By Tom Perry and Abdelrahman Youssef

ALEXANDRIA/CAIRO, Dec 2 (Reuters) - Young Egyptian Islamists seeking a way to confront the military-led state are turning to the ideas of a radical ideologue who waged the same struggle half a century ago and later became a source of inspiration for al Qaeda.

The revolutionary ideas of Sayyid Qutb, a Muslim Brotherhood leader executed in 1966, are spreading among Islamists who see themselves in an all-out struggle with generals who deposed President Mohamed Mursi in July.

Their radical conclusions underline the risks facing a nation more divided than ever in its modern history: after Mursi's downfall, the state killed hundreds of Islamists, and attacks on the security forces have become commonplace.

Qutb's writing, much of it produced while a prisoner in President Gamal Abdel Nasser's jails, has supplied ideological fuel for militancy in Egypt and beyond for decades.

He has been cited as a source of inspiration by Ayman al-Zawahri, the Egyptian doctor who was Osama bin Laden's deputy as leader of al Qaeda and took over the militant network after bin Laden's death in 2009.

Within the Brotherhood itself, which decades ago declared itself opposed to violence, Qutb's writings were widely respected but his revolutionary approach took a back seat as the 85-year-old movement focused on seeking power within the system.

Not any more, said Omar Magdy, 23, a Brotherhood activist who likens the crackdown on Islamists today with Nasser's.

"The era in which Sayyid Qutb wrote his work resembles the one we are in now, so his ideas are being revived," Magdy explained in a seafront cafe in Alexandria. "Sayyid Qutb embodies the revolutionary Islamist idea. I support it."

After the fall of Hosni Mubarak in 2011, the Brotherhood pursued its agenda through the ballot box, relying on its organisational muscle to win two parliamentary elections, a presidential vote and two constitutional referenda.

But that all ended in July, when the military, responding to mass demonstrations against Mursi, toppled Egypt's first freely elected leader and launched a crackdown on his followers.

Thousands have been rounded up and many hundreds killed, particularly in the storming of a pro-Mursi protest camp which Islamists see as a massacre that proved the generals wanted to eradicate the Brotherhood once and for all.

Since Mursi's downfall, the Brotherhood has experienced an ideological crisis. For many youths, the ideas of democracy - and even the very concept of the nation state itself - have been discredited.

Magdy, 23, said his uncle was among those shot dead by police. He evokes Qutb by likeningEgypt with the Jahiliya - the period before the emergence of Islam in 7th century Arabia.

"Does society have the features of the Jahiliya? Yes it does," he said.

BATTLE

Qutb was one of thousands of Islamists tortured in jail under Nasser. He was eventually tried and executed for calling for the overthrow of the state.

The Brotherhood's leader, Mohamed Badie, served jail time with Qutb in the 1960s, as did Mahmoud Ezzat, a highly influential figure and one of the few Brotherhood leaders yet to be caught. Qutb has been cited as a major influence over both.

His main political work, "Milestones", was banned in Egypt until the 1990s. After its publication,Egypt's official Islamic establishment declared some of Qutb's ideas blasphemous. His writing also stirred controversy within the Brotherhood itself.

Magdy said Qutb's work is more widely discussed than before by Islamists who, with the benefit of hindsight, now believe the Brotherhood was mistaken to focus on gradual change.

"Mursi was waging the battle to reform the state. I see that we must wage the battle to break up the institutions of state," Magdy said. Asked how, Magdy echoes the Brotherhood's position: "Popular, peaceful activism against military rule".

But other Islamists are more openly following the revolutionary logic through to more extreme conclusions: that violence is the way forward.

"The idea is now discussed," said another Islamist activist, also in his mid-20s, who asked not to be identified. "Even thinking about it before was scary. But now, to a degree, it is acceptable."

"NO MIDDLE GROUND"

Khalil al-Anani, an expert on Islamist movements based at the Middle East Institute in Washington, said the Brotherhood was experiencing "a spiritual crisis".

"After the coup, many of the rank and file lost hope in politics, lost faith in democracy and look at the political conflict from a religious perspective: a confrontation between believers and non-believers," he said. "This idea comes mainly from Sayyid Qutb. There is no middle ground."

After Mubarak's downfall, even hardline Islamists followed the Brotherhood into mainstream politics. They shelved their rejection of democracy as a system alien to Islam, set up parties and contested elections.

Now, the hardliners' logic, which always found an audience at the margins, is starting to resonate among youths who were part of the more moderate mainstream until recently.

"Is there really a Brother out there who still believes ... democracy is the way to Islamic government?" one Brotherhood activist asked in a recent discussion on Facebook with other Brotherhood members.

The Brotherhood, which estimates it has up to 1 million members in a country of 85 million, is in disarray. The crackdown has sapped its capacity to organise, making it harder to maintain the official message of peaceful resistance.

More radical Islamist groups, some inspired by al Qaeda, have stepped up attacks against the state in the Sinai Peninsula. Such attacks have also spread to the more densely populated Nile Valley, reaching Cairo. Around 200 members of the security forces have been killed since Mursi's ouster.

Army chief Abdel Fattah al-Sisi's supporters are comparing him to Nasser, reflecting the deep polarisation in the nation.

The state has declared a war on terrorism. In a narrative with echoes of the 1990s - when militants last fought a sustained insurrection against the Egyptian state - Islamists accuse the government of trying to provoke a confrontation.

"Many of the Islamist youth started drifting to the option of violence after the coup," said an independent Islamist activist, speaking on condition of anonymity for fear of arrest.

In recent weeks, the activist said he had dissuaded four people from taking up arms. "They are desperate. I told them you cannot use violence on the basis of desperation."

"They could have taken dozens with them," he added.

Since Mursi's fall, some Egyptian Islamists on Internet social media have begun rallying around a slogan advocating a pan-Islamic order: "Down with nationalism - borders are earth."

"WE'VE SEEN THIS MOVIE BEFORE"

An Islamist dream since the collapse of the Ottoman Caliphate in the early 20th century, the slogan marks a radical challenge to the modern day frontiers of the Middle East and dovetails with al Qaeda's thinking. It is also a challenge to the Brotherhood's approach of working within the system.

"Many Islamist youth are convinced by this idea. Is it spreading? It is spreading in a dangerous way. If it spreads without maturing first, it will only produce a new al Qaeda," said the activist.

The course of events in Egypt has evoked comparisons with Algeria, where the state aborted an experiment with democracy in 1991 because of Islamists' success at the ballot box, setting off a decade of civil war.

"After the coup in Algeria, the Islamists said: 'Democracy is the idol of the West ... We have been tricked into playing by democratic rules'. That is what happened in Algeria, and I think we have entered the Algerian condition," said Mohamed Soffar, a professor of political science at Cairo University who wrote his doctoral thesis on Sayyid Qutb at the Free University of Berlin.

But, predicting "a passing phase of youthful anger", he argued that militancy in Egypt will ultimately be curbed by the country's experience of it from the 1970s to the 1990s, including the 1981 assassination of President Anwar Sadat.

"We have seen this movie before, and we know where it ended," Soffar said. "Certain groups ... bred this kind of thought and political action, and then they all failed." (Writing by Tom Perry; Editing by Michael Georgy and Peter Graff)