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IEEE Access
Article . 2024 . Peer-reviewed
License: CC BY
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IEEE Access
Article . 2024
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A New Security Measure in Secret Sharing Schemes and Secure Network Coding

Authors: Itaru Kurihara; Jun Kurihara; Toshiaki Tanaka;

A New Security Measure in Secret Sharing Schemes and Secure Network Coding

Abstract

Linear secret sharing schemes protect secret information from leakage and destruction by encoding secret information into multiple shares, where the secret information can be reconstructed by collecting a certain subsets of shares. Perfect Security, $\alpha $ -strong Security, and Individual Security (IS) have been given as security measures of linear secret sharing schemes. Consider the threshold for each security measure, which is defined as the maximum allowable size of the set of leaked shares. Kurihara et al. have revealed that thresholds for Perfect Security and $\alpha $ -strong Security are characterized in terms of a relative code parameter Relative Generalized Hamming Weight (RGHW). However, the threshold for IS is not yet characterized. In this paper, we focus on individual elements of secret information and give the threshold for IS (Individual Security Threshold IST) as a new security measure, where each element of secret information cannot be uniquely determined from subsets of shares with size less than or equal to the IST. We show that the IST can be characterized in terms of RGHW as well as Perfect Security and $\alpha $ -strong Security. We also give a precoding method for secret information that can guarantee IST above a certain value in any existing linear secret sharing schemes. Moreover, we extend the notion of the IST to universal secure network coding (USNC) and present the Universal IST. We also show that the Universal IST can be represented by the code parameter Relative Generalized Rank Weight (RGRW) similarly to the IST of the linear secret sharing schemes.

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Keywords

nested coset coding, individual security threshold, perfect security, linear secret sharing schemes, relative generalized Hamming weight, Electrical engineering. Electronics. Nuclear engineering, Individual security, TK1-9971

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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