Residue Number Systems : Theory and Applications

This new and expanded monograph improves upon Mohan's earlier book, __Residue Number Systems__ __(Springer, 2002) with a state of the art treatment of the subject__. Replete with detailed illustrations and helpful examples, this book covers a host of cutting edge topics such as the core function, the quotient function, new Chinese Remainder theorems, and large integer operations. It also features many significant applications to practical communication systems and cryptography such as FIR filters and elliptic curve cryptography. Starting with a comprehensive introduction to the basics and leading up to current research trends that are not yet widely distributed in other publications, this book will be of interest to both researchers and students alike. This text is an excellent reference for both professional and academic researchers in the field of VLSI using residue number systems. It is also of interest to those working in the general fields of VLSI design, DSP design, and cryptography. Topics covered include choice of moduli; architectures for conversion from binary to RNS; RNS to binary conversion techniques; quadratic RNS; and applications. Numerous examples illustrate the ideas developed. The area and computational requirements are highlighted for all designs, so the selection of a particular architecture is facilitated. Some of the topics covered have application in cryptography. The book includes a comprehensive bibliography in this area. Residue Number Systems: Algorithms and Architectures is also suitable for a graduate-level course as part of a VLSI curriculum. Front Matter....Pages i-x Introduction....Pages 1-7 Modulo Addition and Subtraction....Pages 9-25 Binary to Residue Conversion....Pages 27-38 Modulo Multiplication and Modulo Squaring....Pages 39-79 RNS to Binary Conversion....Pages 81-132 Scaling, Base Extension, Sign Detection and Comparison in RNS....Pages 133-162 Error Detection, Correction and Fault Tolerance in RNS-Based Designs....Pages 163-175 Specialized Residue Number Systems....Pages 177-193 Applications of RNS in Signal Processing....Pages 195-261 RNS in Cryptography....Pages 263-347 Back Matter....Pages 349-351