Is there a common strategy to measure if a difference-significance of two areas under two ROC curves
The AUC is a summary statistic of your dataset. As such, if you did the same experiment again you would get a slightly different value - and if repeated several times, you'd get a distribution of values.  You probably want to show that your distribution rarely or never includes 0.5 (indicating random classification). When you have an empirical distribution like this, or a histogram of repeated experiments, you can just count how many of your estimates are $\approx 0.5$.  If none, you're golden.

Since you don't want to do your experiment multiple times, you could 'simulate' that scenario by using samples of your data, but otherwise performing the same process. This is called 'bootstrapping'.  You can use this method to construct confidence intervals around your AUC metric, or equivalently, do a statistical test to see if the metric you get is different from 0.5.  

Some packages have bootstrapped confidence intervals built in to the AUC calculation, so you could just use that.