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New hardware algorithms and designs ...

Gutub, Adnan Abdul-Aziz.

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New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n).

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n)./
作者:	Gutub, Adnan Abdul-Aziz.
面頁冊數:	93 p.
附註:	Adviser: Alexandre Ferreira Tenca.
Contained By:	Dissertation Abstracts International63-08B.
標題:	Computer Science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3061894
ISBN:	0493777253

New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n).
Gutub, Adnan Abdul-Aziz.

New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n). - 93 p.

Adviser: Alexandre Ferreira Tenca.

Thesis (Ph.D.)--Oregon State University, 2003.

The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2<super>n</super>), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementations to compute the Montgomery modular inverse. We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. It is also presented how to obtain a fast hardware algorithm to compute the inverse by multi-bit shifting method. The proposed designs have the hardware scalability feature, which means that the design can fit on constrained areas and still handle operands of any size. In order to have long-precision calculations, the module works on small precision words. The word-size, on which the module operates, can be selected based on the area and performance requirements. The upper limit on the operand precision is dictated only by the available memory to store the operands and internal results. The scalable module is in principle capable of performing infinite-precision Montgomery inverse computation of an integer, modulo a prime number.

ISBN: 0493777253Subjects--Topical Terms:

626642
Computer Science.

New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n).
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100 1 $a Gutub, Adnan Abdul-Aziz. $3 1249425
245 1 0 $a New hardware algorithms and designs for Montgomery modular inverse computation in Galois fields GF(p) and GF(2n).
300 $a 93 p.
500 $a Adviser: Alexandre Ferreira Tenca.
500 $a Source: Dissertation Abstracts International, Volume: 63-08, Section: B, page: 3787.
502 $a Thesis (Ph.D.)--Oregon State University, 2003.
520 $a The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2<super>n</super>), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementations to compute the Montgomery modular inverse. We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. It is also presented how to obtain a fast hardware algorithm to compute the inverse by multi-bit shifting method. The proposed designs have the hardware scalability feature, which means that the design can fit on constrained areas and still handle operands of any size. In order to have long-precision calculations, the module works on small precision words. The word-size, on which the module operates, can be selected based on the area and performance requirements. The upper limit on the operand precision is dictated only by the available memory to store the operands and internal results. The scalable module is in principle capable of performing infinite-precision Montgomery inverse computation of an integer, modulo a prime number.
520 $a We also propose a scalable and unified architecture for a Montgomery inverse hardware that operates in both GF(p) and GF(2<super>n</super>) fields. We adjust and modify a GF(2<super>n</super>) Montgomery inverse algorithm to benefit from multi-bit shifting hardware features making it very similar to the proposed best design of GF(p) inversion hardware.
520 $a We compare all scalable designs with fully parallel ones based on the same basic inversion algorithm. All scalable designs consumed less area and in general showed better performance than the fully parallel ones, which makes the scalable design a very efficient solution for computing the long precision Montgomery inverse.
590 $a School code: 0172.
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710 2 0 $a Oregon State University. $3 625720
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