2015/04/10 by Masahito Hayashi, Vincent Y. F. Tan, Hayashi, Masahito +1 · 3 citations
Computer Science · Engineering · Mathematics · #Chaos-based Image/Signal Encryption #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1504.02536
openalex publication_date 2015/04/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We evaluate the asymptotics of equivocations, their exponents as well as their second-order coding rates under various Rényi information measures. Specifically, we consider the effect of applying a hash function on a source and we quantify the level of non-uniformity and dependence of the compressed source from another correlated source when the number of copies of the sources is large. Unlike previous works that use Shannon information measures to quantify randomness, information or uniformity, we define our security measures in terms of a more general class of information measures--the Rényi information measures and their Gallager-type counterparts. A special case of these Rényi information measure is the class of Shannon information measures. We prove tight asymptotic results for the security measures and their exponential rates of decay. We also prove bounds on the second-order asymptotics and show that these bounds match when the magnitudes of the second-order coding rates are large. We do so by establishing new classes non-asymptotic bounds on the equivocation and evaluating these bounds using various probabilistic limit theorems asymptotically.