A Multisecret-Sharing Scheme Based on LCD Codes

Adel Alahmadi, Alaa Altassan, Ahmad AlKenani, Selda Çalkavur, Hatoon Shoaib and Patrick Solé
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Adel Alahmadi: Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Alaa Altassan: Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ahmad AlKenani: Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Selda Çalkavur: Math Department, Köseköy Vocational School, Kocaeli University, Kocaeli 41135, Turkey
Hatoon Shoaib: Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Patrick Solé: CNRS, Aix Marseille University, Centrale Marseille, I2M, 13009 Marseille, France

Mathematics, 2020, vol. 8, issue 2, 1-10

Abstract: 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.

Keywords: secret sharing; multisecret-sharing; linear codes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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