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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 𝔽pFp, (pp 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: generating random points on an Elliptic Curve over a finite field. R=aP+bQR=aP+bQ (a, b random integers) solving systems of summation polynomial equations (as per your reference). Sm(X1,…,Xm)=0Sm(X1,…,Xm)=0 linear algebra ( using using Gr\"obner basis algorithms ) All the papers I see use Magma, 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 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.

Solving discrete logarithm problem for elliptic curves

most papers I see use Magma for solving summation polynomials, can SageMath do this?