Post
Topic
Board Development & Technical Discussion
Merits 2 from 2 users
Re: Why gcd between base point and any other point will give us one or three?
by
j2002ba2
on 29/12/2023, 18:40:57 UTC
⭐ Merited by garlonicon (1) ,hugeblack (1)
Because 0x1110...f784 has many small factors:
2^2 * 17 * 4289 * 6196937 * 9672199247 * 441571470858719851994038335827739586159888848835828007

While 0x1b88...e5e9 has factor 3, and then some unholy big numbers.

Your funny random mapping then produces some random integer, which is very very unlikely to have one of the big factors in the second one.

That said, what is the purpose of this exercise?

Point coordinates are not integers, they are instead infinite sets of all kind of numbers, represented by integers.

Specially y^2 = x^3 + 7 does not have integer or rational number solutions. Plugging integers makes even less sense here.

Why not use an isomorphic curve of rank>0, i.e. y^2 = x^3 - 2. Then at least you'd know that there are rational solutions, and have a single nice generator (3,5).