Security of Secret-Sharing Schemes Can Be Characterized by Relative Parameters of Linear Codes

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  • 線形符号の相対パラメータによって表される秘密分散法の安全性
  • 招待講演 線形符号の相対パラメータによって表される秘密分散法の安全性
  • ショウタイ コウエン センケイ フゴウ ノ ソウタイ パラメータ ニ ヨッテ アラワサレル ヒミツ ブンサンホウ ノ アンゼンセイ

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Abstract

In this paper, we first introduce Shamir’s construction of the (k; n)-threshold scheme as a typical linear secret-sharing scheme and explain the construction of the (k; l; n)-threshold ramp scheme proposed by Yamamoto and Blakley-Meadows as its extension. Then, by generalizing threshold ramp schemes with a linear code C1 and its subcode C2, we represent a linear secret-sharing scheme in terms of C1 and C2. As examples, we represent Shamir’s (k; n)-threshold scheme and the (k; l; n)-threshold ramp scheme of Yamamoto and Blakley-Meadows using linear codes. Furthermore, we show that in linear secret-sharing schemes, the maximum amount of information leakage of a secret message and their strong security are characterized by the relative generalized Hamming weights (RGHW’s) of C1 and C2 when every share is an element of a finite field.

Journal

  • IEICE ESS Fundamentals Review

    IEICE ESS Fundamentals Review 9 (1), 14-23, 2015

    The Institute of Electronics, Information and Communication Engineers

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