They're not Greeks. They're Hellenized EteoCypriot Middle Easterners. Even a lot of Mainland Greeks have middle eastern blood. So do Southern Italians, etc. That's why Mainland Greeks, s. italians, etc. can look similar to ashkenazi jews.

Cypriots are basically genetically the same as (sephardic) arab jews.

(http://www.autoadmit.com/thread.php?thread_id=2260230&forum_id=2#23228907)

Sephardic Jews cluster identical to cypriots as well as druze. Ashkenazis, overall, cluster more with southern italians and mainland greeks.

(http://www.autoadmit.com/thread.php?thread_id=2260230&forum_id=2#23231146)

Granted Cypriots, and levantines may have some european admixture, but italians/greeks/albanians, etc. have far more middle eastern admixture from the neolithic, e3b, j2, j1, + phoenicians, anatolians (before they were turkified), etc.

Basically, Ancient Rome was a cosmopolitan environment. The elite greeks/romans were white, but the general population absorbed huge middle eastern elements. Ashkenazi Jews came into being during that process. 1/8th of the empire was jewish.

The original khazars were asians who looked like this:

http://www.youtube.com/watch?v=7d8NH3VMtVI

Caucasus people like Chechens can overlap phenotypically with southern europeans/jews, but that's because caucasians are basically the descendants of ancient fertile crescent people (just depigmented) and Mediterraneans have heavy middle eastern admixture. So, that Mediterranean 'italian' look is actually a mixed one, that's why mixed latinos and various mixed people can also have pseudo-mediterranean features and resemble 'italians'.

(http://www.autoadmit.com/thread.php?thread_id=2260230&forum_id=2#23231232)