a. Due to a false view of the nature of Christ His "righteousness" is a meaningless term. Calvinistic views limit His righteousness to substitution and ignore the reality of His example to us.
b. "Christ's righteousness" is a household term to us, but our confusion on the nature of Christ makes the concept hazy. It is generally assumed that Christ was good because He had a different genetic inheritance from us. It's our good luck that He is a moral millionaire who can "cover" our moral debts for us. You'll have to keep sinning, at least unknowingly. Keep your "insurance" paid up by trusting and you're "covered."
c. Christ's righteousness is the norm for each person in his particular circumstance at any moment. In other words, through the surrender to the principle of the cross. Christ met your particular problem as of now by complete victory over sin and self. This is His righteousness--it is something relevant to you. Truly, from this moment Christ has set you free so you need never sin again! The key is true, genuine faith. Christ is both Example and Substitute.