Violence escalated in Israel and Gaza after a multi-pronged attack by Palestinian militants along the Egyptian border killed eight Israelis on Thursday. Within hours of those strikes, Israel had killed at least four members of the armed Palestinian group, the Popular Resistance Committees, which it blamed for the attack. Israel also launched nighttime air strikes in the Gaza Strip, saying the attackers had left Gaza and entered southern Israel through Egypt's Sinai Peninsula. Here are three crucial lessons to take from the initial attack, and Israel's response:

1. Egypt's chaos exposes Israel to new terrorist attacks
"This isn’t just another terrorist attack — it's a major escalation" that makes the Egyptian border a "new front in the war," says Barry Rubin at Pajamas Media. Thanks to the chaos in Egypt in the wake of Hosni Mubarak's downfall, these killers managed to travel unchallenged from Gaza through Egypt, and murder Israelis, including two parents and their 4- and 6-year-old kids. And the "prime suspect" — the Palestinian Popular Resistance Committees — is an al Qaeda affiliate, which would make this the "first successful al Qaeda attack on Israel."

2. Retaliation won't bring peace
"The attacks in the south should remind us that in the Israeli-Palestinian military arena there is no knockout victory," says Akiva Eldar in Israel's Haaretz. You hammer the Palestinian Liberation Organization, you get Hamas. Go after Hamas, and al Qaeda jumps into the fight. "Had Israel acted wisely, not only powerfully, the retaliation should have been an immediate resumption of peace talks" with Fatah, "the Palestinian faction that stands for the two-state solution."

3. Israel has to make a tough choice
Under a 1979 peace treaty, Egypt has to observe strict limitations on the forces it puts in Sinai, say the editors of The Economist, which has been "so often a battle-field between Israel and Egypt." But judging by Thursday's attacks, "further reinforcements of men, vehicles and weapons may be needed." So "Israel faces a dangerous dilemma" — it's understandably reluctant to invite more Egyptian soldiers into the area, especially "given the turbulence and uncertainty still shrouding Egypt's future." But there is no other way to restore security in Sinai.