1 | initial version |

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:

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

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

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.

2 | No.2 Revision |

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:

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

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

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.

3 | No.3 Revision |

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:

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

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

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.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.