A Study on Multisecret-Sharing Schemes Based on Linear Codes

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.

An Efficient Decoding Algorithm for Block Codes Based on the Communication Channel Reliability Information

“…There are two kinds of algorithms that provide the conceptual basis for soft-decision decoding. One is to select the code word which minimizes the distance from the received sequence in order to minimize the block error probability [5,6]. The other is to decode each symbol in a code word in order to minimize the symbol error probability [7].…”

“…In this paper, we shall investigate the former approach. The conventional algorithms have excellence in either error probability or decoding complexity [1, [4][5][6][7][8][9][10]. Zhang et al (2017) [11] proposed a feedback method combined with the low-density parity-check codes for building the wiretap channel.…”