The Odyssey of Entropy: Cryptography.

After being introduced by Shannon as a measure of disorder and unavailable information, the notion of entropy has found its applications in a broad range of scientific disciplines. In this paper, we present a systematic review on the applications of entropy and related information-theoretical concepts in the design, implementation and evaluation of cryptographic schemes, algorithms, devices and systems. Moreover, we study existing trends, and establish a roadmap for future research in these areas.

From Random Numbers to Random Objects.

Many security-related scenarios including cryptography depend on the random generation of passwords, permutations, Latin squares, CAPTCHAs and other types of non-numerical entities. Random generation of each entity type is a different problem with different solutions. This study is an attempt at a unified solution for all of the mentioned problems. This paper is the first of its kind to pose, formulate, analyze and solve the problem of random object generation as the general problem of generating random non-numerical entities. We examine solving the problem via connecting it to the well-studied random number generation problem. To this end, we highlight the challenges and propose solutions for each of them. We explain our method using a case study; random Latin square generation.

Cryptography in Hierarchical Coded Caching: System Model and Cost Analysis.

The idea behind network caching is to reduce network traffic during peak hours via transmitting frequently-requested content items to end users during off-peak hours. However, due to limited cache sizes and unpredictable access patterns, this might not totally eliminate the need for data transmission during peak hours. Coded caching was introduced to further reduce the peak hour traffic. The idea of coded caching is based on sending coded content which can be decoded in different ways by different users. This allows the server to service multiple requests by transmitting a single content item. Research works regarding coded caching traditionally adopt a simple network topology consisting of a single server, a single hub, a shared link connecting the server to the hub, and private links which connect the users to the hub. Building on the results of Sengupta et al. (IEEE Trans. Inf. Forensics Secur., 2015), we propose and evaluate a yet more complex system model that takes into consideration both throughput and security via combining the mentioned ideas. It is demonstrated that the achievable rates in the proposed model are within a constant multiplicative and additive gap with the minimum secure rates.

Authentication of variable length messages in quantum key distribution.

Authentication plays a critical role in the security of quantum key distribution (QKD) protocols. We propose using Polynomial Hash and its variants for authentication of variable length messages in QKD protocols. Since universal hashing is used not only for authentication in QKD but also in other steps in QKD like error correction and privacy amplification, and also in several other areas of quantum cryptography, Polynomial Hash and its variants as the most efficient universal hash function families can be used in these important steps and areas, as well. We introduce and analyze several efficient variants of Polynomial Hash and, using deep results from number theory, prove that each variant gives an ε-almost-Δ-universal family of hash functions. We also give a general method for transforming any such family to an ε-almost-strongly universal family of hash functions. The latter families can then, among other applications, be used in the Wegman-Carter MAC construction which has been shown to provide a universally composable authentication method in QKD protocols. As Polynomial Hash has found many applications, our constructions and results are potentially of interest in various areas.