Preface

The challenges in and solutions for cryptography are the core subject of this book. Core security concepts and solutions were proposed decades ago. However, mainly due to technology advancements, the increase of data transmission volume and the evolving of Internet infrastructure, challenges to cryptography systems have been found, calling for adjustments and solutions. In this book, we start with improvements proposed to symmetric cryptography by construction of Boolean functions for generating orthogonal variable spreading factor codes used in cryptographic applications. We proceed with asymmetric cryptography by outlining RSA voluntaries followed by ECC performance improvements of its Fast Scalar Multiplication and improved performance of the encryption used in numerical problem applications. We conclude the book with two proposals to cope with the quantum computing challenge to Internet security. One approach uses a combination of overlay security, Blockchain, and Merkle trees to provide a quantum safe Internet. The second employs the MOR cryptosystem in a asymmetric cryptography, by generalizing the discrete logarithm problem from a cyclic group to an arbitrary group.

I would like to acknowledge AAC for its help and Mrs. Nina Kalinic Babic for her assistance as the Author Service Manager of this project.

> **Menachem Domb** Ashkelon Academy College, Ashkelon, Israel

Chapter 1

Samed Bajrić

certain cryptographic applications.

1. Introduction

1

nonlinearity, resiliency, (fast) algebraic attack

Abstract

Implementing Symmetric

of Semi-Bent Functions

Cryptography Using Sequence

Symmetric cryptography is a cornerstone of everyday digital security, where

two parties must share a common key to communicate. The most common primitives in symmetric cryptography are stream ciphers and block ciphers that guarantee confidentiality of communications and hash functions for integrity. Thus, for securing our everyday life communication, it is necessary to be convinced by the security level provided by all the symmetric-key cryptographic primitives. The most important part of a stream cipher is the key stream generator, which provides the overall security for stream ciphers. Nonlinear Boolean functions were preferred for a long time to construct the key stream generator. In order to resist several known attacks, many requirements have been proposed on the Boolean functions. Attacks against the cryptosystems have forced deep research on Boolean function to allow us a more secure encryption. In this work we describe all main requirements for constructing of cryptographically significant Boolean functions. Moreover, we provide a construction of Boolean functions (semi-bent Boolean functions) which can be used in the construction of orthogonal variable spreading factor codes used in code division multiple access (CDMA) systems as well as in

Keywords: symmetric cryptography, Boolean functions, Walsh spectrum,

Cryptography has become a branch of information theory and is used within a mathematical approach to study the transmission of information from place to place. In a modern society, exchange and storage of information in an efficient, reliable, and secure manner are of fundamental importance. Applications of cryptography are present in many aspects of our society, and they include authentication and encryption (bank cards, wireless telephone, e-commerce), access control (car lock systems, ski lifts), and payment (prepaid telephone cards, e-cash). Behind all the previously mentioned applications, an underlying cryptographic system has to satisfy a number of security goals. Some important aspects in information security are data confidentiality, data integrity, authentication, and non-repudiation, and some of these goals will be elaborated later in the framework of Boolean
