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» Short Memory Scalar Multiplication on Koblitz Curves
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CHES
2005
Springer
99views Cryptology» more  CHES 2005»
11 years 4 months ago
Short Memory Scalar Multiplication on Koblitz Curves
Abstract. We present a new method for computing the scalar multiplication on Koblitz curves. Our method is as fast as the fastest known technique but requires much less memory. We ...
Katsuyuki Okeya, Tsuyoshi Takagi, Camille Vuillaum...
DCC
2000
IEEE
10 years 10 months ago
Efficient Arithmetic on Koblitz Curves
It has become increasingly common to implement discrete-logarithm based public-key protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: ta...
Jerome A. Solinas
PKC
2004
Springer
158views Cryptology» more  PKC 2004»
11 years 3 months ago
Faster Scalar Multiplication on Koblitz Curves Combining Point Halving with the Frobenius Endomorphism
Let E be an elliptic curve deļ¬ned over F2n . The inverse operation of point doubling, called point halving, can be done up to three times as fast as doubling. Some authors have t...
Roberto Maria Avanzi, Mathieu Ciet, Francesco Sica
JUCS
2008
140views more  JUCS 2008»
10 years 10 months ago
Parallel Formulations of Scalar Multiplication on Koblitz Curves
We present an algorithm that by using the and -1 Frobenius operators concurrently allows us to obtain a parallelized version of the classical -and-add scalar multiplication algor...
Omran Ahmadi, Darrel Hankerson, Francisco Rodr&iac...
ALGORITHMICA
2006
97views more  ALGORITHMICA 2006»
10 years 10 months ago
Scalar Multiplication on Koblitz Curves Using the Frobenius Endomorphism and Its Combination with Point Halving: Extensions and
Abstract. In this paper we prove the optimality and other properties of the -adic nonadjacent form: this expansion has been introduced in order to efficiently compute scalar multip...
Roberto Maria Avanzi, Clemens Heuberger, Helmut Pr...
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