It is perhaps one of the C.I.A.’s most mischievous secrets.

“Kryptos,” the sculpture nestled in a courtyard of the agency’s Virginia headquarters since 1990, is a work of art with a secret code embedded in the letters that are punched into its four panels of curving copper.

“Our work is about discovery  discovering secrets,” said Toni Hiley, director of the C.I.A. Museum. “And this sculpture is full of them, and it still hasn’t given up the last of its secrets.”

Not for lack of trying. For many thousands of would-be code crackers worldwide, “Kryptos” has become an object of obsession. Dan Brown has even referred to it in his novels.

The code breakers have had some success. Three of the puzzles, 768 characters long, were solved by 1999, revealing passages  one lyrical, one obscure and one taken from history. But the fourth message of “Kryptos”  the name, in Greek, means “hidden”  has resisted the best efforts of brains and computers.