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math.AG2023
On the Discrete Logarithm Problem for elliptic curves over local fields
Giuseppe Filippone
The Discrete Logarithm Problem (DLP) for elliptic curves has been extensively studied since, for instance, it is the core of the security of cryptosystems like Elliptic Curve Crypt…
math.AG2023★ 1 cited
Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve
Giovanni Falcone, Giuseppe Filippone
For an (imaginary) hyperelliptic curve of genus , with a Weierstrass point , taken as the point at infinity, we determine a basis of the Riemann-Roch space $\…
math.AG2023
Goppa codes over Edwards curves
Giuseppe Filippone
Given an Edwards curve, we determine a basis for the Riemann-Roch space of any divisor whose support does not contain any of the two singular points. This basis allows us to comput…