The IDF, when speaking of its enemies, tends to take a stern pedagogical tone. Hamas, for example, is often told what “it needs to understand.”

But as the ongoing intermittent rocket fire and counter fire across the Gaza border shows, the timing and scale of conflict in the South is actually dictated by Hamas, not Israel. And Israel’s difficulties may well intensify now that the Muslim Brotherhood has come to power in Egypt — requiring still greater Israeli sensitivity in tackling Hamas, the Brotherhood’s ally, to avoid providing pretexts for a further deterioration in ties with Cairo.

“Quiet will be met with quiet and fire will be met with fire,” military sources said after a meeting with IDF Chief of the General Staff Lt.-Gen. Benny Gantz on Saturday, during an escalation in the latest round of violence between Israel and Gaza, which continued Tuesday night with five rockets fired on the Israeli city of Netivot. That equation might give the impression that Israel gets to determine how it wants to respond, but in reality it means that Hamas can snipe at Israel, bait her, fire or allow others to fire, with full knowledge that it controls the tempo and severity of Israel’s response.

“The initiative is entirely in the hands of the terrorists,” said Reuven Pedatzur, a former fighter pilot and lecturer at Tel Aviv University’s security studies program, “and we’re trapped in an impossible situation.”

Ever since April 16, 2001, Gaza-based terror organizations have fired roughly 12,700 mortars and rockets at Israel. The IDF, in turn, has launched one large-scale ground invasion and hundreds of airstrikes — insisting on immediately responding to cross-border fire.

These wearying and painful strikes and counter-strikes have unfolded within a fairly rigid set of parameters: Too grave an assault on Israel, Hamas has known, would trigger a very substantial Israeli response. And too severe an Israeli offensive would trigger an international outcry.

The ascent of Mohammed Morsi to the Egyptian presidency complicates these parameters for Israel; the imperative for the IDF and its political masters will be to find a way to effectively counter Hamas without provoking new tensions with Egypt.

Speaking earlier in the year, Maj. Gen. Amir Eshel, today the commander of the air force, said that Egypt faces “unbelievable internal challenges” and that its economy is “in need of a Marshall Plan” that will not likely arrive. He stressed that Israel does not consider Egypt an enemy and that the IDF and the Egyptian armed forces continue to enjoy “great cooperation.” There will be no immediate change, he said, but he predicted that a process had begun and “in the next decade we will see the rise of the Brotherhood all across the region.”

Eshel, at the time the head of IDF Plans and Policy Directorate, traced a crescent from Egypt through Gaza to Jordan, Syria and Turkey and said that while it had not yet coalesced “into an axis,” the links were forming.

Morsi’s presidential victory confirms Eshel’s assessment. And the long-term processes he highlighted play into the hands of Hamas.

In pure military terms, Israel enjoys and will continue to enjoy an immense advantage over Hamas, even though the Islamist rulers of Gaza have clawed their way toward a degree of military deterrence, smuggling weapons underground and creating rockets in basement laboratories. But Israel neither wants to, nor easily can, exercise its military advantage — least of all in the shadow of its newly complicated relationship with Egypt.

Still, former Israeli ambassador to Egypt Yitzhak Levanon is less bleak than commentators like Pedatzur. Notably, where Egypt is concerned, he does not foresee a drastic shift in orientation. “Hamas is very pleased with the current situation in Egypt,” Levanon said, noting that Morsi would certainly side more readily with Hamas than his predecessor. “But I believe that Egypt has an agenda of its own.”

Yes, Levanon said, Israel’s options in Gaza are now slightly more constricted. But Egypt’s primary goals in this context, he believes, will be to assert sovereignty over Sinai — making sure that it does not have “a wasp’s nest” on its border — and to push Hamas toward reconciliation with Fatah and an agreement with Israel.

“Egypt’s goal,” he said, speaking of the short-term in a country swamped with internal difficulties, “will be to limit the friction.”

That may be true for now. But the long-term processes look profoundly worrying. During a recent talk on the effects of the Arab Spring, Maj. Gen. Aviv Kochavi, head of the IDF Intelligence Corps, said that the fall of dictators across the Arab world would lead to a decrease in nationalism and a rise in religious affiliation.

“The nationalist element is being replaced and the Islamic element is on the rise,” he said, “and that is why in terms of Israel, the foundations of the conflict will be more religious.”

Israel has far-reaching intelligence and military capabilities to grapple with these changing realities. But there can be no mistaking the historic trends. The ongoing battle of wits and weaponry with Hamas, it appears, may be just a taste of the wider challenges to come.