# solving summation polynomials

Solving discrete logarithm problem for elliptic curves

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

solving summation polynomials

Solving discrete logarithm problem for elliptic curves

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

0

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. UPDATE: I've been told by the author of one of the papers , that I should be able to do this in SageMath.

I could be wrong, but I think you are allowed to edit your own question to provide more details--if possible you should do that rather than update your question in the form of an "answer".

Asked: **
2017-12-12 11:14:31 -0500
**

Seen: **101 times**

Last updated: **Dec 15 '17**

Stein-Watkins Database of Elliptic Curves

Polynomials with multiple variables and abstract coefficients

Solving a system of 5 polynomial equations

Sage showed "TypeError: need a summation variable" when i used sum function with for loop

Is there any easy way to parallel grĂ¶bnerbasis computations in sage?

Define a polynomial ring in other polynomials

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What do you mean precisely? Most programming languages are Turing complete (Python is one of them).

For reference, "summation polynomials" are introduced in section 2 of the paper "Summation polynomials and the discrete logarithm problem on elliptic curves" by Igor Semaev, available at https://eprint.iacr.org/2004/031.pdf.

See also a discussion of summation polynomials by Steven Galbraith on "The Elliptic Curve Cryptography blog" .

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 đť”˝pFp, (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,â€¦,Xm)=0Sm(X1,â€¦,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.