Some background here,
Some personal background. When I was studying Public International Law my teacher was preofessor Mazawi, who at the time was also Britain's representative at the Law of the Sea conference so I followed the situation closley and with good first hand info. At that time, early 70s, Greece did not want to change the territorial waters from the then customary 3 miles, with some states claiming 6 miles. The reason was obvious, Greece being a major international civilian maritime power wanted maximum freedom of the high seas. Greece was overriden by most other nations and the norm for territorial waters was set at 12 miles. With some new additions- all ships, including warships can cross national waters of another state going to and from their ports to international waters.
The end result was that Greece found itself with a legal right it had not pursued- namely to extend its territorial waters to 12 miles. Turkey reacted with the now famous casus belli, if Greece were to exercise her right then it would be cause for war. Since then there are daily skirmishes in the Aegean, in the sea and air as each side tests the other. Apart from the danger there is also the expense, it costs about the price of a school classroom to send up two jets to intercept two other jets.
The USA was till now wary of ratifying the Law of the Sea. If it does then there will be no more excuses for Greece not following suit and demand the same rights, and it would be pretty hard to refuse. As noted above, where the sea is too narrow (less than 24 miles) tne median line is the border.
Cyprus too would have the added weight of the USA practice behind it when it claims rights to the Exclusive Economic Zone between Cyprus and Egypt.
If this situation materializes thirty five years of tension, expense and a few dozen lives will have been wasted for nothing. All it takes to solve the problem is for someone in the USA to put a signature on a piece of paper.