Abstract
Secret sharing has been a subject of study since 1979. In the secret sharing schemes there are some participants and a dealer. The dealer chooses a secret. The main principle is to distribute a secret amongst a group of participants. Each of whom is called a share of the secret. The secret can be retrieved by participants. Clearly the participants combine their shares to reach the secret. One of the secret sharing schemes is threshold secret sharing scheme. A threshold secret sharing scheme is a method of distribution of information among participants such that can recover the secret but cannot. The coding theory has been an important role in the constructing of the secret sharing schemes. Since the code of a symmetric design is a linear code, this study is about the multisecret-sharing schemes based on the dual code of code of a symmetric design. We construct a multisecret-sharing scheme Blakley’s construction of secret sharing schemes using the binary codes of the symmetric design. Our scheme is a threshold secret sharing scheme. The access structure of the scheme has been described and shows its connection to the dual code. Furthermore, the number of minimal access elements has been formulated under certain conditions. We explain the security of this scheme.
Highlights
A secret sharing scheme is a process of distributing a secret to a set of participants in such a way that only certain subsets of them can determine the secret
The access structure of schemes based on self-dual codes was analyzed in Dougherty et al (2008) research using some properties of the codes [6]
We developed in Molla and Çalkavur (2018) research [16] a new approach to construct secret sharing schemes based on field extensions
Summary
A secret sharing scheme is a process of distributing a secret to a set of participants in such a way that only certain subsets of them can determine the secret. An important class of secret sharing schemes is those which are based on linear codes. The relation between secret sharing schemes and linear codes was first presented in McEliece and Sarwate (1981) research [4]. Massey (1993) [5] used to linear codes to construct the secret sharing schemes. We constructed a multisecret-sharing scheme based on error correcting codes in Çalkavur and Solé (2015) research [12]. In Alahmadi et al (2020) [13] we presented a new multisecret-sharing scheme based on LCD codes. Secret sharing schemes based on extension fields were explored in Çalkavur (2018) study [15]. This paper deals with constructions of multisecret-sharing schemes based on binary linear codes of symmetric designs.
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