Circular external difference families, graceful labellings and cyclotomy
Combinatorics
2023-10-30 v2 Cryptography and Security
Abstract
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied in recent years. We provide a variety of constructions for CEDFs based on graceful labellings (-valuations) of lexicographic products , where denotes a cycle of length . SCEDFs having more than two subsets do not exist. However, we can construct close approximations (more specifically, certain types of circular algebraic manipulation detection (AMD) codes) using the theory of cyclotomic numbers in finite fields.
Keywords
Cite
@article{arxiv.2310.02810,
title = {Circular external difference families, graceful labellings and cyclotomy},
author = {Maura B. Paterson and Douglas R. Stinson},
journal= {arXiv preprint arXiv:2310.02810},
year = {2023}
}