Fast implementation of extension fields with Typell ONB and cyclic vector multiplication algorithm

Yasuyuki Nogami; Shigeru Shinonaga; Yoshitaka Morikawa

doi:10.1093/ietfec/e88-a.5.1200

Fast implementation of extension fields with Typell ONB and cyclic vector multiplication algorithm

Yasuyuki Nogami, Shigeru Shinonaga, Yoshitaka Morikawa

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF F_p5 is about 20% faster than those in OFF F_p5, Then, since CVMA is suitable for parallel processing, we show that Typell AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.

Original language	English
Pages (from-to)	1200-1208
Number of pages	9
Journal	IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Volume	E88-A
Issue number	5
DOIs	https://doi.org/10.1093/ietfec/e88-a.5.1200
Publication status	Published - Jan 1 2005

Keywords

Extension field
Fast implementation
Optimal extension field
Optimal normal basis
Public-key cryptosystem

ASJC Scopus subject areas

Signal Processing
Computer Graphics and Computer-Aided Design
Electrical and Electronic Engineering
Applied Mathematics

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10.1093/ietfec/e88-a.5.1200

Cite this

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abstract = "This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF Fp5 is about 20% faster than those in OFF Fp5, Then, since CVMA is suitable for parallel processing, we show that Typell AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.",

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AU - Nogami, Yasuyuki

AU - Shinonaga, Shigeru

AU - Morikawa, Yoshitaka

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N2 - This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF Fp5 is about 20% faster than those in OFF Fp5, Then, since CVMA is suitable for parallel processing, we show that Typell AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.

AB - This paper proposes an extension field named TypeII AOPF. This extension field adopts TypeII optimal normal basis, cyclic vector multiplication algorithm, and Itoh-Tsujii inversion algorithm. The calculation costs for a multiplication and inversion in this field is clearly given with the extension degree. For example, the arithmetic operations in TypeII AOPF Fp5 is about 20% faster than those in OFF Fp5, Then, since CVMA is suitable for parallel processing, we show that Typell AOPF is superior to AOPF as to parallel processing and then show that a multiplication in TypeII AOPF becomes about twice faster by parallelizing the CVMA computation in TypeII AOPF.

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KW - Fast implementation

KW - Optimal extension field

KW - Optimal normal basis

KW - Public-key cryptosystem

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Fast implementation of extension fields with Typell ONB and cyclic vector multiplication algorithm

Abstract

Keywords

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