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Mathematics
Volume 8
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10.3390/math8020272
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Article

A Multisecret-Sharing Scheme Based on LCD Codes

by
Adel Alahmadi
1,
Alaa Altassan
1,
Ahmad AlKenani
1,
Selda Çalkavur
2,
Hatoon Shoaib
1 and
Patrick Solé
3,*
1
Math Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Math Department, Köseköy Vocational School, Kocaeli University, Kocaeli 41135, Turkey
3
CNRS, Aix Marseille University, Centrale Marseille, I2M, 13009 Marseille, France
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 272; https://doi.org/10.3390/math8020272
Submission received: 13 January 2020 / Revised: 11 February 2020 / Accepted: 12 February 2020 / Published: 18 February 2020
(This article belongs to the Special Issue Algebra and Its Applications)
Versions Notes

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 secret sharing; multisecret-sharing; linear codes

Share and Cite

MDPI and ACS Style

Alahmadi, A.; Altassan, A.; AlKenani, A.; Çalkavur, S.; Shoaib, H.; Solé, P. A Multisecret-Sharing Scheme Based on LCD Codes. Mathematics 2020, 8, 272. https://doi.org/10.3390/math8020272

AMA Style

Alahmadi A, Altassan A, AlKenani A, Çalkavur S, Shoaib H, Solé P. A Multisecret-Sharing Scheme Based on LCD Codes. Mathematics. 2020; 8(2):272. https://doi.org/10.3390/math8020272

Chicago/Turabian Style

Alahmadi, Adel, Alaa Altassan, Ahmad AlKenani, Selda Çalkavur, Hatoon Shoaib, and Patrick Solé. 2020. "A Multisecret-Sharing Scheme Based on LCD Codes" Mathematics 8, no. 2: 272. https://doi.org/10.3390/math8020272

APA Style

Alahmadi, A., Altassan, A., AlKenani, A., Çalkavur, S., Shoaib, H., & Solé, P. (2020). A Multisecret-Sharing Scheme Based on LCD Codes. Mathematics, 8(2), 272. https://doi.org/10.3390/math8020272

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