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Concept
Shamir's secret sharing
Summary
Shamir's secret sharing (SSS) is an efficient secret sharing algorithm for distributing private information (the "secret") among a group so that the secret cannot be revealed unless a quorum of the group acts together to pool their knowledge. To achieve this, the secret is mathematically divided into parts (the "shares") from which the secret can be reassembled only when a sufficient number of shares are combined. SSS has the property of information-theoretic security, meaning that even if an attacker steals some shares, it is impossible for the attacker to reconstruct the secret unless they have stolen the quorum number of shares.
Shamir's secret sharing is used in some applications to share the access keys to a master secret.
SSS is used to secure a secret in a distributed form, most often to secure encryption keys. The secret is split into multiple shares, which individually do not give any information about the secret.
To reconstruct a secret secured by SSS, a number of shares is needed, called the threshold. No information about the secret can be gained from any number of shares below the threshold (a property called perfect secrecy). In this sense, SSS is a generalisation of the one-time pad (which can be viewed as SSS with a two-share threshold and two shares in total).
A company needs to secure their vault. If a single person knows the code to the vault, the code might be lost or unavailable when the vault needs to be opened. If there are several people who know the code, they may not trust each other to always act honestly.
SSS can be used in this situation to generate shares of the vault's code which are distributed to authorized individuals in the company. The minimum threshold and number of shares given to each individual can be selected such that the vault is accessible only by (groups of) authorized individuals. If fewer shares than the threshold are presented, the vault cannot be opened.
By accident or as an act of opposition, some individuals might present incorrect information for their shares.
Official source
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