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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Twisted Edwards Curves Revisited
verfasst von : Huseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson
Erschienen in: Advances in Cryptology - ASIACRYPT 2008
Verlag: Springer Berlin Heidelberg
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This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses
$8\mathrm{\textbf{M}}$
for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use
$9\mathrm{\textbf{M}} + 1\mathrm{\textbf{S}}$
. It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to
$2\mathrm{\textbf{M}}$
. This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).