Secret Sharing scheme. A secret sharing scheme (or secret splitting [18]) is a method used for a secret distribution between a group of a defined number of parties, where each then stores a share of the secret. Distributed shares alone are of no use. Such distributed secret can then be reconstructed by, at least, a defined minimum of parties. Such minimum is called the threshold and is in most secret sharing schemes marked as 𝑡 and with the number of involved parties can describe the scheme as (𝑛, 𝑡)- or (𝑡, 𝑛)- threshold schemes. There are two particular cases of trivial sharing, and those are cases where 𝑡 = 1, where is the whole secret distributed to all participants and where 𝑡 = 𝑛, where to recover a secret, all parties must participate. Of course, there exist constructions that can reconstruct the given secret without the defined threshold, such as the Secret Sharing Scheme Realising General Access Structure proposed by Xxxxxxx Xxx, Xxxxx Xxxxx, and Xxxxx Xxxxxxxxx [16]. The scheme employs a dealer that owns the secret and gives out the shares of such secret to 𝑛-number of players under specific conditions, which allows the secret reconstruction operation from the distributed shares. The requirements for the secret sharing are two: • Correctness that states that the distributed secret can reconstruct any au- thorised set of party ≥ 𝑡, and • Perfect Privacy that states that every unauthorised set of parties can learn no theoretical information about the secret from their shares. Secret sharing schemes can use many cryptographic protocols as building blocks such as multiparty computation, generalised oblivious transfer, or attribute-based encryption [9]. Two most known secret sharing schemes are the Shamir’s Secret Sharing (SSS) which is a simple (𝑡, 𝑛)-threshold scheme and the Blakley’s scheme, which use the (𝑛− 1)-dimensional nonparallel hyperplanes to recover the secret that is represented by the planes intersection [7].
