Egypt's political upheaval is by no means over, but its uneasy neighbour Israel is not waiting for the outcome. Desert defences are being strengthened and strategy revised as a once stable relationship splinters.

Shortly after the Muslim Brotherhood claimed victory in Egypt's presidential vote on Monday, unidentified gunmen crossed the Sinai border and killed an Israeli worker.

There was no suggestion the two events were linked, but the violence underscores how security in the Sinai Peninsula has deteriorated since the downfall of President Hosni Mubarak in 2011, with no hope of any swift solution while Cairo remains convulsed by political uncertainty.

"What is going on along the southern border worries me ... and the ideology of political Islam in Egypt worries me, so I need to sleep with one eye open," said Ilan Mizrahi, a former Israeli national security adviser and ex-deputy head of Mossad.

Israel faces a dilemma of major strategic consequences.

Its 33-year peace with Egypt has been a cornerstone of regional stability and an economic boon for both countries, thanks in part to generous U.S. aid.

No one expects Cairo to bin the peace accord any time soon, even if the Muslim Brotherhood, which is traditionally hostile to the Jewish State, does manage to consolidate power in the face of an Egyptian military out to conserve its own authority.

A demilitarised Sinai is the keystone of the peace. But for the past year there has been growing lawlessness in the vast desert expanse, as Bedouin bandits, jihadists and Palestinian militants from next-door Gaza fill the vacuum, tearing at already frayed relations between Egypt and Israel.

"We need to be sensitive about what is going on in Cairo and try to make Egypt understand that this needs to be stopped," said Mizrahi in a telephone interview.

"If nothing happens, then I expect my country to react as we know how to react and stop these attacks on our civilians," he added, suggesting that if needs be, Israel should cross the border to track down its enemies.

Such a move would mark a dangerous turning point in an already inflammatory region.

GROWING FRUSTRATION

Israel has remained largely silent as Egypt has struggled in the difficult transition from de-facto dictatorship to democracy, via revolution and growing Islamisation. Prime Minister Benjamin Netanyahu has ordered ministers not to talk in public about the situation for fear of exacerbating tensions.

But there are signs of growing public frustration in Israel.

Last August, eight Israelis died in a cross-border attack blamed on Palestinian militants from the nearby Gaza Strip. Earlier this week, Israel said two grad rockets that hit its territory were fired out of Sinai - a charge Egypt denied.

The worsening security in the south has come at a time of increased tensions in the north, tied to the 15-months-long Syrian crisis, and continuous, low-level warfare in Gaza.

A cartoon in left-leaning Haaertz newspaper on Tuesday showed Netanyahu crouching in a ditch alongside Defence Minister Ehud Barak as rockets fly in from Egypt. "Just make sure you don't upset the Egyptians," the prime minister says.

Israeli officials have so far ruled out direct intervention in the Sinai and have instead urged Egypt to resolve the problem by itself, letting its military dispatch more troops to the peninsula than allowed for by their historic, 1979 peace treaty.

At the same time, Israel is speeding up construction of a 5-metre (16-foot) high barrier that will run most of the 266 km (165 miles) from Eilat on the Red Sea's Gulf of Aqaba up to the Gaza Strip on the Mediterranean.

"We are in a race against the clock to close the border," said Gaza Division Southern Brigade Commander Tal Harmoni following Monday's attack, in which the Israeli army shot dead at least two of the militants before they could return to Egypt.

But as the Israelis have discovered in Gaza, a fence does not keep out rockets or missiles. So unless it opts for direct intervention, it will have to depend on Egyptian intervention.

APPROVING MILITARY MANOEUVRES

The Israeli government has remained in close contact with the Egyptian security apparatus since the downfall of Mubarak and officials, speaking off the record, say relations with the generals in Cairo remain essentially good.

Certainly there was no murmuring from Israel this week when Egypt's military announced it would drastically limit the remit of the new president - most probably Brotherhood candidate Mohamed Morsy.

By contrast, Washington said it was "deeply concerned" by this and asked the army to transfer full power to an elected civilian government as previously promised.

"All in all, the play that was put in motion by the Supreme Council of the Armed Forces against Morsy isnt bad for us," the leading Israeli newspaper Yedioth Ahronoth said on Tuesday.

But an analysis in the same paper warned of bad times ahead. "It isnt the same Egypt, it isnt the same border, the peace accords are on their deathbed and we had better change our operating manual," wrote prominent columnist Alex Fishman.

One of Mubarak's greatest services to Israel was the role he played in containing the Islamist Hamas movement, which rejects Israel's right to exist and has close ties to the Brotherhood, limiting its access to weapons and hemming in its leadership.

Israel believes an empowered Brotherhood will reverse that policy, creating instant friction between the erstwhile allies.

"The announcement of the official presidential results will not mark the end of the turmoil in Egypt and will not bring us any relief. We are going to have a very long hot summer," said Israel's former ambassador to Egypt, Eli Shaked.