with the belt of truth buckled around you waist, with the breastplate of righteousness in place....."

This piece is the "breastplate of righteousness". But which righteousness is this? You see, we are accustomed to reading this verse using a preconceived idea of righteousness by works. Thus, we think that the righteousness referred to in that verse is our self-righteousness. We say "if I am good enough and do good works then I'll be righteous". However, we forget that the Bible says "therefore no-one will be declared righteous in his [God's] sight by the works of the law" (Romans 3:20). The righteousness here is not our self-righteousness but the righteousness of God. The full armor has been made ready for us by God. It is the "armor of God". It is not an armor that we constructed. The Word does not say "Make up the armor". It says "put on the full armor of God" (Ephesians 6:11). If the armor is of God, whose then is the breastplate of that armor? It is God's. Whose therefore is the righteousness that is the breastplate? Is it your self-righteousness gained through your good works? No! It is the righteousness of God, as indeed the whole armor is of God, and so therefore is each separate piece. You did not make up the armor. You just put it on. In the case of righteousness this means that you place deep in your mind, in your heart, that you are righteous before God BY GRACE ("righteousness of God") and thus you do not try to achieve a self-righteousness standing before Him. It means that you understand that before Him "no-one will be justified by the works of the law" (Romans 3:20) and that "all have sinned and fall short of the glory of God and are justified freely by His grace" (Romans 3:23-24). You must accept that grace is grace and works are works. You must understand that when the Bible says grace does not mean grace with some works. As the Scripture says: "And if by grace it is no longer by works; if it were, grace would no longer be grace" (Romans 11:6). Then, you will have "the breastplate of righteousness in place" (Ephesians 6:14). Otherwise, you will leave your heart unprotected and be vulnerable to the disease of condemnation. Satan will trap you through his cunningness because you are not wearing the full armor of God but something that you yourself made up. You are wearing the breastplate of self-righteousness instead of the breastplate of righteousness of God. However, the breastplate of self-righteousness has been declared faulty by the Word of God. No wonder therefore that if you put on that “breastplate” you will be vulnerable to the Satan-caused disease of self condemnation. On the other hand, when we protect our hearts with the true breastplate of the righteousness of God then that which the Scripture says in Romans 8:1 will be fulfilled in our lives:

Romans 8:1 
"THEREFORE THERE IS NOW NO CONDEMNATION FOR THOSE WHO ARE IN CHRIST JESUS"