KOTA BHARU, Malaysia—Umar Vadillo bounds into a hotel room here in northern Malaysia with several stacks of gold and silver coins in his hands and slaps them down on a coffee table. "This," Mr. Vadillo says, "is what it means to be free."

A quarter century ago, this Spanish-born Muslim convert set to work with other European Muslims to find a substitute for the U.S. dollar and other paper currencies.

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