How does justification relate to the concept of righteousness in the Bible?

Justification is a central doctrine in the Bible that describes God's act of declaring sinners righteous based on their faith in Jesus Christ (Romans 5:1). Unlike righteousness derived from one's own efforts, which is deemed as 'filthy rags' (Isaiah 64:6), the righteousness obtained through justification is an alien righteousness, a righteousness that is not our own, but is credited to us through faith in Christ (Philippians 3:9). This ensures that all believers, regardless of their past, can stand justified before a holy God, emphasizing that salvation is solely by grace through faith, apart from works, which is a foundational element of sovereign grace theology.