Spectral methods have been widely used in various fields of engineering and applied mathematics.
In the field of computer arithmetic: data compression, polynomial multiplication and
the spectral integer multiplication of Sch¨ / onhage and Strassen are among the most important
successful utilization. Recent advancements in technology report the spectral methods may
also be beneficial for modular operations heavily used in public key cryptosystems.
In this study, we evaluate the use of spectral methods in modular multiplication. We carefully
compare their timing performances with respect to the full return algorithms. Based on our
evaluation, we introduce new approaches for spectral modular multiplication for polynomials
and exhibit standard reduction versions of the spectral modular multiplication algorithm for
polynomials eliminating the overhead of Montgomery&rsquo / s method.
Moreover, merging the bipartite method and standard approach, we introduce the bipartite
spectral modular multiplication to improve the hardware performance of spectral modular
multiplication for polynomials. Finally, we introduce Karatsuba combined bipartite method
for polynomials and its spectral version.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/3/12610463/index.pdf |
| Date | 01 February 2008 |
| Creators | Akin, Ihsan Haluk |
| Contributors | Doganaksoy, Ali |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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