Count points on elliptic curve secp256k1 with another p

asked 2020-07-30 12:23:24 -0500

Duglas gravatar image

updated 2020-08-03 11:09:18 -0500

slelievre gravatar image

Example:

secp192k1': 

_ECData( p=2192 - 232 - 212 - 28 - 27 - 26 - 2**3 - 1, a=0, b=3, 
Gx=0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D, 
Gy=0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D,
n=0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D

I have another curve (with another p(!), similar base point and equation ) parameters.

I need to calculate n

How can I do it with code in sage, python or another software please?

Br

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Comments

Welcome to Ask Sage! Thank you for your question!

It seems there are formatting problems in the way your question was entered, can you fix them?

slelievre gravatar imageslelievre ( 2020-07-30 15:48:09 -0500 )edit

I edited the lines in the question, marking the many letters that may be part of a pseudo-code as code, but we still have no well defined question. To have a well defined question, we need the "other" p and the parameters for the "new" curve. For small values of p, sage can compute via E.order() the number of $\Bbb F_p$-rational points, e.g.

sage: E = EllipticCurve(GF(7), [3,4])                                                                                         
sage: E.order()                                                                                                               
10

but for greater values, we have to invest mathematical effort to find the "order". (Of $E(\Bbb F_p)$.) Please fill in all needed defining data. And best give references / links.

dan_fulea gravatar imagedan_fulea ( 2020-08-03 10:57:58 -0500 )edit

Possibly related

But for anything to happen here, can you please edit your post into a better formed question?

slelievre gravatar imageslelievre ( 2020-08-03 11:19:22 -0500 )edit