But unlike Al Qaeda, Hizb ut-Tahrir believes it can recreate the Caliphate peacefully. Its activists aim to pursuade Muslim political and military leaders that reestablishing the Caliphate is their Islamic duty. Once these leaders invite Hizb ut-Tahrir to take power - effectively staging a military coup - the party would then repeat the process in other countries before linking them up to form a revived Caliphate.
"We spread our ideas by addressing people directly," says Abdullah Shakr, a fluent English-speaker, who, like all three men, spent time in Jordanian jails for membership in the party. "We don't care if the government knows about us, but ... we try not to catch their attention."
The party was founded in Jerusalem in 1953 by a Palestinian judge, Sheikh Taqiuddin Al-Nabhani. He taught that the Muslim world had grown poor and weak ever since the Caliphate was abolished by Turkish leader Kemal Ataturk in 1924.
The Caliphate was created after the death of Islam's founder Muhammad in 632 AD. During the following centuries the Caliphate expanded Islam's territories by conquest and treaty to cover most of the Middle East, Central Asia, and North Africa. As the Ottoman Turks lost ground to the West, they increasingly donned the cloak of the Caliphate. In the 1920s, Muslims throughout the British empire, particularly in India, used the restoration of the Caliphate as an anti-colonial rallying point. "People look back on the Caliphate and see its success as a poor reflection on the condition of the Muslim world today," says Mr. Ulph.
Hizb ut-Tahrir promises that a revived Caliphate will end corruption and bring prosperity - though the group doesn't say how. It will let Muslims challenge, and ultimately conquer, the West, its followers say.