Application of Tsallis entropy in defining a new generalized strong and weak secrecy

Abstract

In this paper, we explore the diverse applications and distinctive properties of Tsallis entropy by introducing generalized definitions of strong and weak secrecy. Tsallis entropy suggests that generalized weak secrecy and strong secrecy are commonly employed in information-theoretic security challenges. Additionally, we examine the interplay between Tsallis entropy and the criteria for strong and weak secrecy. The primary motivation behind this study is to elucidate the concept of “generalized weak secrecy,” a widely utilized notion. Also, this research delves into the precise relationship between conditional entropy and the minimum adversarial error probability, illustrating how generalized weak security can be translated into practical guarantees. For static and memoryless sources, it is demonstrated that the vanishing of the leakage rate requires the adversarial error probability to reach its upper bound. Moreover, generalized strong security, characterized by the vanishing of the variational distance, results in the complete operational failure of the adversary. These findings underscore the critical role of Tsallis entropy in assessing the security of systems.