Name
Abstract | ||
|---|---|---|
We introduce three new constructions of systematic authentication codes over finite fields and Galois rings. Our first construction uses resilient functions over finite fields and provides optimal impersonation and substitution probabilities. Our two other constructions are defined over Galois rings: one is based on resilient maps attaining optimal probabilities as well, while the other is based on maps with maximum Fourier transforms. For the special case of characteristic $$p^2$$p2, the maps used on our third construction are bent. Furthermore, we give a generalised construction for the case of characteristic $$p^s$$ps, with $$s \\ge 2$$s¿2. The second and third codes over Galois rings, restricted to the particular case of Galois fields, are different than the first code introduced in this paper: the corresponding source and tag spaces differ, and the encoding maps classes are pairwise different. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s10623-015-0121-3 | Des. Codes Cryptography |
Keywords | Field | DocType |
Authentication schemes,Resilient maps,Finite fields,Galois rings,11T71,14G50,94A60,94A62 | Embedding problem,Discrete mathematics,Pairwise comparison,Combinatorics,Finite field,Normal basis,Field norm,Galois module,Fundamental theorem of Galois theory,Mathematics,Special case | Journal |
Volume | Issue | ISSN |
80 | 3 | 0925-1022 |
Citations | PageRank | References |
1 | 0.37 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Juan Carlos Ku-Cauich | 1 | 5 | 2.93 |
| Guillermo Morales-luna | 2 | 99 | 28.89 |