Paper 2017/428

Optimal Ramp Schemes and Related Combinatorial Objects

Douglas R. Stinson

Abstract

In 1996, Jackson and Martin proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp schemes to a new variant of orthogonal arrays that we term augmented orthogonal arrays}. We give some constructions for these new kinds of arrays, and, as a consequence, we also provide parameter situations where ideal ramp schemes exist but strong ideal ramp schemes do not exist.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
secret sharingcombinatorial cryptography
Contact author(s)
dstinson @ uwaterloo ca
History
2017-05-22: received
Short URL
https://ia.cr/2017/428
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/428,
      author = {Douglas R.  Stinson},
      title = {Optimal Ramp Schemes and Related Combinatorial Objects},
      howpublished = {Cryptology ePrint Archive, Paper 2017/428},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/428}},
      url = {https://eprint.iacr.org/2017/428}
}
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