On counting and generating curves over small finite fields
نویسندگان
چکیده
منابع مشابه
On counting and generating curves over small finite fields
We consider curves defined over small finite fields with points of large prime order over an extension field. Such curves are often referred to as Koblitz curves and are of considerable cryptographic interest. An interesting question is whether such curves are easy to construct as the target point order grows asymptotically. We show that under certain number theoretic conjecture, if q is a prim...
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Article history: Received 25 August 2014 Received in revised form 10 September 2014 Accepted 18 September 2014 Available online 4 November 2014 Communicated by H. Stichtenoth MSC: 11G20 10D20 14G15 14H10
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Stanford University) Abstract: A curve is a one dimensional space cut out by polynomial equations, such as y2=x3+x. In particular, one can consider curves over finite fields, which means the polynomial equations should have coefficients in some finite field and that points on the curve are given by values of the variables (x and y in the example) in the finite field that satisfy the given polyn...
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-We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large; it is based on Shanks’s baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is ...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2004
ISSN: 0885-064X
DOI: 10.1016/j.jco.2003.08.022