How Edward Snowden's encrypted "insurance" file might work

The simplest form of cryptography that Snowden and his allies could be employing would involve one person keeping an encrypted copy of the files and someone else holding the key necessary to decrypt it. But that method is vulnerable, relying on the trustworthiness of the person who has the key, and it doesn’t sound like what Snowden has done.

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More complex, more secure, and more interesting would be a form of “secret sharing.” Essentially, the files can only be unlocked if each member of a group shares his portion of the encrypted information; or, alternatively, if several people are given encrypted portions and a combination of, say, any three of them is sufficient to unlock the files. For instance, this illustration represents the data shared by three people as intersecting planes; the point where they intersect represents the secret that is unlocked when they’re shared:

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