David expresses a similar understanding in Psalm 4: 1 when he prays to Elohim Tzedeki - God of my righteousness. The names come from the Hebrew word ṣeḏeq, meaning right, correct, innocent or righteous.
All through the Bible, we read that God is righteous: He only does what is just and right; He never does anything wrong. But these names of God take that righteousness a bit further, saying that He imparts or accredits His righteousness to us - a righteousness that we could never achieve by our own efforts.
As far back as Genesis 15: 6 (quoted again in Romans 4: 3 and Galatians 3: 6) we read that Abraham trusted God and God credited it to him as righteousness. Likewise, Romans 10: 4 tells us that Jesus fulfilled all of the Law, so that those who believe in Him could be seen as righteous. (Greek dikaiosynē)
In Psalm 24: 4 - 5, the Israelites are urged to have, "clean hands and a pure heart," but reminded that their righteousness is actually a blessing from the Lord and not a result of their own efforts. Similarly, Isaiah told them that every accusation or condemning word spoken against them would be silenced - not because they always did what was right, but because their righteousness came from the Lord.
This understanding gives incredible hope and security to those of us who follow Jesus. Paul sums it up in Philippians 3: 9, saying that we don't rely on a self-made righteousness that comes from keeping the Law, but rather on a righteousness that comes from God Himself and is based on our faith in Christ. The Lord is our righteousness!