Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two |
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Authors: | Volker Müller |
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Institution: | Fachbereich Informatik, Technische Universit?t Darmstadt, Alexanderstrasse 10, 64283, Darmstadt, Germany
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Abstract: | We discuss new algorithms for multiplying points on elliptic curves defined over small finite fields of characteristic two.
This algorithm is an extension of previous results by Koblitz, Meier, and Staffelbach. Experimental results show that the
new methods can give a running time improvement of up to 50 % compared with the ordinary binary algorithm for multiplication.
Finally, we present a table of elliptic curves, which are well suited for elliptic curve public key cryptosystems, and for
which the new algorithm can be used.
Received 14 January 1997 and revised 4 September 1997 |
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Keywords: | , Elliptic curves, Characteristic two, Multiplication, Frobenius expansion, Frobenius endomorphism, |
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