Both Jews and Gentiles can receive the righteousness of God by the same kind of faith that Abraham had. Paul described Abraham's faith further.
Romans 4:17-25 (KJV)
(As it is written, I have made thee a father of many nations,) before him whom he believed, even God, who quickeneth the dead, and calleth those things which be not as though they were.
Who against hope believed in hope, that he might become the father of many nations, according to that which was spoken, So shall thy seed be.
And being not weak in faith, he considered not his own body now dead, when he was about an hundred years old, neither yet the deadness of Sara's womb:
He staggered not at the promise of God through unbelief; but was strong in faith, giving glory to God;
And being fully persuaded that, what he had promised, he was able also to perform.
And therefore it was imputed to him for righteousness.
Now it was not written for his sake alone, that it was imputed to him;
But for us also, to whom it shall be imputed, if we believe on him that raised up Jesus our Lord from the dead;
Who was delivered for our offences, and was raised again for our justification.
Paul began by quoting Genesis 17:4 (verse 17).
Genesis 17:4 (KJV)
As for me, behold, my covenant is with thee, and thou shalt be a father of many nations.
God told Abraham that he would be the father of many nations. (Although Abraham looked upon this in a physical way, God intended it to refer to Abraham's spiritual descendants as well, to those who were grafted into the Kingdom by the same kind of faith that Abraham had.) Abraham believed that God was able to raise the living from the dead (Think about the faith Abraham had when he was willing to sacrifice his son on Mount Moriah. This of course also connects to Yeshua's death and resurrection.) and call into reality those things that aren't real. Paul explained this further in the next verses.
Even though the promises of God seemed impossible, Abraham believed that he would become the father of many nations just as God had said (verse 18). (Mention of "seed" connects back to Genesis 3:15 and Yeshua's being the remedy for man's fall.)
Genesis 3:15 (KJV)
And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel.
And since his faith was not weak, Abraham didn't take into consideration the fact that he had reached the age of about one hundred, where he was unable to have children (verse 19). Nor did he take into consideration the deadness of Sarah's womb. This is how Abraham physically viewed his body. It was dead and only God could make it come alive again.
Instead of unbelief Abraham was strong in faith and gave glory to God (verse 20).
He was confident that what God had promised He could do (verse 21).
Therefore, that faith was imputed (or credited) to Abraham for righteousness (verse 22).
In verse 23 Paul informed his readers that this description of Abraham's faith had not been written for Abraham alone, but also for those who believed in the God who had raised Yeshua from the dead (verse 24). It was Yeshua who had been crucified for our sin and raised again for our justification (or salvation) (verse 25).
This section of Paul's discussion of faith is multifaceted. The verses refer not only to Abraham in both a physical and spiritual sense, but to Yeshua also. The meanings are deep, but the conclusion is simply that we can be justified by Abraham-like faith, trusting in the work that Yeshua accomplished on the cross and the God that raised Him from the dead.