Shamir’s Secret Sharing is a scheme to securely share highly sensitive information such as encryption keys by splitting the information into multiple parts called shares.
Let’s assume a company called ABC with 12 members wanting to safeguard a vault using Shamir’s Secret Sharing. The key to the vault is encrypted and is divided into 12 parts, called shares. These shares are then distributed to the members on the network, meaning that the vault would require a certain number of these members to allow access. Now, due to the threshold feature, even if one or two members are not available at a specific time, the vault could still be accessed with the presence of the other members. This helps to mitigate the risk of failing to decrypt the passcode while keeping the vault safe and secure.
Shamir’s Secret Sharing is developed through a complex algebraic algorithm that estimates unknown values in a gap between two points. It is called polynomial interpolation. What this means is that the algorithm encodes the information needed to be encrypted into a polynomial expression. This is basically the dividing phase before distributing it through the network to the members. Instead of requiring all the members, only the threshold number is needed which provides enough data points to correctly estimate the values between the gaps in the encrypted shares.
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