Affine precomputation with sole inversion in elliptic curve cryptography

Authors:
Erik Dahmen;Katsuyuki Okeya;Daniel Schepers
Affiliations:
Technische Universität Darmstadt, Fachbereich Informatik, Darmstadt, Germany;Hitachi, Ltd., Systems Development Laboratory, Kawasaki-shi, Kanagawa-ken, Japan;Technische Universität Darmstadt, Fachbereich Informatik, Darmstadt, Germany
Venue:
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Year:
2007

Citing 13
Cited 4

Use of elliptic curves in cryptography

Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Efficient Arithmetic on Koblitz Curves

Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic curves in cryptography

Elliptic curves in cryptography
Guide to Elliptic Curve Cryptography

Guide to Elliptic Curve Cryptography
Analysis of Fractional Window Recoding Methods and Their Application to Elliptic Curve Cryptosystems

IEEE Transactions on Computers
Trading Inversions for Multiplications in Elliptic Curve Cryptography

Designs, Codes and Cryptography
Improved techniques for fast exponentiation

ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Fast elliptic curve arithmetic and improved weil pairing evaluation

CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
A note on the signed sliding window integer recoding and a left-to-right analogue

SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
New minimal weight representations for left-to-right window methods

CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Using an RSA accelerator for modular inversion

CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Fractional windows revisited: improved signed-digit representations for efficient exponentiation

ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition

Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition

Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves

EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
New composite operations and precomputation scheme for elliptic curve cryptosystems over prime fields

PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Software implementation of binary elliptic curves: impact of the carry-less multiplier on scalar multiplication

CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Improved precomputation scheme for scalar multiplication on elliptic curves

IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a new approach to precompute all odd points [3]P, [5]P,..., [2k -1]P, k ge; 2 on an elliptic curve over Fp. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.