Mackwheaton: Here's a study on keeping secrets which includes formulas for maintaining them. The tables are interesting in that all measures of time are made in days, not weeks or months. Math geeks might enjoy the formulations, but focus on the tables will give you the outcomes. Bottom line, for any single secret, when you include more than 4 people, no single secret can be expected to remain secure for more than a week.

With all due respect, I beg to disagree with your bottom line. Looking at the tables is not enough, because those tables are just representing certain scenarios with certain assumptions.

For example, the first table assumes that the number of communications between each pair of persons who are in on the secret is λ = 2 per day, and that the probability for each of these communications to get compromised is p = 0.01. Reduce λ to 1 per day and the estimated time before the secret gets revealed doubles. Make your communication channels more secure, reduce p to 0.001, and that time becomes tenfold. Examples for more secure communication channels would be to use encrypted e-mails instead of the usual postcard-like style or to meet face to face in a tap-proof room instead of using the phone.

Bottom line: You can't completely avoid leaks and secrets to be revealed. However, you can do a lot to maximize the estimated time until that happens:

• Minimize the number n of people being in on the secret. This is most important as the impact of n is inversely proportional to the square of n.
• Minimize the communication rate λ (inversely proportional linear impact).
• Minimize the hazard rate p of your communication channels (inversely proportional linear impact).
• Use countermeasures, the most important one being disinformation, changing the impact of p from being linear to quadratic, i.e. p = 0.01 with disinformation would lengthen the estimated time until the secret is compromised by a factor of 100.

Oh, and I would recommend to read at least the summary at the end of the article.