Summary: Boasting excluded
Having provedn conclusively that universal sinfulness of man and his need for righteousness in 1:18-3:20, Paul develops the theme he introduced in 1:17; God has graciously provided a righteousness that comes from Him on the basis of faith alone (3:21-5:21). After all this bad news about our sinfulness and God’s condemnation, Paul gives the wonderful news. There is a way to be declared not guilty-by trusting Jesus Christ to take away our sins. Trusting means putting our confidence in Christ to forgive our sins, to make us right with God, and to empower us to live the way he taught us. God’s solution is available to all of us regardless of our background or past behavior.
But now: Not a reference to time, but a change in the flow of the apostle’s argument. Having shown the impossibility of gaining righteousness by human effort, he turns to explain the righteous that God Himself has provided. Righteousness: This again goes back to 1:17, this righteousness is unique: 1) God is its source (Is 45:8); 2) It fulfills the penalty and precept of God’s Law. Christ’s death as a substitute pays the penalty exacted on those who failed to keep God’s law, and His perfect obedience to every requirement of God’s law fulfills God’s demand for comprehensive righteousness (2nd Cor 5:21; 1 Peter 2:24 (quickview) Heb 9:28); and 3) Because God’s righteousness is eternal (Psalm 119:142 (quickview) Is 51:8; Daniel 9:24 (quickview) ), the only one who receives it from Him enjoys it forever. Apart from the law: Entirely apart from obedience to any law (4:15; Galatians 2:16 (quickview) 3:10,11; 5:1-2; Eph 2:8-9; Phli 3:9; 2 tim 1:9; Titus 3:5 (quickview) ).
Righteousness of God in context is not an attribute of God, but an act of God whereby He declares a sinner righteous. This righteousness from God. This righteousness is apart from the law. This expression categorically stating that righteousness is given totally apart from any law. The same use of this word is used in Hebrews 4:15 (quickview)  where the Lord Jesus was tempted in all points as we are ‘yet without sin.” Just as sin and Jesus Christ have nothing in common, so too the righteousness was not manifested in keeping the law but it was manifested at the Cross when “He (God the Father) made Him (God the Son) who knew no sin to be sin for us, that we might become the righteousness of God in Him” (2 Cor 5:21).
Romans 3:22-23 (quickview) , “22even the righteousness of God, through faith in Jesus Christ, to all and on all[h] who believe. For there is no difference; 23for all have sinned and fall short of the glory of God,”
There is no difference.. glory of God: A parenthetical comment explaining that God can bestow His righteousness on all who believe, Jew or Gentile, because all men-without distinction-fail miserable to live up to the divine standard.
All have sinned which Paul is just putting here, because he has already proved the case (1:18-3:20). Some sins may seem bigger than others because of their obvious consequences are much more serious. Murder, for example seems to us to be worse than hatred, and adultery seems worse than pride. But this does not mean that because we only commit little sins in secret that we deserve eternal life. All sins make us sinners, and death (because they disqualify us from living with God), regardless of how great or small they seem. Don’t minimize little sins or overrate big sins. They all separate us from God, but they can all still be forgiven.