Computer Arithmetic and Cryptography
- Date: 12/04/2007
Vassil Dimitrov (University of Calgary)
Calgary Place Tower (Shell)
Computer arithmetic is a fascinating subject, and not at all the drudgery that most of us experienced in mastering the third 'R' of the three R's at school. Efficiency in performing computer arithmetic is of paramount importance to signal processing and cryptographic systems, and much research takes place in this area; the novelty however, is often in the circuits and technology, rather than in the number representations. In this talk, we shall explore the latter. We can recall tricks we learned in grade school to improve our "mental arithmetic" prowess such as, memorizing multiplication tables and simple algorithms involved in multiplication. In computer arithmetic, we also search for ways to improve performance of basic operations, including using tables of stored computations. There are various flavours of number representations, other than basic binary integer representation, that use a base of 2. Finding an efficient number representation is only part of the battle in implementing arithmetic. Many applications in cryptography involve an enormous number of multiplications that can be very time consuming or require a large amount of hardware. Smart selection of a number representation can lead to very significant improvements in speed and area complexity of various cryptographic protocols. We shall demonstrate the advantages of some nonstandard number representations in cryptographic applications, including key exchange and digital signature algorithms.
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PIMS is presenting a series of lectures at the Calgary Place Tower 1 in downtown Calgary. These lectures, given by experts from the PIMS Universities, will focus on mathematical techniques and applications relevant to the oil and gas industry and will demonstrate the utility and beauty of applied mathematics. The talks are aimed at a general audience. Attendance may qualify for APEGGA Professional Development Hours.