A Study on Multisecret-Sharing Schemes Based on Linear Codes

Secret sharing has been a subject of study since ۱۹۷۹. 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 𝑎(𝑡,𝑛)− threshold secret sharing scheme. A 𝑎(𝑡,𝑛)− threshold secret sharing scheme is a method of distribution of information among 𝑛 participants such that 𝑡≥۱ can recover the secret but (𝑡−۱) cannot. The coding theory has been an important role in the constructing of the secret sharing schemes. Since the code of a symmetric (𝑣,𝑘,𝜆)− design is a linear code, this study is about the multisecret-sharing schemes based on the dual code 𝐶⊥ of 𝐹۲− code 𝐶 of a symmetric (𝑣,𝑘,𝜆)− 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.

Keywords:

Secret Sharing , Multisecret-Sharing , Linear Code , Symmetric Design