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Steganography from perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers and Lipschitz integers

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Abstract

Steganography is the science of communicating a secret message by hiding it in a cover object. The well known F5 algorithm is based on binary Hamming codes in Hamming graph. It has been an interesting research problem to construct other steganographic schemes from mathematically structured graphs. In this paper, we construct steganographic schemes explicitly from r-perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers, and Lipschitz integers, respectively. Then we further compute various parameters for the suggested steganographic schemes.

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Acknowledgements

The authors would like to thank the reviewers for their helpful discussions and constructive comments on improving this paper.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 04107, Korea

    Jon-Lark Kim & JunYong Park

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  1. Jon-Lark Kim
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  2. JunYong Park
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Correspondence to Jon-Lark Kim.

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The author is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2019R1A2C1088676)

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”

Appendix

Appendix

See Tables 12 and 13.

Table 12 Values of emb(x, y) on G\(_{5+i}\)
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Table 13 Values of rec(x) on G\(_{5+i}\)
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Kim, JL., Park, J. Steganography from perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers and Lipschitz integers. Des. Codes Cryptogr. 90, 2967–2989 (2022). https://doi.org/10.1007/s10623-022-01063-x

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  • DOI: https://doi.org/10.1007/s10623-022-01063-x

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