Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

Perfectly-secure cryptography is a branch of information-theoretic cryptography. A perfectly-secure cryptosystem guarantees that the malicious third party cannot guess anything regarding the plain text or the key, even in the case of full access to the cipher text. Despite this advantage, there are only a few real-world implementations of perfect secrecy due to some well-known limitations. Any simple, straightforward modeling can pave the way for further advancements in the implementation, especially in environments with time and resource constraints such as IoT. This book takes one step towards this goal via presenting a hybrid combinatorial-Boolean model for perfectly-secure cryptography in IoT. In this book, we first present an introduction to information-theoretic cryptography as well as perfect secrecy and its real-world implementations. Then we take a systematic approach to highlight information-theoretic cryptography as a convergence point for existing trends in research on cryptography in IoT. Then we investigate combinatorial and Boolean cryptography and show how they are seen almost everywhere in the ecosystem and the life cycle of information-theoretic IoT cryptography. We finally model perfect secrecy in IoT using Boolean functions, and map the Boolean functions to simple, well-studied combinatorial designs like Latin squares. This book is organized in two parts. The first part studie s information-theoretic cryptography and the promise it holds for cryptography in IoT. The second part separately discusses combinatorial and Boolean cryptography, and then presents the hybrid combinatorial-Boolean model for perfect secrecy in IoT.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

Physically Unclonable Functions (PUFs) translate unavoidable variations in certain parameters of materials, waves, or devices into random and unique signals. They have found many applications in the Internet of Things (IoT), authentication systems, FPGA industry, several other areas in communications and related technologies, and many commercial products. Statistical Trend Analysis of Physically Unclonable Functions first presents a review on cryptographic hardware and hardware-assisted cryptography. The review highlights PUF as a mega trend in research on cryptographic hardware design. Afterwards, the authors present a combined survey and research work on PUFs using a systematic approach. As part of the survey aspect, a state-of-the-art analysis is presented as well as a taxonomy on PUFs, a life cycle, and an established ecosystem for the technology. In another part of the survey, the evolutionary history of PUFs is examined, and strategies for further research in this area are suggested. In the research side, this book presents a novel approach for trend analysis that can be applied to any technology or research area. In this method, a text mining tool is used which extracts 1020 keywords from the titles of the sample papers. Then, a classifying tool classifies the keywords into 295 meaningful research topics. The popularity of each topic is then numerically measured and analyzed over the course of time through a statistical analysis on the number of research papers related to the topic as well as the number of their citations. The authors identify the most popular topics in four different domains; over the history of PUFs, during the recent years, in top conferences, and in top journals. The results are used to present an evolution study as well as a trend analysis and develop a roadmap for future research in this area. This method gives an automatic popularity-based statistical trend analysis which eliminates the need for passing personal judgments about the direction of trends, and provides concrete evidence to the future direction of research on PUFs. Another advantage of this method is the possibility of studying a whole lot of existing research works (more than 700 in this book). This book will appeal to researchers in text mining, cryptography, hardware security, and IoT.