How to define a polynomial A(x,y) that (x,y) satisfying y^2+y=x^3

asked 2018-07-07 03:59:55 -0500

albertcz gravatar image

updated 2018-07-08 01:36:41 -0500

I am working on a elliptic curve like y^2+y=x^3 over GF(2^6)

and i want to define a polynomial A(x,y) over GF(2^6) that x,y satisfying y^2+y=x^3

Hope to get your help, thank you!

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Please describe mathematically the situation. It is hard to figure out the "map between variables", so maybe we have a map $f$ from a polynomial ring $R$ to some other ring $S$, and the map $f:R\to S$ is determined by the images through $f$ of the generators of $R$.

dan_fulea gravatar imagedan_fulea ( 2018-07-07 11:37:06 -0500 )edit

I have reorganize my language. Thank you a lot for your attention

albertcz gravatar imagealbertcz ( 2018-07-07 21:02:34 -0500 )edit

A polynomial function on your curve is given by an element in the quotient K[x,y] / (y^2 + y - x^3). The answer to your question really depends on what you want to do with such function.

vdelecroix gravatar imagevdelecroix ( 2018-07-08 10:40:37 -0500 )edit

This is what i need! thank you!

albertcz gravatar imagealbertcz ( 2018-07-09 06:33:30 -0500 )edit