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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제33권 제1호
- 발행연도
- 2015.1
- 수록면
- 145 - 155 (11page)
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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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참고문헌 (18)
참고문헌 신청
L. Adleman / 1996 / ANTS-II / Springer-Verlag :1~16
I. Blake. / 1999 / Elliptic curves in cryptography / London Math. Soc. Lecture Note Series 265
J. Denef. / 2006 / An Extension of Kedlaya’s Algorithm to Hyperelliptic Curves in Characteristic 2 / J, Cryptology 19:1~25
N. Elkies / 1998 / Computational perspectives on number theory, vol. 7 of AMS/IP Stud. Adv. Math / Am. Math. Soc :21~76
P. Gaudry. / 2000 / Counting points on hyperelliptic curves over finite fields / ANTSIV :297~312
I. Blake. / 1999 / Elliptic curves in cryptography / London Math. Soc. Lecture Note Series 265
J. Denef. / 2006 / An Extension of Kedlaya’s Algorithm to Hyperelliptic Curves in Characteristic 2 / J, Cryptology 19:1~25
N. Elkies / 1998 / Computational perspectives on number theory, vol. 7 of AMS/IP Stud. Adv. Math / Am. Math. Soc :21~76
P. Gaudry. / 2000 / Counting points on hyperelliptic curves over finite fields / ANTSIV :297~312
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