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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Memory-Constrained Implementations of Elliptic Curve Cryptography in Co-Z Coordinate Representation
verfasst von : Michael Hutter, Marc Joye, Yannick Sierra
Erschienen in: Progress in Cryptology – AFRICACRYPT 2011
Verlag: Springer Berlin Heidelberg
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It has been recently shown that sharing a common coordinate in elliptic curve cryptography implementations improves the performance of scalar multiplication. This paper presents new formulæ for elliptic curves over prime fields that provide efficient point addition and doubling using the Montgomery ladder. All computations are performed in a common projective
Z
-coordinate representation to reduce the memory requirements of low-resource implementations. In addition, all given formulæ make only use of
out-of-place
operations therefore insuring that it requires no additional memory for any implementation of the underlying finite-field operations whatsoever. Our results outperform existing solutions in terms of memory and speed and allow a fast and secure implementation suitable for low-resource devices and embedded systems.