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Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer *h* in addition to characteristic *p* and extension degree *m*, namely type-⟨*h*.*m*⟩ GNB in extension field **F*** _{pm}*. The parameter

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.1 pp.172-179

- Publication Date
- 2011/01/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E94.A.172

- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)

- Category
- Mathematics

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Kenta NEKADO, Yasuyuki NOGAMI, Hidehiro KATO, Yoshitaka MORIKAWA, "Cyclic Vector Multiplication Algorithm and Existence Probability of Gauss Period Normal Basis" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 1, pp. 172-179, January 2011, doi: 10.1587/transfun.E94.A.172.

Abstract: Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer *h* in addition to characteristic *p* and extension degree *m*, namely type-⟨*h*.*m*⟩ GNB in extension field **F*** _{pm}*. The parameter

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.172/_p

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@ARTICLE{e94-a_1_172,

author={Kenta NEKADO, Yasuyuki NOGAMI, Hidehiro KATO, Yoshitaka MORIKAWA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Cyclic Vector Multiplication Algorithm and Existence Probability of Gauss Period Normal Basis},

year={2011},

volume={E94-A},

number={1},

pages={172-179},

abstract={Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer *h* in addition to characteristic *p* and extension degree *m*, namely type-⟨*h*.*m*⟩ GNB in extension field **F*** _{pm}*. The parameter

keywords={},

doi={10.1587/transfun.E94.A.172},

ISSN={1745-1337},

month={January},}

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TY - JOUR

TI - Cyclic Vector Multiplication Algorithm and Existence Probability of Gauss Period Normal Basis

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 172

EP - 179

AU - Kenta NEKADO

AU - Yasuyuki NOGAMI

AU - Hidehiro KATO

AU - Yoshitaka MORIKAWA

PY - 2011

DO - 10.1587/transfun.E94.A.172

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E94-A

IS - 1

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - January 2011

AB - Recently, pairing-based cryptographic application sch-emes have attracted much attentions. In order to make the schemes more efficient, not only pairing algorithm but also arithmetic operations in extension field need to be efficient. For this purpose, the authors have proposed a series of cyclic vector multiplication algorithms (CVMAs) corresponding to the adopted bases such as type-I optimal normal basis (ONB). Note here that every basis adapted for the conventional CVMAs are just special classes of Gauss period normal bases (GNBs). In general, GNB is characterized with a certain positive integer *h* in addition to characteristic *p* and extension degree *m*, namely type-⟨*h*.*m*⟩ GNB in extension field **F*** _{pm}*. The parameter

ER -