Brooking's Tamara Coffman-Wittes and former senior Israeli diplomat Itamar Rabinovich write that for the Egypt-Israel peace treaty to survive it should be renegotiated:

In order to sustain the peace treaty, Egypt and Israel should renegotiate its military annex to allow Egypt to deploy forces in previously restricted zones and re-establish full sovereignty over the Sinai. Such a move would strengthen bilateral relations, generate goodwill in Egypt, and increase Israel’s confidence in the Muslim Brotherhood’s commitment to peace.

During such a renegotiation, the two countries would discuss in detail the most effective approach to tackling their shared challenges related to terrorism and transnational crime, in order to ensure that Egypt’s increased military presence in the Sinai also enhances Israel’s security. Egypt’s newly democratic government would be more strictly accountable for fulfilling the treaty’s terms if it played an active role in establishing them. At the same time, the agreement would boost domestic support for Egypt’s government and enhance its regional standing.

This is the option I've heard many Israelis officials and pundits argue as a possible silver lining to the rise of the Muslim Brotherhood in Egypt: getting Islamists to directly re-affirm their approval of the treaty in exchange for regaining full sovereignty. Between the lines is that such a negotiation would have to be carried out by elected civilian officials and approved by the president (and perhaps parliament), rather than conducted through the only existing channels of the Egypt-Israel relationship at the moment, the military, intelligence and lower rungs of the ministry of foreign affairs.

I'm not sure the Brothers would bite (although they could certainly be incentivized by "sweeteners" such as more US aid.) They are more likely to push for an arrangement that would gradually impose the regaining of sovereignty in eastern Sinai as a fait accompli, leveraging Western concern about the security situation there. Or, should direct talks be unavoidable, they would be much more likely to take place in the case of a major breakthrough in the Israeli-Palestinian conflict that would provide some cover.

Khaled Guindy writes:

Despite a general sense that things might still change for the worse, especially given Egypt’s instability and its strongly anti-Israel political culture, Israeli military officials have nothing but praise for Egyptian-Israeli security cooperation, which they say is better today than it was under Mubarak. According to Israeli analyst, Avi Issacharoff, “Whatever uncertainty Israelis may have had at the start of the transition, they now know they have a partner on the Egyptian side.” That claim was backed up by Morsi’s pivotal role in securing a Gaza ceasefire last November.

Even the highly unpopular Gaza blockade, which the Brotherhood had always vowed to overturn, has been loosened but not yet lifted. Thus, despite the Brotherhood’s ideological and historical affinity with Hamas, itself a Brotherhood offshoot, Gaza’s Islamist rulers remain in a box—albeit a bigger one than before.

This reminds me that recently someone who was recently in Israel said the security establishment thinks that Egypt will keep a lid on Hamas for them. I wouldn't expect that to last (if only because Hamas may have more clout over Egypt than vice-versa these days), but it's true that so far they're probably not too unhappy.

↪ Operation Pillar of Defense is Ehud Barak's test

Interesting interpretation by Aluf Benn in Haaretz:

Barak believes in the "leverage and pressure" method - first employed by Israel during Operation Accountability, in Lebanon in the summer of 1993. In this method, which Barak likes to demonstrate through the use of hand gestures and timetables, the goal of the warfare is to obtain a reasonable cease-fire arrangement between Israel and its adversary, whether Hezbollah or Hamas. The tactic is to apply pressure on the enemy's "state patron." Israeli firepower, or the threat of such, demonstrated through a wide call-up of reserve troops, is intended to signal to the patron state that its proteges are at risk of receiving a massive blow and it must intervene to calm the situation.

Egypt is the state patron of Hamas in the current round, and Israel's actions are aimed at prodding the new rulers in Cairo to stop the fighting and to act as guarantor of a future cease-fire. That is the role played by Syria and Iran, Hezbollah's sponsors, in the rounds of fighting in Lebanon. "It is obvious that Egypt's Muslim Brotherhood regime provides a tailwind for Hamas in Gaza," together with economic aid from Qatar, Barak said last Sunday during a lecture. He also warned that Israel would not quail at any military measure in order to restore calm and security to Israelis living near the Gaza border.