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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/10293

Title: Scalar multiplication on Weierstraß elliptic curves from Co-Z arithmetic
Authors: Goundar, Raveen R.
Joye, Marc
Miyaji, Atsuko
Rivain, Matthieu
Venelli, Alexandre
Keywords: Elliptic curves
Meloni’s technique
Jacobian coordinates
regular ladders
implementation attacks
Issue Date: 2011-08-09
Publisher: Springer
Magazine name: Journal of Cryptographic Engineering
Volume: 1
Number: 2
Start page: 161
End page: 176
DOI: 10.1007/s13389-011-0012-0
Abstract: In 2007, Meloni introduced a new type of arithmetic on elliptic curves when adding projective points sharing the same Z-coordinate.This paper presents further co-Z addition formula (and register allocations) for various point additions on Weierstrass elliptic curves. It explains how the useof conjugate point addition and other implementation tricks allow one to develop efficient scalar multiplication algorithms making use of co-Z arithmetic. Specifically, this paper describes efficient co-Z based versions of Montgomery ladder, Joye’s double-add algorithm, and certain signed-digit algorithms, as well as faster (X, Y )-only variants for left-to-right versions. Further, the proposed implementations are regular, thereby offering a natural protection against a variety of implementation attacks.
Rights: This is the author-created version of Springer, Raveen R. Goundar, Marc Joye, Atsuko Miyaji, Matthieu Rivain and Alexandre Venelli, Journal of Cryptographic Engineering, 1(2), 2011, 161-176. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s13389-011-0012-0
URI: http://hdl.handle.net/10119/10293
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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