🤖 AI Summary
This work addresses the challenge of constructing efficient authentication codes that simultaneously ensure confidentiality, provide strong authentication guarantees, and effectively resist impersonation and substitution attacks. The authors propose a novel class of linear authentication codes grounded in linear algebraic structures. By leveraging specialized Weil sum analysis techniques, they rigorously derive tight upper bounds on the maximum success probabilities of both substitution and impersonation attacks. Furthermore, they demonstrate that the proposed scheme achieves asymptotically optimal security under a specific theoretical bound. Featuring simple encoding rules and low computational complexity, the scheme offers robust confidentiality alongside strong authentication, thereby balancing rigorous theoretical security with practical deployability.
📝 Abstract
In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and impersonation attack are calculated, and these codes are proven to be asymptotically optimal with respect to certain bounds.