Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight
スポンサーリンク
概要
- 論文の詳細を見る
This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Δm of the secret vector $\vec{s}$=[s1,...,sl] given m shares in terms of the RDLP of linear codes. We also characterize two thresholds t1 and t2 in the secret sharing schemes by the RGHW of linear codes. One shows that any set of at most t1 shares leaks no information about $\vec{s}$, and the other shows that any set of at least t2 shares uniquely determines $\vec{s}$. It is clarified that both characterizations for t1 and t2 are better than Chen et al.'s ones derived by the regular minimum Hamming weight. Moreover, this paper characterizes the strong security in secret sharing schemes based on linear codes, by generalizing the definition of strongly-secure threshold ramp schemes. We define a secret sharing scheme achieving the α-strong security as the one such that the mutual information between any r elements of (s1,...,sl) and any α-r+1 shares is always zero. Then, it is clarified that secret sharing schemes based on linear codes can always achieve the α-strong security where the value α is precisely characterized by the RGHW.
著者
-
Uyematsu Tomohiko
Department Of Communications And Integrated Systems Tokyo Institute Of Technology
-
Matsumoto Ryutaroh
Department Of Communications And Integrated Systems Tokyo Institute Of Technology
-
Kurihara Jun
Department Of Communications And Integrated Systems Tokyo Institute Of Technology
関連論文
- Key Rate Available from Mismatched Measurements in the BB84 Protocol and the Uncertainty Principle
- Secret Key Agreement by Soft-Decision of Signals in Gaussian Maurer's Model
- An Improved Bound for the Dimension of Subfield Subcodes
- Asymptotical Optimality of Two Variations of Lempel-Ziv Codes for Sources with Countably Infinite Alphabet(Source Coding,Information Theory and Its Applications)
- FOREWORD
- Decodability of Network Coding with Time-Varying Delay and No Buffering
- Universal Coding for Correlated Sources with Complementary Delivery(Information Theory and Its Applications)
- Universal source coding for complementary delivery
- Information-theoretical analysis of index searching : Revised
- Multiterminal source coding with complementary delivering(HISC2006)
- Fixed-Slope Universal Lossy Coding for Individual Sequences and Nonstationary Sources
- Network Design for Multi-Layered Photonic IP Networks Considering IP Traffic Growth(Internet)
- Significance of Measurement of Prostate Specific Antigen (PSA) in Familial Prostate Cancer Lines
- Strongly Secure Privacy Amplification Cannot Be Obtained by Encoder of Slepian-Wolf Code
- Two Methods for Decreasing the Computational Complexity of the MIMO ML Decoder(Communication Theory)(Information Theory and Its Applications)
- On the Feng-Rao Bound for the L-construction of Algebraic Geometry Codes
- Using C_ Curves in the Function Field Sieve
- Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound(Information Theory and Its Applications)
- Linear Codes on Nonsingular Curves are Better than Those on Singular Curves
- Randomness of Individual Sequences
- Universal Variable-to-Fixed Length Codes Achieving Optimum Large Deviations Performance for Empirical Compression Ratio
- A Novel Realization of Threshold Schemes over Binary Field Extensions
- Secret Sharing Schemes Based on Linear Codes Can Be Precisely Characterized by the Relative Generalized Hamming Weight