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Shamir's Secret Sharing
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Shamir's Secret Sharing : ウィキペディア英語版
Shamir's Secret Sharing

Shamir's Secret Sharing is an algorithm in cryptography created by Adi Shamir. It is a form of secret sharing, where a secret is divided into parts, giving each participant its own unique part, where some of the parts or all of them are needed in order to reconstruct the secret.
Counting on all participants to combine the secret might be impractical, and therefore sometimes the ''threshold scheme'' is used where any k of the parts are sufficient to reconstruct the original secret.
==Mathematical definition==
The goal is to divide secret S (e.g., a safe combination) into n pieces of data S_1,\ldots,S_n in such a way that:
# Knowledge of any k or more S_i pieces makes S easily computable.
# Knowledge of any k-1 or fewer S_i pieces leaves S completely undetermined (in the sense that all its possible values are equally likely).
This scheme is called \left(k,n\right) threshold scheme.
If k=n then all participants are required to reconstruct the secret.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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