In a bizarre twist of fate, the offensive, which began Sunday with some 1,000 security personnel backed by several hundred armored vehicles, has the backing of Hamas, the Palestinian fundamentalist organization that controls the Gaza Strip that has been trying to eradicate jihadist interlopers for years.
Israel gave its approval for the push. Under its landmark 1979 peace treaty with Egypt, it returned the Sinai, captured in 1967, to Egypt on condition Cairo demilitarized the Sinai, creating a buffer zone.
Amos Gilad, head of the Israeli Defense Ministry's diplomatic-security bureau, visited Cairo early in August to coordinate the planned offensive against a common threat.
Israel doesn't want security in the Sinai to collapse and provide a sanctuary for al-Qaida nor does it want Egyptian forces in the region in strength once again because it fears that the military-led interim government in Cairo might seek to distance itself from the 1979 treaty under pressure from Egypt's 80 million people, most of whom oppose the treaty.
In recent weeks, Egyptian security officials estimate that 400-500 al-Qaida operatives infiltrated the Sinai amid the anarchy that has descended on the vast desert region since Mubarak's ouster.
The jihadists, who are Sunnis like Hamas and its sympathizers, have entrenched themselves in Gaza to present an ideological challenge to the fundamentalists.
Hamas, which wrested control of Gaza from the mainstream Fatah movement, in a mini-civil war in June 2007, has found itself under attack not for being extremist and violent -- but not extremist and violent enough.
The jihadists of al-Qaida consider Hamas has betrayed its revolutionary origins and abandoned the war against Israel for the privileges of political power. Indeed, many of these jihadists are former Hamas hard-liners.
The stronger these al-Qaida offshoots become, not just in Gaza but in the wider wastes of the Sinai as well, the tougher Hamas will find it to maintain stability in Gaza, opening the way for a renewed Israeli onslaught.
With travel between the territory and Sinai more accessible since Mubarak's fall, coordination between al-Qaida cells in Gaza with fellow travelers in Sinai has been greatly enhanced.
With the Israelis threatening to again invade Gaza, which Israel unilaterally relinquished in September 2005, if it continues to be a thorn in their side, Hamas is under pressure to eradicate the jihadist groups that operate in the coastal territory.
The jihadists, who include other Arabs as well, have established links with the Bedouin tribes of Sinai, long-neglected and suppressed by Cairo and who have been deeply involved in smuggling arms into Gaza.
This activity has intensified since security in Sinai collapsed after Mubarak's downfall.
Ayman al-Zawahiri, Osama bin Laden's longtime deputy, took over al-Qaida Central after bin Laden was killed May 2 by U.S. Navy SEALs Forces in Pakistan.
Zawahiri is Egyptian and spent several years in top security prisons following the assassination of Egyptian President Anwar Sadat in October 1981 by Islamist militants.
Zawahiri fled Egypt on his release in the mid-1980s and helped establish al-Qaida and still advocates overthrowing the Egyptian state and establishing Islamic rule.
Meantime, Bedouin militants are believed to be responsible for sabotaging a trans-Sinai pipeline carrying natural gas from Egypt to Israel and Jordan five times since February, harming the economies of all three countries.
On July 29, heavily armed Bedouins attacked an Egyptian police post in the northern Sinai capital of El Arish, west of the Gaza border, and killed five officers -- a major challenge to the military-led interim government in Cairo.
The current Egyptian offensive, codenamed Operation Eagle, is concentrated in northern Sinai along the Mediterranean coast where Bedouin militants have sanctuaries and hideouts.
But it is unlikely to be enough to crush the jihadists or stem the Bedouins' shift toward extremism.
The Bedouins may well be killed, rounded up, imprisoned or tortured and their animosity toward Cairo would increase, probably triggering bigger offensives.
A rerun of 2003-06 suicide bombings in the southern resorts on the Red Sea like Sharm el-Sheik, playground of Egypt's elite, in which 130 people were killed and hundreds wounded, could be the response.