Secret Sharing Schemes from Linear Codes over $\mathbb{F}_2$+v$\mathbb{F}_2$+v2$\mathbb{F}_2$

WANG Yaru; LI Fulin; ZHU Shixin

doi:10.1049/cje.2021.06.012

Volume 30 Issue 5

Sep. 2021

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WANG Yaru, LI Fulin, ZHU Shixin, “Secret Sharing Schemes from Linear Codes over $\mathbb{F}_2$+v$\mathbb{F}_2$+v2$\mathbb{F}_2$,” Chinese Journal of Electronics, vol. 30, no. 5, pp. 895-901, 2021, doi: 10.1049/cje.2021.06.012

Citation:

WANG Yaru, LI Fulin, ZHU Shixin, “Secret Sharing Schemes from Linear Codes over $\mathbb{F}_2$+v$\mathbb{F}_2$+v²$\mathbb{F}_2$,” Chinese Journal of Electronics, vol. 30, no. 5, pp. 895-901, 2021, doi: 10.1049/cje.2021.06.012

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Secret Sharing Schemes from Linear Codes over $\mathbb{F}_2$+v$\mathbb{F}_2$+v²$\mathbb{F}_2$

doi: 10.1049/cje.2021.06.012

School of Mathematics, Hefei University of Technology, Hefei 230000, China

Funds:

This work is supported by the National Natural Science Foundation of China (No.61772168, No.60973125, No.61572168) and the Natural Science Foundation of Anhui Province (No.1508085MA13).

Received Date: 2018-03-05
Available Online: 2021-09-02

Abstract

Abstract

Secret sharing is an important concept in cryptography, however it is a difficult problem to determine the access structure of the secret sharing scheme based on a linear code. In this work, we construct two-weight linear codes over finite field by using linear codes over finite ring. We first study MacDonald codes over the finite ring $\mathbb{F}_2$+v$\mathbb{F}_2$+v²$\mathbb{F}_2$ with v³=v. Then we give torsion codes of MacDonald codes of type α and β, which are two-weight linear codes. Finally we give the access structures of secret sharing schemes based on the dual codes of the two-weight codes.
- Secret sharing,
- Finite ring,
- MacDonald codes,
- Torsion codes,
- Access structure

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References(20)

References

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