How long can a conspiracy be kept secret?

One common argument against the existence of any and all conspiracies is that it's impossible to keep secret any project requiring more than a few individuals. 

This sounds plausible, but is it? After all, I grew up around massive secret projects. Friends of the family worked on the crown jewels of the national security state, such as Area 51, the U-2 spy plane, the awesome SR-71, and the F-117 Stealth Fighter. 

Stealth work began in 1975 at both Lockheed and Northrop (which eventually became the B-2 Stealth Bomber) and Lockheed had a stealth prototype, Have Blue, flying at Area 51 by the end of 1977. Carter's defense secretary Harold Brown announced the existence of stealth in August 1980, claiming that leaks in the preceding days had made it impossible to keep the entire concept secret anymore. Republicans angrily claimed he spilled the beans early to defuse Reagan's attack on Carter canceling the B-1 program. The Russians apparently were still clueless about stealth. (It came as a surprise to me, too.)

Airline pilots frequently spotted the otherworldly-looking Skunk Works planes being tested out of Area 51, especially the 2000 mph 80000' altitude SR-71 which covered enormous amounts of territory and caused sonic booms (the SR-71 was announced fairly quickly by LBJ). One theory is that the U.S. government encouraged rumors of flying saucers at Area 51 to discredit these highly credible witnesses.

But all these pale in comparison to the huge Bletchley Park decoding operation in WWII England, which had a staff of nearly 10,000 working on site by the end of the war, and didn't surface in the popular press until the early 1970s. It required the history of computing to be rewritten.

Besides decoding the German Enigma machine, there were other projects at Bletchley that weren't declassified until much more recently, such as Tunny, the breaking of Hitler's personal cipher.

An obituary in today's NYT:

Jerry Roberts, Last of Team of British Code Breakers, Dies at 93 

By PAUL VITELLO   APRIL 2, 2014

Jerry Roberts, the last surviving member of the British code-breaking team that cracked strategic ciphers between Hitler and his top generals, helping to hasten the end of World War II, died on March 25 in Hampshire, England. He was 93. 

His death was confirmed by the Bletchley Park Trust, a nonprofit group that administers the Victorian estate north of London where the British government lodged Mr. Roberts and hundreds of other code breakers during the war, among them linguists, mathematicians and puzzle masters of various backgrounds. 

Mr. Roberts, a German linguist, was part of a small top-secret group assembled in 1941 to help decrypt messages picked up in radio signals between Hitler and his field marshals on the front. The team’s very existence remained a secret until 2006, when the British government declassified wartime intelligence files.

This 2006 date seems exaggerated. Here's the obituary in The Telegraph from 2002 of Roberts' colleague W.T. Tutte:

PROFESSOR BILL TUTTE, who has died aged 84, was responsible for one of Bletchley Park's greatest codebreaking achievments during the Second World War when he cracked the teleprinter cipher, known as Tunny, which Hitler used to communicate with his generals. ...

This was a far more complicated mechanism than the famous Enigma cipher machine, since the Lorenz SZ40 had 12 wheels compared with the three or four on the Enigma. 

It also led to Bletchley Park's other great achievement, the construction of the world's first semi-programmable electronic computer, Colossus, which was used to decipher the Tunny messages.

Looking at the bibliography on Wikipedia, there are sources for the Tunny decryption going back to 1993, but that's still a half century after William Tutte broke Tunny in a tour de force of cryptography.

Roberts' NYT obituary continues:

By 1941, Bletchley Park cryptographers had already deciphered thousands of messages transmitted by lower-level German commanders in the field, thanks to the work of the mathematician Alan Turing, who in 1940 cracked the daunting German secret code that the British called Enigma. But they were stumped by the even more complex ciphered messages being transmitted among Hitler and the generals Erwin Rommel, Wilhelm Keitel, Gerd von Rundstedt and Alfred Jodl. 

 Code breakers initially called the system Fish, taking the name from a German code operator who, in an unguarded moment, had referred to the code as “sägefisch” (sawfish). Mr. Roberts and his group nicknamed it Tunny — as in tuna fish — and they were able to crack it. 

Mr. Roberts eventually served as the head cryptologist for the team, which grew to more than 100.

A maximum staff of 118.

The messages the team deciphered enabled the British government to warn Soviet leaders in 1943 about a major German offensive planned at Kursk that summer. The Soviet Army’s repulse of the attack in the Battle of Kursk was a turning point of the war.

Kursk was the biggest tank battle of all time. Kursk is in Russia today, right near the border with Ukraine.

The Tunny code breakers later helped set the stage for D-Day, establishing in the weeks before June 1944 that Hitler and his commanders expected an Allied invasion along the French coast at Calais, preceded by a feint at Normandy. The Germans were caught off guard by the full assault at Normandy. ...

In an interview with The Telegraph, he conveyed the excitement code breakers experienced when deciphering strategic information, and the frustration they felt at having to keep their work secret. When sharing the information with allies, British intelligence always attributed it to “spies.” 

“I can remember myself breaking messages about Kursk,” Mr. Roberts recalled. “We were able to warn the Russians that the attack was going to be launched, and the fact that it was going to be a pincer movement. We had to wrap it all up and say it was from spies, that we had wonderful teams of spies.”

From The Telegraph:

Capt Roberts later received an MBE in recognition of his service and he became a tireless ambassador for the memory of those who had served this country in secret during the war. 

He spent years campaigning for greater acknowledgement of his colleagues, including Alan Turing, who broke the naval Enigma code. 

Capt Roberts also called for the entire Testery group to be honoured, including Bill Tutte, who broke the Tunny system, and Tommy Flowers, who designed and built the Colossus, which sped up some stages of the breaking of Tunny traffic.

Roberts then had a long successful career in market research.

It's interesting to look at the class background of these codebreakers:

Tommy Flowers was the son of a bricklayer.
William Tutte was the son of a gardener.
Jerry Roberts was the son of a pharmacist.
Alan Turing was highly upper middle class:

Turing was born in Paddington, London, while his father was on leave from his position with the Indian Civil Service (ICS) at Chhatrapur, Bihar and Orissa Province, in British India.[10][11]

The Indian Civil Service was an examination-only elite service.

Turing's father, Julius Mathison Turing (1873–1947), was the son of a clergyman from a Scottish family of merchants which had been based in the Netherlands and included a baronet. Julius's wife, Alan's mother, was Ethel Sara (née Stoney; 1881–1976), daughter of Edward Waller Stoney, chief engineer of the Madras Railways. The Stoneys were a Protestant Anglo-Irish gentry family from both County Tipperary and County Longford, while Ethel herself had spent much of her childhood in County Clare.[12] Julius' work with the ICS brought the family to British India, where his grandfather had been a general in the Bengal Army.