Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers.
Computing the cardinality of CM elliptic curves using torsion points
Let be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field . The field of definition of is the ring class field of the order. If the prime splits completely in , then we can reduce modulo one the factors of and get a curve defined over . The trace of the Frobenius of is known up to sign and we need a fast way to find this sign, in the context of the Elliptic Curve Primality Proving algorithm (ECPP). For this purpose, we propose...
Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications.
Criptografía y curvas elípticas.