Secret sharing schemes from three classes of linear codes

• Published in: IEEE transactions on information theory Vol. 52; no. 1; pp. 206 - 212
• Main Authors: Yuan, Jin, Ding, Cunsheng
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Codes; Coding; Coding, codes; Computer science; Construction; Councils; Covering; covering problem; Cryptography; Error correction codes; Exact sciences and technology; exponential sums; Hamming weight; Information theory; Information, signal and communications theory; Linear code; linear codes; Linear equations; secret sharing; Signal and communications theory; Sufficient conditions; Sums; Telecommunications and information theory; Theory; Vectors; Linear code; linear codes; Coding; Covering problem; exponential sums; Data processing; Secret sharing; Cryptography
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2005.860412

Secret sharing has been a subject of study for over 20 years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code, which is a difficult problem in general. In this paper, a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums. Some linear codes whose covering structure can be determined are constructed, and then used to construct secret sharing schemes with nice access structures.