Did H.H Holmes have it right? He notoriously fired workmen who were, unwittingly, helping construct his murder castle before they could put two and two together. Can you build a massive, secret infrastructure and have employees? Or do you have to be a lone ranger. link
As you can guess, the more people you let in on a secret basically ensures that the secret won't stay secret for long. An Oxford University physicist, David Grimes, hypothesizes that even if everyone is dedicated to keeping it a secret it is only a matter of time before something slips through the cracks.
In order to better inform his idea that the more people involved means the smaller amount of time a secret is kept secret he researched three well-documented conspiracies (The Tuskegee syphilis experiment - 25 years, FBI forensic scandal (approx. 6 years), and NSA's PRISM program (approx. 6 years).
With this data collected, Grimes surmised the chance of a leak (deliberate OR accidental) to be 1 in 250,000.
He extrapolated more data and has come out with more predictions, such as...
-If you want to keep something a secret for 5 years, have less than 2,531 people involved
-If you're shooting for a decade, 1,257 is the absolute largest you can go
-If you want a conspiracy that lasts a century or more (a la the Davinci Code) then you need to keep it down to 125.
Grimes reminds us that this is simply a thought experiment, in the "real world" other factors would quite certainly come into play, most notably the actions/motivations of an individual person.
He also added a caveat to the end of his findings, "This work did not require specific funding, from nebulous clandestine cabals or otherwise".