Oh, that word...righteousness. It's a loaded concept. For some, that righteousness is where we boast of our love of God, and of God's love for God's favored people (supposing that we are in that cohort, and others are not). For some, that righteousness is something we see in others as we observe them from far off. They are nearer God than we could ever hope to be, almost to the point of admitting the futility of even trying to draw closer to the throne of grace. Their shininess is not ours. Gosh, they seem to have it all together, faith-wise.
Given those dipoles of relationship, where can us regular folks possibly find a positive relationship with the Almighty? For the confidently sanctified, it means being taken down a peg or two. We may know God's blessings...but that means we are now bound to recognize that God's grace exceeds our assumptions about our neighbors. That reject down the street? Guess what, God is loving him with the same abandon that you are enjoying. For the fearful and self-doubting...well, we need the blessing of hope, that with and by God's grace we might draw closer and experience the gift of a blessing.
This is when Paul brings up Abraham. By his world-view, Abraham is the common denominator, the ground-point of a more unitive relationship between God and humanity: Jew, Greek, Roman...gentile, all of us are children of the great father (with Sarah and Hagar as mothers) of us all. Paul holds Abraham up as the signal example of what a life of faith-work looks like as God reckons it as righteousness. To Abraham, whose whole being bowed in obedience to a God who called him up and out of his routine life, that willingness to say "yes" to God is the key. From that affirmation, from that obedience, all else flowed. The basic covenant is this: God will be our God, and we will be God's people. From there, we work it out. For Abraham, the mark of circumcision was not proof of sanctity, but a recognition outwardly of a way of being in God that ordered his life apart from what had previously happened.
It's all about a hope that births faith, and a righteousness springing up from that faith, that we know ourselves to be one before God as God's beloved.
From there, Paul promises to build, and build, and build up the certainty in his audience among the Romans the awareness that God is God of all people...and thereby all people are called into an active and vital relationship with the Almighty in service to the grace pouring forth as the justice of the Kingdom of God prevails over every nation and empire.