Counting curves over finite fields
نویسندگان
چکیده
منابع مشابه
Counting curves over finite fields
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...
متن کاملCounting points on curves over finite fields
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The group law on elliptic curves is well-known and gives rise to elliptic curve cryptography systems which find application to government and industry today. However, the generalisation to higher genus requires the manipulation of divisor classes rather than points, and analogues of key genus 1 results have yet to be found. Nonetheless, effective computation within the group is possible, and te...
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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: Finite Fields and Their Applications
سال: 2015
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2014.09.008