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Koblitz Curves over Quadratic Fields.
- Source :
- Journal of Cryptology; Jul2019, Vol. 32 Issue 3, p867-894, 28p
- Publication Year :
- 2019
-
Abstract
- In this work, we retake an old idea that Koblitz presented in his landmark paper (Koblitz, in: Proceedings of CRYPTO 1991. LNCS, vol 576, Springer, Berlin, pp 279–287, 1991), where he suggested the possibility of defining anomalous elliptic curves over the base field F 4 . We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. We also introduce two ordinary Koblitz-like elliptic curves defined over F 4 that are equipped with efficient endomorphisms. To the best of our knowledge, these endomorphisms have not been reported before. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field F 4 m , with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also suggest a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over binary and prime fields. [ABSTRACT FROM AUTHOR]
- Subjects :
- QUADRATIC fields
PRIME numbers
ARITHMETIC
LIBRARY software
ELLIPTIC curves
Subjects
Details
- Language :
- English
- ISSN :
- 09332790
- Volume :
- 32
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Cryptology
- Publication Type :
- Academic Journal
- Accession number :
- 137453351
- Full Text :
- https://doi.org/10.1007/s00145-018-9294-z