On the distribution of orders of Frobenius action on l-torsion of abelian surfaces
The computation of the order of Frobenius action on the ^-torsion is a part of Schoof - Elkies - Atkin algorithm for point counting on an elliptic curve E over a finite field Fq. The idea of Schoof's algorithm is to compute the trace of Frobenius t modulo primes I and restore it by the Chinese...
| Published in: | Прикладная дискретная математика № 48. С. 22-33 |
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| Format: | Article |
| Language: | English |
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| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000721635 Перейти в каталог НБ ТГУ |
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| 039 | 9 | |a 202006091811 |c 202006091810 |d cat34 |c 202006081817 |d VLOAD |y 202006081800 |z Александр Эльверович Гилязов | |
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| 100 | 1 | |a Kolesnikov, N. S. |9 502908 | |
| 245 | 1 | 0 | |a On the distribution of orders of Frobenius action on l-torsion of abelian surfaces |c N. S. Kolesnikov, S. A. Novoselov |
| 504 | |a Библиогр.: 24 назв. | ||
| 520 | 3 | |a The computation of the order of Frobenius action on the ^-torsion is a part of Schoof - Elkies - Atkin algorithm for point counting on an elliptic curve E over a finite field Fq. The idea of Schoof's algorithm is to compute the trace of Frobenius t modulo primes I and restore it by the Chinese remainder theorem. Atkin's improvement consists of computing the order r of the Frobenius action on E[£] and of restricting the number t (mod F) to enumerate by using the formula t2 = q(Z + Z-1)2 (mod £). Here Z is a primitive r-th root of unity. In this paper, we generalize Atkin's formula to the general case of abelian variety of dimension g. Classically, finding of the order r involves expensive computation of modular polynomials. We study the distribution of the Frobenius orders in case of abelian surfaces and q = 1 (mod F) in order to replace these expensive computations by probabilistic algorithms. | |
| 653 | |a абелевы поверхности | ||
| 653 | |a эллиптические кривые | ||
| 653 | |a абелево многообразие | ||
| 653 | |a Фробениуса эндоморфизм | ||
| 653 | |a подсчет точек | ||
| 655 | 4 | |a статьи в журналах |9 879358 | |
| 700 | 1 | |a Novoselov, S. A. |9 477237 | |
| 773 | 0 | |t Прикладная дискретная математика |d 2020 |g № 48. С. 22-33 |x 2071-0410 |w 0210-48760 | |
| 852 | 4 | |a RU-ToGU | |
| 856 | 4 | |u http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000721635 | |
| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=467563 | ||
| 908 | |a статья | ||
| 999 | |c 467563 |d 467563 | ||