If righteousness is defined in the Bible as believing that God will do what He says He will do, then does that in turn apply to God's righteousness and if so, how? Is it possible that God's righteousness is defined the same way as the Bible defines our (true) righteousness?
If that is true, then it must look something like God trusting us to do what we say we can do. (I am exploring this while I am writing so I am not currently expressing something that I have uncovered or yet understand.) That seems to be what happened in what is called the Old Covenant. The people at Mt. Sinai claimed that they would do everything that God had said they must do. It's pretty obvious that was a complete failure and disaster. But still, God acted in a way all through the centuries that could easily be seen as trusting them to do what they claimed they could do even though He knew from before the start that it was impossible for them to do it.
This thread does seem to remain consistent right on into the New Covenant but with very important alterations. It seems to me that in a New Covenant relationship with God, to be “successful” we must become completely honest and admit that we cannot live a godly life ourself. In this situation from God's perspective it would be consistent with this definition of righteousness that God could still trust us to be what we say – that is, we will be consistent with our own claims. God is trusting us to do (and not do) what we say. So when we admit and agree with God (confess) that we are completely and utterly helpless to change ourselves and live a life that measures with the life of God, then God trusts us that we are in fact what we say we are and that our lives are consistent with what we are saying.
From that point we can move to the next which is called repentance which is a gift from God. Remember, the only thing we truly can do is choose who we are to be slaves to. We will never, ever be able to live godly lives independently like Satan has led us to believe. So our only hope of escape from this body of death is to throw ourselves on the mercy of the only Source of life and exercise our will to become His love-slaves. So when we choose to receive repentance, which means a change of thinking, of direction, of heart-motives, and live in that repentance by continual surrender of our rights to ourself, then the incredible arrangement of indwelling divinity accomplished by the death and resurrection of Jesus for this very purpose is installed in our soul and a new life is experienced within.
From this position we move on to an experience that theologians call “sanctification” which has its own hazards of misunderstanding. Very many people who seem to “get it right” up to this point fall into Old Covenant thinking at this stage and end up right back in the mire of struggle, defeat and “works religion” that plagues anyone attempting this route. It also puts God in the position, according to application of the above definition of righteousness, of trusting us to do the impossible which is just as impossible now as it was in Old Testament days. In essence, we are putting God in a terrible situation when we believe that we can be “good” through any efforts of our own, even when those efforts are supposedly combined with “help” from God.
In the experience of sanctification we must continue to remain in the same relationship with God as we did when we first came to Him for justification and trusted Him fully to apply the merits of Jesus to our lives in place of our sin and guilt. Sanctification is not discovering new formulas that will now enable us to live perfect lives with help from God. Sanctification is living in total consciousness of our continuing utter inability to live “right” at all from any of our own strength and instead resting fully in the resurrection power of an indwelling Divinity gifted to us in Jesus Christ. It is learning to live from the heart Jesus gives us.
When we live in that kind of relationship with God, then His trust in us to do what we say we can do – which is nothing but choose to allow Him to do what He says He can do in us – is a revelation of His righteousness. This is the gospel, the good news that Paul preached and was so pumped up about. This also allows the same definition of righteousness that is used by the Bible to equally apply both us and to God.
For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. For in it the righteousness of God is revealed from faith to faith; as it is written, "BUT THE RIGHTEOUS man SHALL LIVE BY FAITH." (Romans 1:16-17)