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Efficient Algorithms for ECC Using New Coordinates Systems Over GF(P): The six Genus-1 elliptic curves using projective coordinates - Couverture souple

Abu Al-Haija, Qasem

 
9783659260186: Efficient Algorithms for ECC Using New Coordinates Systems Over GF(P): The six Genus-1 elliptic curves using projective coordinates
Couverture souple
ISBN 10 : 3659260185 ISBN 13 : 9783659260186
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

The use of projective coordinates to define the Elliptic Curves (EC) instead of affine coordinates replaced the inversion operations by several multiplication operations. Many types of projective coordinates have been proposed for the elliptic curve E: y2= x3+ ax+ b which is defined over a field GF(p) to do EC arithmetic operations such as: Standard projective coordinates, Jacobean projective coordinates, Chudnovsky coordinates. In this thesis, we studied new projective coordinates systems to perform Elliptic Curves Cryptography (ECC) operations with exploiting maximum parallelism to achieve higher performance. The elected coordinates were tested by using parallel multipliers to obtain maximum gain. The result showed that three new attractive projective coordinates systems that can be used as an alternatives for the standard projective coordinates that already in use. These new coordinates are : Doubling Oriented, Tripling Oriented and Montgomery Curves. Montgomery curves gave the best results for area and time when applied for AT measure. However, the difference between these curves is very small which makes those curves to be three choices for efficient ECC Cryptprocessor design.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The use of projective coordinates to define the Elliptic Curves (EC) instead of affine coordinates replaced the inversion operations by several multiplication operations. Many types of projective coordinates have been proposed for the elliptic curve E: y2= x3+ ax+ b which is defined over a field GF(p) to do EC arithmetic operations such as: Standard projective coordinates, Jacobean projective coordinates, Chudnovsky coordinates. In this thesis, we studied new projective coordinates systems to perform Elliptic Curves Cryptography (ECC) operations with exploiting maximum parallelism to achieve higher performance. The elected coordinates were tested by using parallel multipliers to obtain maximum gain. The result showed that three new attractive projective coordinates systems that can be used as an alternatives for the standard projective coordinates that already in use. These new coordinates are : Doubling Oriented, Tripling Oriented and Montgomery Curves. Montgomery curves gave the best results for area and time when applied for AT measure. However, the difference between these curves is very small which makes those curves to be three choices for efficient ECC Cryptprocessor design.

Biographie de l'auteur

Eng. Qasem Abu Al-Haija’ is a lecturer and Researcher at King Faisal University, College Of Engineering, Department of Electrical and Computer Engineering.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
3659260185
ISBN 13 
9783659260186
Reliure
Broché
Nombre de pages
92
Coordonnées du fabricant
non disponible
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