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A class of asymptotically optimal authentication codes with secrecy
Abstract
In this paper, a class of linear authentication codes with secrecy, which are equipped with simple encoding rules, is constructed. By means of a special Weil sum, the maximum success probabilities of impersonation attack (denoted by PI) and of substitution attack (denoted by PS) for these codes are explicitly derived. It is further proven that the codes are asymptotically optimal, in the sense that both the information theoretic bound and the combinatorial bound for authentication codes are asymptotically attained by PI and PS.
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BibTeX
@misc{liu2026class,
title = {{A class of asymptotically optimal authentication codes with secrecy}},
author = {Haibo Liu and Chengzhi Wei and Qunying Liao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.14823},
eprint = {2605.14823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.14823},
}
RIS
TY - UNPB
TI - A class of asymptotically optimal authentication codes with secrecy
AU - Haibo Liu
AU - Chengzhi Wei
AU - Qunying Liao
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2605.14823
UR - https://arxiv.org/abs/2605.14823
AB - In this paper, a class of linear authentication codes with secrecy, which are equipped with simple encoding rules, is constructed. By means of a special Weil sum, the maximum success probabilities of impersonation attack (denoted by P_I) and of substitution attack (denoted by P_S) for these codes are explicitly derived. It is further proven that the codes are asymptotically optimal, in the sense that both the information theoretic bound and the combinatorial bound for authentication codes are asymptotically attained by P_I and P_S.
ER -