ANTS-8 Poster Abstracts here, C is the natural degree 2 cover of C onto P1 and E is the degree 2 projection of E onto P1 induced by C . Gerhard Frey and Ernst Kani give a complete description of this induced cover Ï of the projective lines in their 1988 paper [2]. Using this commutative diagram, it is possible to show that if n is odd, then there is only a handful of possible con gurations of the rami cation points. It was by studying these few possibilities that the (3, 3) and (5, 5) split Jacobians were characterized. The next section of the poster deals with the case where n = 4. In general, the even cases have fewer restrictions on the distribution of the rami cation points, and are therefore more di cult to characterize. In order to get around this hurdle, we build up the degree 4 case by rst looking at the degree 2 case. The ability to precisely describe and construct (n, n)-split Jacobians has important computational applications. It allows the construction of abelian varieties with special isogenies and allows new explicit visibility constructions (N. Bruin [1]). References [1] N. Bruin and
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A variant of Wiener's attack on RSA with small secret exponent
Dujella, Andrej
Follow ACM Communications in Computer Algebra
, Volume 42 (1-2)
Association for Computing Machinery – Jul 25, 2008
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