Residue number systems in cryptography: Design, challenges, robustness

As conventional arithmetic solutions have improved at a fine-grain level, researchers have turned their attention to alternative number system representations in an effort to further boost up cryptosystem performance. The ancient Residue Number System (RNS) has emerged as a key-player in this endeavor. This chapter attempts to highlight important concepts of residue arithmetic and new RNS applications in modern cryptography are presented in a systematic and holistic manner. Progressing from algorithm and complexity analysis to state-of-the-art hardware implementations and useful cryptanalytic properties, the prospective reader is acquainted with most of the implications and challenges of this emerging field, while open research points are also highlighted.