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Spectral modular arithmetic.

Saldamli, Gokay.

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Spectral modular arithmetic.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Spectral modular arithmetic./
作者:	Saldamli, Gokay.
面頁冊數:	135 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5595.
Contained By:	Dissertation Abstracts International66-10B.
標題:	Engineering, Electronics and Electrical. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3190916
ISBN:	9780542334832

Spectral modular arithmetic.
Saldamli, Gokay.

Spectral modular arithmetic. - 135 p.

Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5595.

Thesis (Ph.D.)--Oregon State University, 2006.

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 pi to millions of digits of precision, factoring and also big prime search projects.

ISBN: 9780542334832Subjects--Topical Terms:

626636
Engineering, Electronics and Electrical.

Spectral modular arithmetic.
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500 $a Source: Dissertation Abstracts International, Volume: 66-10, Section: B, page: 5595.
500 $a Adviser: Cetin K. Koc.
502 $a Thesis (Ph.D.)--Oregon State University, 2006.
520 $a 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 pi to millions of digits of precision, factoring and also big prime search projects.
520 $a When it comes to the utilization of spectral techniques for modular operations in public key cryptosysterns 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.
520 $a 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.
520 $a An obvious example of such an operation is the modular exponentiation i.e., the computation of c = me 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.
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