Best Paper Award
Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight
Jun Kurihara , Tomohiko Uyematsu , Ryutaroh Matsumoto
[Trans. Fundamentals., Vol. E95-A No.11, Nov. 2012]

Jun Kurihara

Tomohiko Uyematsu

Ryutaroh Matsumoto
 
@A secret sharing scheme (SSS) encodes a secret into multiple shares in such a way that the secret can be reconstructed only from specified sets of shares. Secret sharing, which is used to make distributed storage systems secure, has recently attracted considerable attention. The ramp linear secret sharing scheme has the advantage of allowing the size of a secret to be larger than that of an individual share, and it can be constructed from a pair of linear codes. However, few investigations of ramp linear SSSs have been conducted from a coding theoretic perspective.
@In this award-winning paper, the authors showed that the maximum mutual information between m shares and the secret S is equal to the relative dimension/length profile (RDLP) of linear codes. They also investigated the largest number t1 such that any t1 shares give no information on S, and the smallest number t2 such that any t2 shares allow decoding of S. Next, they showed that both t1 and t2 are exactly expressed by the relative generalized Hamming weights (RGHWs). Then, they extended the strong security definition of SSSs proposed by H. Yamamoto, and defined the α - strong security of SSSs, in which any m shares do not leak information of any combinations of α - m +1 components of the secret vector S. Finally, they showed that the maximum of α is exactly expressed by the RGHW.
@In summary, the paper opens new vistas, suggests new directions in research of SSSs from the coding theoretic perspective, reveals new operational meanings of RDLP and RGHW, and provides new motivation for investigating RDLP and RGHW, which have been investigated to a far lesser extent than have the original DLP proposed by Forney and the original GHW proposed by Wei in coding theory. Therefore, this work is deserving of the 2014 IEICE KIYASU-Zen'iti Award.

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