Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / secret sharing, combinatorial cryptography

Date: received 18 May 2017

Contact author: dstinson at uwaterloo ca

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Version: 20170522:213348 (All versions of this report)

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