'By one righteousness'
δι ενος δικαιωματος means 'by one righteousness'. It cannot mean anything else. Compare with δι ενος ανθρωπου in the twelfth verse. 'By one man, sin entered into the world'. (Or, more strictly and more accurately, 'by one humanity'). This cannot be made to mean 'by the man of one . . . . etc'.
In both cases, the genitive (both enos, dikaiwmatos and anthrwpou) is present due to the preposition dia. In 5:12 it is the genitive singular masculine. In 5:18 it is the genitive singular neuter. See Biblehub 5:12 and Biblehub 5:18
δι ενος δικαιωματος cannot be made to mean other than 'by one righteousness'. (See Footnote 1.)
For there only is one righteousness, the righteousness of God. And it is this righteousness that justifies. His righteousness.
The words 'righteousness of God' occur ten times in scripture. The words 'righteousness of Christ' never appear. The righteousness of God is not a human righteousness. (See Footnote 2.)
God is righteous in punishing sinful acts and in condemning (and eradicating) sin itself.
Sinful acts have been punished when Jesus Christ 'bore our sins in his body on the tree', 1 Peter 2:24.
God is righteous in condemning sin when Jesus Christ was 'made sin that we might be made righteousness of God in him', 2 Corinthians 5:21. Sin was judged in him and eradicated (in him) in his death.
[These are two separate aspects of the doctrine of Christ - his sufferings, prior to death, and his actual death (only after which, was blood shed). These two aspects need to be considered, in depth, separately.]
It is this righteousness - the righteousness of God - which is seen to be righteous in the demonstration of judgment. The word dikaioma, specifically used in Romans 5:18, is a matter of seen righteousness - demonstrated righteousness.
This is the righteousness displayed when God judged sins and sin in his own Son, in humanity, at Golgotha. Believing this demonstration, one believes in the righteousness of God.
And, thus believing, the righteousness of God is seen in the faith of the believer.
God, seeing this faith and seeing its content (the righteousness of God) God justifies such, counting such faith (and only such faith) unto righteousness, that is to say, unto the righteousness of God.
It is neither obtained by law, nor is it received by law.
Faith unto Righteousness
This is what Abraham believed, Genesis 15:6 : that God was true and God was honest and God would do what he promised he would do. That God was righteous. And thus could be trusted. In faith.
Abraham believed God - and there was evaluated to him unto righteousness.
This statement is made four times in scripture : once in Genesis (Septuagint LXX) then in Romans 4:3, Galatians 3:6, and James 2:23 (with supporting statements in Habakkuk 2:4 and Romans 4:22). It is identical on all four occasions and the grammar is meticulously precise. No subject, no direct object and a deponent verb, that is to say a 'responsive' (middle voice) verb.
God sees his own righteousness in the faith of the believer and God responds, evaluating that faith . . . unto righteousness.
To him. And . . . Unto righteousness. Was all that could be revealed at the time. Now it can be revealed, in Paul's epistles particularly, just what that righteousness is. And whose is that righteousness.
Footnote 1. 'By righteousness of one' would have to be expressed as δι δικαιωματος εκ ενος in order to avoid any ambiguity.
Footnote 2. 'Jesus Christ righteous', 1 John 2:1 (there is no article) is a title used once in scripture for a particular purpose. It does not imply a human righteousness obtained by legal means.
There is not a single text of scripture that bears such a meaning - that Jesus Christ, in humanity, did what was originally forbidden to all humanity : to partake of the tree of knowledge of good and evil in order to obtain (legal, human) righteousness.
Righteousness is of God. Humanity believeth.
Out of the heart, man believeth . . . unto righteousness. [Romans 10:10]
For the righteousness of God is revealed (in the gospel) out of faith (ek) and unto faith (eis). That is to say, out of the faith of Christ unto the faith of the believer, Romans 1:17.
Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified. Galatians 2:16.
This whole subject is treated in depth in the book Jehovah Tsidkenu (The Lord our Righteousness) by Nigel Johnstone, available from Belmont Publications. See my profile for PDF download, free of charge and free of any registration.