The erosion of a set in Euclidean space by a radius r > 0 is the subset of X consisting of points at distance ≥ r from the complement of X. A set is resilient to erosion if it is similar to its erosion by some positive radius. We give a somewhat surprising characterization of resilient sets, consisting in one part of simple geometric constraints on convex resilient sets, and, in another, a corr...

The main construction for resilient functions uses linear error-correcting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if there exists a resilient function, then there exists a linear function with the same parameters. In this note, we construct innnite classes of non-linear resilient functions from the Kerdock and Preparata codes. We a...

The aim of this paper is to elucidate the implications of quantum computing in present cryptography and to introduce the reader to basic post-quantum algorithms. In particular the reader can delve into the following subjects: present cryptographic schemes (symmetric and asymmetric), differences between quantum and classical computing, challenges in quantum computing, quantum algorithms (Shor’s ...

Repair mechanisms are important within resilient systems to maintain the system in an operational state after an error occurred. Usually, constraints on the repair mechanisms are imposed, e.g., concerning the time or resources required (such as energy consumption or other kinds of costs). For systems modeled by Markov decision processes (MDPs), we introduce the concept of resilient schedulers, ...

Hierarchical and identity-based encryption (HIBE) is very valuable widely used in many occasions. In the Internet of Things based on cloud services, efficient HIBE likely to be applied service scenarios for limited computing ability some terminal devices. What’s more, because insecurity cryptographic systems caused by side channel attacks, design leakage resilient scheme has attracted more cryp...

To resolve both certificate management and key escrow problems, a certificateless public-key system (CLPKS) has been proposed. However, CLPKS setting must provide revocation mechanism to revoke compromised users. Thus, revocable (RCLPKS) was presented address the issue and, in such system, generation centre (KGC) is responsible run this functionality. Furthermore, RCLPKS with an outsourced auth...

Signature can be used to verify the integrity of both a message and identity signer, whereas encryption ensure confidentiality message. In past, cryptography researchers have studied proposed numerous certificateless signcryption (CLSC) schemes combine benefits signature encryption. However, these may not robust enough withstand side-channel attacks. Through such attacks, an attacker constantly...