General Error Decodable Secret Sharing Scheme and Its Application

• Published in: IEEE transactions on information theory Vol. 57; no. 9; pp. 6304 - 6309
• Main Author: Kurosawa, K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-09-2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Cheater; Coding, codes; Computational modeling; Cryptography; Decoding; error decodable; Errors; Exact sciences and technology; Information theory; Information, signal and communications theory; Noise measurement; perfectly secure message transmission schemes (PSMT); Polynomials; Receivers; Reconstruction algorithms; secret sharing; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); perfectly secure message transmission schemes (PSMT); error decodable; Cheater; Secret sharing; Decoding; Algorithm; Message transmission; Polynomial time
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2161927

Consider a model of secret sharing schemes with cheaters. We say that a secret sharing scheme is error decodable if we can still recover the secret s correctly from a noisy share vector (share 1 ', ..., share n '). In this paper, we first prove that a perfect secret sharing scheme is error decodable if and only if the adversary structure Γ satisfies a certain condition called Q 3 . Next, for such Γ , we show a scheme such that the decoding algorithm runs in polynomial-time in | S | and the size of a linear secret sharing scheme which realizes Γ. We finally show an application to 1-round perfectly secure message transmission schemes (PSMT).