Secret sharing is one of the most important cryptographic protocols. Secret sharing schemes (SSS) have been created to that end. This protocol requires a dealer and several participants. The dealer divides the secret into several pieces ( the shares), and one share is given to each participant. The secret can be recovered once a subset of the participants (a coalition) shares their information. In this paper, we present a new multisecret-sharing scheme inspired by Blakley's method based on hyperplanes intersection but adapted to a coding theoretic situation. Unique recovery requires the use of linear complementary (LCD) codes, that is, codes in which intersection with their duals is trivial. For a given code length and dimension, our system allows dealing with larger secrets and more users than other code-based schemes.
Secret sharing has been a subject of study since 1979. It is important that a secret key, passwords, information of the map of a secret place or an important formula must be keptsecret. The main problem is to divide the secret into pieces instead of storing the whole for a secret sharing. A secret sharing scheme is a way of distributing a secret among a nite set of people such that only some distinguished subsets of these subsets can recover the secret. The collection of these special subsets is called the access structure of the scheme.In this paper, we propose a new approach to construct secret sharing schemes based on field extensions.
A (t,n)-secret sharing scheme is a method of distribution of information among n participants such that any t>1 of them can reconstruct the secret but any t−1 cannot. A ramp secret sharing scheme is a relaxation of that protocol that allows that some (t−1)-coalitions could reconstruct the secret. In this work, we explore some ramp secret sharing schemes based on quotients of polynomial rings. The security analysis depends on the distribution of zero-sum sets in abelian groups. We characterize all finite commutative rings for which the sum of all elements is zero, a result of independent interest. When the quotient is a finite field, we are led to study the weight distribution of a coset of shortened Hamming codes.
A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot. Such schemes can be used for sharing a private key, for digital signatures or sharing the key that can be used to decrypt the content of a file. There are many methods for secret sharing. One of them was developed by Blakley. In this work, we construct a multisecret-sharing scheme over finite fields. The reconstruction algorithm is based on Blakley’s method. We determine the access structure and obtain a perfect and ideal scheme.
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.
In this paper, we examine a secret sharing scheme based on polynomials over finite fields. In the presented scheme, the shares can be used for the reconstruction of the secret using polynomial multiplication. This scheme is both ideal and perfect.
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