6 research outputs found
Fast multi-computations with integer similarity strategy
Abstract. Multi-computations in finite groups, such as multiexponentiations and multi-scalar multiplications, are very important in ElGamallike public key cryptosystems. Algorithms to improve multi-computations can be classified into two main categories: precomputing methods and recoding methods. The first one uses a table to store the precomputed values, and the second one finds a better binary signed-digit (BSD) representation. In this article, we propose a new integer similarity strategy for multi-computations. The proposed strategy can aid with precomputing methods or recoding methods to further improve the performance of multi-computations. Based on the integer similarity strategy, we propose two efficient algorithms to improve the performance for BSD sparse forms. The performance factor can be improved from 1.556 to 1.444 and to 1.407, respectively
Novel arithmetic implementations using cellular neural network arrays.
The primary goal of this research is to explore the use of arrays of analog self-synchronized cells---the cellular neural network (CNN) paradigm---in the implementation of novel digital arithmetic architectures. In exploring this paradigm we also discover that the implementation of these CNN arrays produces very low system noise; that is, noise generated by the rapid switching of current through power supply die connections---so called di/dt noise. With the migration to sub 100 nanometer process technology, signal integrity is becoming a critical issue when integrating analog and digital components onto the same chip, and so the CNN architectural paradigm offers a potential solution to this problem. A typical example is the replacement of conventional digital circuitry adjacent to sensitive bio-sensors in a SoC Bio-Platform. The focus of this research is therefore to discover novel approaches to building low-noise digital arithmetic circuits using analog cellular neural networks, essentially implementing asynchronous digital logic but with the same circuit components as used in analog circuit design. We address our exploration by first improving upon previous research into CNN binary arithmetic arrays. The second phase of our research introduces a logical extension of the binary arithmetic method to implement binary signed-digit (BSD) arithmetic. To this end, a new class of CNNs that has three stable states is introduced, and is used to implement arithmetic circuits that use binary inputs and outputs but internally uses the BSD number representation. Finally, we develop CNN arrays for a 2-dimensional number representation (the Double-base Number System - DBNS). A novel adder architecture is described in detail, that performs the addition as well as reducing the representation for further processing; the design incorporates an innovative self-programmable array. Extensive simulations have shown that our new architectures can reduce system noise by almost 70dB and crosstalk by more than 23dB over standard digital implementations.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .I27. Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6159. Thesis (Ph.D.)--University of Windsor (Canada), 2005
Modern Computer Arithmetic (version 0.5.1)
This is a draft of a book about algorithms for performing arithmetic, and
their implementation on modern computers. We are concerned with software more
than hardware - we do not cover computer architecture or the design of computer
hardware. Instead we focus on algorithms for efficiently performing arithmetic
operations such as addition, multiplication and division, and their connections
to topics such as modular arithmetic, greatest common divisors, the Fast
Fourier Transform (FFT), and the computation of elementary and special
functions. The algorithms that we present are mainly intended for
arbitrary-precision arithmetic. They are not limited by the computer word size,
only by the memory and time available for the computation. We consider both
integer and real (floating-point) computations. The book is divided into four
main chapters, plus an appendix. Our aim is to present the latest developments
in a concise manner. At the same time, we provide a self-contained introduction
for the reader who is not an expert in the field, and exercises at the end of
each chapter. Chapter titles are: 1, Integer Arithmetic; 2, Modular Arithmetic
and the FFT; 3, Floating-Point Arithmetic; 4, Elementary and Special Function
Evaluation; 5 (Appendix), Implementations and Pointers. The book also contains
a bibliography of 236 entries, index, summary of notation, and summary of
complexities.Comment: Preliminary version of a book to be published by Cambridge University
Press. xvi+247 pages. Cite as "Modern Computer Arithmetic, Version 0.5.1, 5
March 2010". For further details, updates and errata see
http://wwwmaths.anu.edu.au/~brent/pub/pub226.html or
http://www.loria.fr/~zimmerma/mca/pub226.htm