A Multisecret-Sharing Scheme Based on LCD Codes

Adel Alahmadi (1) , Alaa Altassan , Ahmad Alkenani (2) , Selda Çalkavur , Hatoon Shoaib , Patrick Sole (3)

1 MECAA - Middle East Center of Algebra and its Applications
2 Department of Mathematics [Jeddah]
3 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: multisecret-sharing; secret sharing; linear codes

Domaines: Mathématiques [math]

Adel Alahmadi, Alaa Altassan, Ahmad Alkenani, Selda Çalkavur, Hatoon Shoaib, et al.. A Multisecret-Sharing Scheme Based on LCD Codes. Mathematics , 2020, ⟨10.3390/math8020272⟩. ⟨hal-02485030⟩