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Sorry, of course any Turing complete language are equivalent, so my question is badly phrased. I am starting writing an MSc dissertation on the Elliptic Curve Discrete Logarithm Problem over Finite Fields $\mathbb{F}_p$, ($p$ large prime) which is considered to be computationally infeasible, but two recent papers have made some advances, they both present results using Magma, the main computation work is:

1. generating random points on an Elliptic Curve over a finite field. $R = aP + bQ$ (a, b random integers)

2. solving systems of summation polynomial equations (as per your reference). $S_m(X_1,\dots,X_m) = 0$

3. linear algebra ( using using Gr\"obner basis algorithms )

All the papers I see use Magma, so question is better phrased, if I ask how easy it is for SageMath to do these computations?, in terms of pre-existing functions.

Sorry, of course any Turing complete language are equivalent, so my question is badly phrased. I am starting writing an MSc dissertation on the Elliptic Curve Discrete Logarithm Problem over Finite Fields $\mathbb{F}_p$, ($p$ large prime) which is considered to be computationally infeasible, but two recent papers have made some advances, they both present results using Magma, the main computation work is:

1. generating random points on an Elliptic Curve over a finite field. $R = aP + bQ$ (a, b random integers)

2. solving systems of summation polynomial equations (as per your reference). $S_m(X_1,\dots,X_m) = 0$

3. linear algebra ( using using Gr\"obner Gr\"oebner basis algorithms )

All the papers I see use Magma, so question is better phrased, if I ask how easy it is for SageMath to do these computations?, in terms of pre-existing functions.functions. UPDATE: I've been told by the author of one of the papers , that I should be able to do this in SageMath.

Sorry, of course any Turing complete language are equivalent, so my question is badly phrased. I am starting writing an MSc dissertation on the Elliptic Curve Discrete Logarithm Problem over Finite Fields $\mathbb{F}_p$, ($p$ large prime) which is considered to be computationally infeasible, but two recent papers have made some advances, they both present results using Magma, the main computation work is:

1. generating random points on an Elliptic Curve over a finite field. $R = aP + bQ$ (a, b random integers)

2. solving systems of summation polynomial equations (as per your reference). $S_m(X_1,\dots,X_m) = 0$

3. linear algebra ( using using Gr\"oebner Gr\"obner basis algorithms )

All the papers I see use Magma, so question is better phrased, if I ask how easy it is for SageMath to do these computations?, in terms of pre-existing functions. UPDATE: I've been told by the author of one of the papers , that I should be able to do this in SageMath.