We investigated constructions of different types of erasure codes that are resilient to node eavesdropping. In particular, we show that in the construction of a well-known class of minimum bandwidth regenerating codes called Product-Matrix codes, if a Cauchy matrix is used instead of a Vandermonde matrix then a certain level of security can be achieved.
[2] H. Dau, W. Song, A. Sprintson, and C. Yuen, (invited paper) “Constructions of MDS Codes via Random Vandermonde and Cauchy Matrices over Small Fields,” 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 949-955, 2015.
[2] H. Dau, W. Song, and C. Yuen, “Secure erasure codes with partial decodability”, IEEE International Conference on Communications (ICC), pages 388-394, 2015.
[1] H. Dau, W. Song, and C. Yuen, “On Block Security of Regenerating Codes at the MBR Point for Distributed Storage Systems,” IEEE International Symposium on Information Theory (ISIT), pages 1967-1971, 2014.