Abstract

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.

Highlights

  • A cryptosystem is an implementation of cryptographic techniques providing information security services

  • The pieces alone have no information about the secret, but the secret can be reached by combining some pieces

  • We show that the Blakley scheme is not adapted to finite fields

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Summary

Introduction

A cryptosystem is an implementation of cryptographic techniques providing information security services. Blakley’s method is based on finite geometry In this scheme, the geometry of hyperplanes over a finite field is used to solve the secret sharing problem [8]. In [16], we constructed a new multisecret-sharing scheme based on LCD codes. Secret sharing satisfies the distribution the private keys to the participants safely and does not trust a creature and central system One type of such systems is blockchain systems. Krawczyk [19] consolidated the DSB scheme with Shamir’s [1] secret sharing scheme and private key encryption and information dispersal algorithm (IDA) [20].

Blakley Threshold Secret Sharing Scheme
Ramp Secret Sharing Scheme
Notation
Scheme Description
Statistics on Coalitions
Security Analysis
Information Theoretic Efficiency
Comparison with other Schemes
Conclusions
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