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AN EFFICIENT SEARCH SPACE IN COUNTING POINTS ON GENUS 3 HYPERELLIPTIC CURVES OVER FINITE FIELDS
AN EFFICIENT SEARCH SPACE IN COUNTING POINTS ON GENUS 3 HYPERELLIPTIC CURVES OVER FINITE FIELDS
Journal of applied mathematics & informatics. 2015. Jan, 33(1_2): 145-155
  • Received : June 11, 2014
  • Published : January 30, 2015
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Sohn Gyoyong

Abstract
In this paper, we study the bounds of the coefficients of the characteristic polynomial of the Frobenius endomorphism of the Jacobian of dimension three over a finite field. We provide explicitly computable bounds for the coefficients of the characteristic polynomial. In addition, we present the counting points algorithm for computing a group of the Jacobian of genus 3 hyperelliptic curves over a finite field with large characteristic. Based on these bounds, we found an efficient search space that was used in the counting points algorithm on genus 3 curves. The algorithm was explained and verified through simple examples.
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