A few weeks ago, South Sinai governor Mohamed Shousha claimed that Mossad was behind a series of shark attacks in the Red Sea. Last Thursday, he sat down to lunch with Israel's Prime Minister Benjamin Netanyahu and other top Israeli officials.

This isn't a story of Mr Shousha making New Year's resolutions not to defame Israel, but a sign of the complicated, multi-faceted relationship between Israel and Egypt.

On one hand, there is growing anti-Israel sentiment in Egypt. Local analysts saw this as a large factor in why, on December 20, three people were accused of spying for Israel. Sometimes, as in the case of Mr Shousha's bizarre declaration, it results in slurs of the worst kind.

But then there is the other side of the relationship, such as the lunch, and the discussion between Mr Netanyahu and Egyptian President Hosni Mubarak, which Mr Netanyahu's office described as "lengthy, friendly and comprehensive".

Sure, there were critical words from Mr Mubarak, including a call for more concessions to the Palestinians, and warnings against another war in Gaza. But these are standard in any meeting Mr Netanyahu attends, even with his closest allies such as America.

So what is the real state of Egypt-Israel relations? There is frustration in Cairo about the lack of progress in the peace process, and distaste towards Israel's hard-line Foreign Minister, Avigdor Lieberman. According to a recent WikiLeaks release, Egyptian officials refuse to talk to him.

Furthermore, the 31-year-old Egyptian-Israeli peace has been a cool one. And the discourse about Israel in Egypt, including in state institutions, is riddled with incitement - experts suggest that Egyptian schoolbooks are just as bad as Palestinian ones.

But the two countries have plenty of shared priorities. Mutual trade in 2008 amounted to $271 million (£175 million), and Israel buys large quantities of gas from Egypt.

However, binding the two countries more than anything is co-operation on security. Egypt and Israel are worried that there is a Hamas-ruled enclave on their border. Egyptian officials remember the day in January 2009 when Gazans breached the border and thousands entered Egypt. Unrest in Gaza, they fear, can lead to chaos in Egypt.

Egyptian officials are also exceedingly concerned about Muslim Brotherhood, the parent movement of Hamas which began in Egypt. A strong Hamas buoys the movement, which they are working hard to repress. Egypt also shares Israel's fears about Iran.

There are two ways of looking at the two-facedness of Egypt's conduct towards Israel. One is to say it is a relationship on shaky ground. The other is to simply say "it works" and note that just like Egypt, the Palestinians have strong security and trade links with Israel but fail to change their language on Israel - meaning that if peace with the Egyptians is possible, so may be peace with the Palestinians.