An Example Secret Sharing Scheme
A secure secret sharing scheme distributes shares so that anyone with fewer than t shares has no extra information about the secret than someone with 0 shares. Consider the naive secret sharing scheme in which the secret phrase "password" is divided into the shares "pa------," "--ss----," "----wo--," and "------rd,". A person with 0 shares knows only that the password consists of eight letters. He would have to guess the password from 268 = 208 billion possible combinations. A person with one share, however, would have to guess only the six letters, from 266 = 308 million combinations, and so on as more persons collude. This system is not a secure secret sharing scheme, because a player with fewer than t shares gains some information about the content of the secret. In a secure scheme, even a player missing only one share should still face 268 = 208 billion combinations. Arbitrary strength can be maintained even with this "naive" secret sharing scheme with sufficiently chosen fragment (and secret) length.
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