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Spectral modular arithmeticSaldamli, Gökay 23 May 2005 (has links)
In many areas of engineering and applied mathematics, spectral methods provide
very powerful tools for solving and analyzing problems. For instance, large to
extremely large sizes of numbers can efficiently be multiplied by using discrete Fourier
transform and convolution property. Such computations are needed when computing
π to millions of digits of precision, factoring and also big prime search projects.
When it comes to the utilization of spectral techniques for modular operations
in public key cryptosystems two difficulties arise; the first one is the reduction needed
after the multiplication step and the second is the cryptographic sizes which are much
shorter than the optimal asymptotic crossovers of spectral methods.
In this dissertation, a new modular reduction technique is proposed. Moreover,
modular multiplication is given based on this reduction. These methods work fully
in the frequency domain with some exceptions such as the initial, final and partial
transformations steps. Fortunately, the new technique addresses the reduction problem
however, because of the extra complexity coming from the overhead of the forward and
backward transformation computations, the second goal is not easily achieved when
single operations such as modular multiplication or reduction are considered. On the
contrary, if operations that need several modular multiplications with respect to the
same modulus are considered, this goal is more tractable.
An obvious example of such an operation is the modular exponentiation i.e., the
computation of c=m[superscript e] mod n where c, m, e, n are large integers. Therefore following
the spectral modular multiplication operation a new modular exponentiation method is
presented. Since forward and backward transformation calculations do not need to be
performed for every multiplication carried during the exponentiation, the asymptotic
crossover for modular exponentiation is decreased to cryptographic sizes. The method
yields an efficient and highly parallel architecture for hardware implementations of
public-key cryptosystems. / Graduation date: 2006
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Residue arithmetic in digital computers /Debnath, Ramesh Chandra. January 1979 (has links) (PDF)
Thesis (Ph.D.) -- University of Adelaide, Dept. of Electrical Engineering, 1979. / Typescript (photocopy).
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Hardware design of scalable and unified modular division and Montgomery multiplication /Park, Song Jun. January 1900 (has links)
Thesis (M.S.)--Oregon State University, 2006. / Printout. Includes bibliographical references (leaves 43-44). Also available on the World Wide Web.
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The last two digits of mk / De sista två siffrorna i mkSchill Collberg, Adam January 2012 (has links)
In this thesis the last two digits of m^k, for different cases of the positive integers m and k, in the base of 10 has been determined. Moreover, using fundamental theory from elementary number theory and abstract algebra, results most helpful in finding the last two digits in any base b has been regarded and developed, such as how to reduce large m and k to more manageable numbers.
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Residue arithmetic in digital computers / Ramesh Chandra DebnathDebnath, Ramesh Chandra January 1979 (has links)
Typescript (photocopy) / 175, 66 leaves : ill., (part col.), charts ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical Engineering, 1979
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Prime numbers and encryptionAnicama, Jorge 25 September 2017 (has links)
In this article we will deal with the prime numbers and its current use in encryption algorithms. Encryption algorithms make possible the exchange of sensible data in internet, such as bank transactions, email correspondence and other internet transactions where privacy is important.
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Parallel multipliers for modular arithmeticSanu, Moboluwaji Olusegun 28 August 2008 (has links)
Not available / text
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Investigating new design alternatives for a radix-2 modular multiplier kernal and I/O subsystem /Chaitheerayanon, Akekalak. January 1900 (has links)
Thesis (M.S.)--Oregon State University, 2004. / Printout. Includes bibliographical references (leaves 63-64). Also available on the World Wide Web.
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Parallel multipliers for modular arithmeticSanu, Moboluwaji Olusegun. January 1900 (has links) (PDF)
Thesis (Ph. D.)--University of Texas at Austin, 2005. / Vita. Includes bibliographical references.
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Uma abordagem da aritmética modular na primeira série do ensino médioAvelar, Renato da Cruz 11 April 2015 (has links)
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Previous issue date: 2015-04-11 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho tem como principal objetivo apresentar um abordagem da aritmética modular
direcionada para o aluno do 1o ano do ensino médio regular, baseado na experiência do
autor nessa modalidade de ensino, fazendo uma breve revisão de alguns requisitos básicos
para compreensão do conteúdo. A teoria é apresentada utilizando uma linguagem simples,
sempre seguida de exemplos, sendo alguns deles retirados de provas de nível nacional,
além de propor atividades para fixação, seguidas das respectivas soluções e atividades de
aplicação, que permitem a verificação e percepção da importância do conteúdo. / This work aims to present a modular arithmetic approach directed to the student on his
first year of regular high school, based on the experience of author in this type of education,
making a brief review of some basic requirements to understand the content. The theory
is presented using simple language, always followed by examples, some of which are drawn
from national tests, and to propose activities for fixation, followed by their solutions and
activities application that allow the verification and perceived importance of the content.
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