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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.

As the bird’s story made headlines, pigeon specialists said they believed it may have been flying home from British units in France around the time of the D-Day landing in 1944 when it somehow expired in the chimney at the 17th-century home where it was found in the village of Bletchingley, south of London.

After sustained pressure from pigeon fanciers, Britain’s Government Communications Headquarters, its code-breaking and communications interception unit in Gloucestershire, agreed to try to crack the code. But on Friday the secretive organization acknowledged that it had been unable to do so.

“The sorts of code that were constructed during operations were designed only to be able to be read by the senders and the recipients,” a historian at the organization told the British Broadcasting Corporation.

“Unless we get rather more idea than we have about who sent this message and who it was sent to, we are not going to be able to find out what the underlying code was,” said the historian, who was identified only as Tony under the organization’s secrecy protocols.

Code breakers, he said, believed that there could be two possibilities about the encryption of the message, both of them requiring greater knowledge about the identity of those who devised or used the code.

One possibility, he said, was that it was based on a so-called one-time pad that uses a random set of letters, known only to the sender and the recipient, to convert plain text into code and is then destroyed.

“If it’s only used once and it’s properly random, and it’s properly guarded by the sender and the recipient, it’s unbreakable,” the historian said.

Alternatively, if the message was based on a code book designed specifically for a single operation or mission, then the code breakers were “unlikely” to crack it, the historian said. “These codes are not designed to be casually or easily broken.”

It took a campaign of many years to get officials to pay attention. The pigeon’s skeleton was initially found in 1982 by David Martin, a retired probation officer, when he was cleaning out a chimney at his home in Bletchingley as part of a renovation. The message, identifying the pigeon by the code name 40TW194, had been folded into a small scarlet capsule attached to its leg.

“Without access to the relevant code books and details of any additional encryption used, it will remain impossible to decrypt,” the Government Communications Headquarters said in a news release. “Although it is disappointing that we cannot yet read the message brought back by a brave carrier pigeon, it is a tribute to the skills of the wartime code makers that, despite working under severe pressure, they devised a code that was undecipherable both then and now.”

Mr. Martin said he was skeptical of the idea that the agency had been unable to crack the code. “I think there’s something about that message that is either sensitive or does not reflect well” on British special forces operating behind enemy lines in wartime France, he said in a telephone interview. “I’m convinced that it’s an important message and a secret message.”

There was some indication on Friday, though, that the agency was not taking 40TW194’s code as seriously as, say, tracking satellite phone communications between militants in the Hindu Kush.

One of the most “helpful” ideas about the code, according to Tony, the agency’s historian, had come from an unidentified member of the public. That person suggested that, with Christmas coming and thoughts turning, in the West at least, to a red-robed, white-bearded, reindeer-drawn bearer of gifts skilled at accessing homes through their chimneys, the first two words of the message might be “Dear Santa.”

Mindfucked

It does look like enigma code format. Help me find this formula.