Title A relation between embedding degrees and class numbers of binary quadratic forms Abstract. In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field F p and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the… (More)
We describe a new method for constructing irreducible polyno-mials modulo a prime number p. The method mainly relies on Chebotarev's density theorem.
We present new methods for computing square roots and factorization of poly-nomials over finite fields. We also describe a method for computing in the Jacobian of a singular hyperelliptic curve. There is a compact representation of an element in the Jacobian of a smooth hyperelliptic curve over any field. This compact representation leads an efficient… (More)