› › Modular Multiplication In The Residue Number System

Residue Number Systems

Author : P.V. Ananda Mohan

Publisher : Birkhäuser

Page : 353 pages

File Size : 22,44 MB

Release : 2016-10-14

Category : Mathematics

ISBN : 3319413856

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Book Description

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.



Modular Arithmetic

Author : N.B. Singh

Publisher : N.B. Singh

Page : 145 pages

File Size : 24,86 MB

Release :

Category : Mathematics

ISBN :

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Book Description

"Modular Arithmetic" is a concise and accessible guide that demystifies the fundamental concepts of modular arithmetic, a mathematical framework essential for various applications. Tailored for students and enthusiasts of mathematics, the book explores the properties and operations within modular systems, shedding light on topics such as modular addition, subtraction, multiplication, and exponentiation. With clear explanations and illustrative examples, it equips readers with the foundational knowledge to solve problems in cryptography, computer science, and other mathematical disciplines. This handbook serves as an indispensable resource for understanding and applying modular arithmetic, making it an ideal companion for those looking to navigate this important mathematical concept.



Modular Multiplication in the Residue Number System

Author : Yinan Kong

Publisher :

Page : 170 pages

File Size : 50,19 MB

Release : 2009

Category : Cryptography

ISBN :

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Book Description

Public-key cryptography is a mechanism for secret communication between parties who have never before exchanged a secret message. This thesis contributes arithmetic algorithms and hardware architectures for the modular multiplication Z = A x B mod M. This operation is the basis of many public-key cryptosystems including RSA and Elliptic Curve Cryptography. The Residue Number System (RNS) is used to speed up long word length modular multiplication because this number system performs certain long word length operations, such as multiplication and addition, much more efficiently than positional systems. A survey of current modular multiplication algorithms shows that most work in a positional number system, e.g. binary. A new classification is developed which classes these algorithms as Classical, Sum of Residues, Montgomery or Barrett. Each class of algorithm is analyzed in detail, new developments are described, and the improved algorithms are implemented and compared using FPGA hardware. Few modular multiplication algorithms for use in the RNS have been published. Most are concerned with short word lengths and are not applicable to public-key cryptosystems that require long word length operations. This thesis sets out the hypothesis that each of the four classes of modular multiplication algorithms possible in positional number systems can also be used for long word length modular multiplication in the RNS; moreover using the RNS in this way will lead to faster implementations than those which restrict themselves to positional number systems. This hypothesis is addressed by developing new Classical, Sum of Residues and Barrett algorithms for modular multiplication in the RNS. Existing Montgomery RNS algorithms are also discussed. The new Sum of Residues RNS algorithm results in a hardware implementation that is novel in many aspects: a highly parallel structure using short arithmetic operations within the RNS; fully scalable hardware; and the fastest ever FPGA implementation of the 1024-bit RSA cryptosystem at 0.4 ms per decryption.



Residue Number Systems

Author : Amos R. Omondi

Publisher : Imperial College Press

Page : 311 pages

File Size : 14,21 MB

Release : 2007

Category : Technology & Engineering

ISBN : 1860948677

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Book Description

Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital signal processing, communications engineering, computer security (cryptography), image processing, speech processing, and transforms, all of which are extremely important in computing today. This book provides an up-to-date account of RNSs and arithmetic. It covers the underlying mathematical concepts of RNSs; the conversion between conventional number systems and RNSs; the implementation of arithmetic operations; various related applications are also introduced. In addition, numerous detailed examples and analysis of different implementations are provided. Sample Chapter(s). Chapter 1: Introduction (301 KB). Contents: Introduction; Mathematical Fundamentals; Forward Conversion; Addition; Multiplication; Comparison, Overflow-Detection, Sign-Determination, Scaling, and Division; Reverse Conversion; Applications. Readership: Graduate students, academics and researchers in computer engineering and electrical & electronic engineering.



Residue Number Systems

Author : P.V. Ananda Mohan

Publisher : Springer Science & Business Media

Page : 262 pages

File Size : 47,34 MB

Release : 2012-12-06

Category : Technology & Engineering

ISBN : 1461509971

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Book Description

There has been continuing interest in the improvement of the speed of Digital Signal processing. The use of Residue Number Systems for the design of DSP systems has been extensively researched in literature. Szabo and Tanaka have popularized this approach through their book published in 1967. Subsequently, Jenkins and Leon have rekindled the interest of researchers in this area in 1978, from which time there have been several efforts to use RNS in practical system implementation. An IEEE Press book has been published in 1986 which was a collection of Papers. It is very interesting to note that in the recent past since 1988, the research activity has received a new thrust with emphasis on VLSI design using non ROM based designs as well as ROM based designs as evidenced by the increased publications in this area. The main advantage in using RNS is that several small word-length Processors are used to perform operations such as addition, multiplication and accumulation, subtraction, thus needing less instruction execution time than that needed in conventional 16 bitl32 bit DSPs. However, the disadvantages of RNS have b. een the difficulty of detection of overflow, sign detection, comparison of two numbers, scaling, and division by arbitrary number, RNS to Binary conversion and Binary to RNS conversion. These operations, unfortunately, are computationally intensive and are time consuming.





Embedded Systems Design with Special Arithmetic and Number Systems

Author : Amir Sabbagh Molahosseini

Publisher : Springer

Page : 390 pages

File Size : 31,42 MB

Release : 2017-03-20

Category : Technology & Engineering

ISBN : 3319497421

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Book Description

This book introduces readers to alternative approaches to designing efficient embedded systems using unconventional number systems. The authors describe various systems that can be used for designing efficient embedded and application-specific processors, such as Residue Number System, Logarithmic Number System, Redundant Binary Number System Double-Base Number System, Decimal Floating Point Number System and Continuous Valued Number System. Readers will learn the strategies and trade-offs of using unconventional number systems in application-specific processors and be able to apply and design appropriate arithmetic operations from these number systems to boost the performance of digital systems.



A Handbook of Modular Arithmetic

Author : N.B. Singh

Publisher : N.B. Singh

Page : 149 pages

File Size : 18,16 MB

Release :

Category : Mathematics

ISBN :

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Book Description

"A Handbook of Modular Arithmetic" is a beginner-friendly guide that introduces readers to the fascinating realm of modular arithmetic, offering clear explanations, practical examples, and engaging exercises. Designed for those with no mathematical background, the book gently introduces the concepts of modular arithmetic, exploring its applications in computer science, cryptography, and number theory. From understanding basic concepts to unraveling the mysteries of modular arithmetic, this handbook serves as a comprehensive resource for anyone eager to delve into the world of numbers and problem-solving.



Notes on Modular Number Systems

Author : Harvard University. Computation Laboratory

Publisher :

Page : 544 pages

File Size : 29,24 MB

Release : 1961

Category : Computer engineering

ISBN :

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Book Description

This is the final report of a one-year research program organized to exploit the possibilities of modular number systems and their applicability to the design of digital computing machinery. In modular number systems, the carry process is eliminatedso that additiion and multiplication operations can be completed in a single computer clock pulse time. Other mathematical operations, such as division, round-off, and number magnitude determination are much more complex to execute and generate problems not encountered in ordered number systems. The report consists of sixty-six independent research notes each of which is a theorem, concept, algorithm development, or similar mathematical tool in modular number system techniques.



Advances in Cryptology — CRYPTO ’93

Author : Douglas R. Stinson

Publisher : Springer

Page : 502 pages

File Size : 14,38 MB

Release : 2003-05-15

Category : Computers

ISBN : 3540483292

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Book Description

The CRYPTO ’93 conference was sponsored by the International Association for Cryptologic Research (IACR) and Bell-Northern Research (a subsidiary of Northern Telecom), in co-operation with the IEEE Computer Society Technical Committee. It took place at the University of California, Santa Barbara, from August 22-26, 1993. This was the thirteenth annual CRYPTO conference, all of which have been held at UCSB. The conference was very enjoyable and ran very of the General Chair, Paul Van Oorschot. smoothly, largely due to the efforts It was a pleasure working with Paul throughout the months leading up to the conference. There were 136 submitted papers which were considered by the Program Committee. Of these, 38 were selected for presentation at the conference. There was also one invited talk at the conference, presented by Miles Smid, the title of which was “A Status Report On the Federal Government Key Escrow System.” The conference also included the customary Rump Session, which was presided over by Whit Diffie in his usual inimitable fashion. Thanks again to Whit for organizing and running the Rump session. This year, the Rump Session included an interesting and lively panel discussion on issues pertaining to key escrowing. Those taking part were W. Diffie, J. Gilmore, S. Goldwasser, M. Hellman, A. Herzberg, S. Micali, R. Rueppel, G. Simmons and D. Weitzner.