Brethren, my heart’s desire, and prayer to God for Israel is, that they might be saved. For I bear them record that they have a zeal of God, but not according to knowledge. For they being ignorant of God’s righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God (Romans 10:1-3).

Isaiah 64:6 tells us that man’s righteousness: his own thought-out ways of trying to serve and please God, are as filthy rags. There’s no use having confidence in your so-called good works, to answer for you before God.
This was the dilemma of the children of Israel, which the Apostle Paul decried in our opening text. Though they were zealous for God and engaged in all forms of religious devotions, purifications, oblations, etc., they erred in three distinct ways in their pursuit of righteousness. First, they were ignorant of God’s righteousness, secondly, they went about to establish their own righteousness, and thirdly, they didn’t submit themselves to the righteousness of God.
The third point gives an indication of God’s expectation: we’re to submit to His righteousness, because righteousness isn’t something you attain by your own works; it’s a gift from God. Romans 5:17 says, “…they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.” The requirement to attain the righteousness of God is simply to believe in Jesus Christ with all your heart and receive the gift of eternal life. That’s why it’s called righteousness by faith.
Philippians 3:8-9 tells us to embrace this righteousness which is through the faith of Christ Jesus: “…that I may win Christ, and be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith.” This righteousness produces in you the rightness of God, such that by instinct you know what is right, and are able to live blameless before God. You didn’t work to attain it, yet it works in you, having been imparted to your spirit as a gift.
The righteousness of God has been imparted to my spirit, therefore I have the ability to do right, and live joyfully without blame before the Father, for His righteousness in me gives me right standing with Him, and superiority over Satan and the demons of darkness.
Further Study/Reading: 2 Corinthians 5:21; Romans 3:21-22