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Secret sharing schemes based on additive codes over GF(4)

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Abstract

A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed–Solomon code. SSSs based on linear codes have been studied by many researchers. However there is little research on SSSs based on additive codes. In this paper, we study SSSs based on additive codes over GF(4) and show that they require at least two steps of calculations to reveal the secret. We also define minimal access structures of SSSs from additive codes over GF(4) and describe SSSs using some interesting additive codes over GF(4) which contain generalized 2-designs.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 121-742, South Korea

    Jon-Lark Kim & Nari Lee

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  1. Jon-Lark Kim
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  2. Nari Lee
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Correspondence to Nari Lee.

Additional information

J.-L. Kim was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2005172). N. Lee was partially supported by the National Institute for Mathematical Sciences (No. A21503).

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Kim, JL., Lee, N. Secret sharing schemes based on additive codes over GF(4). AAECC 28, 79–97 (2017). https://doi.org/10.1007/s00200-016-0296-5

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  • DOI: https://doi.org/10.1007/s00200-016-0296-5

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