They have eavesdropped on the enemy for decades, tracking messages from Hitler’s high command and the Soviet KGB and on to the murky, modern world of satellites and cyberspace. But a lowly and yet mysterious carrier pigeon may have them baffled.

Britain’s code-breakers acknowledged Friday that an encrypted handwritten message from World War II, found on the leg of a long-dead carrier pigeon in a household chimney in southern England, has thwarted all their efforts to decode it since it was sent to them last month.