Timeline for Modifying Elliptic Curve Parameters
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2019 at 8:59 | comment | added | fkraiem | 1024 bits will be more challenging, but it is also not typical. | |
| Jun 24, 2019 at 8:43 | comment | added | THG | Oh, okay. I read up on Lagrange's theorem which states that the order of the generator point will always be divisible by the order of the curve, so if $\#E(\mathbb{F}_p)$ is prime then all generator points (except the point of infinity) have order $p$. Okay, but chances are I won't get a prime order $N$ for my randomly generated curve most of the time, it'll likely be composite. What if I want, say, an elliptic curve with a 1024 bit prime modulus? Is factoring that still efficient? Or am I limited by the prime factorization problem here? Or is there a trick here I'm not seeing? | |
| Jun 24, 2019 at 8:14 | comment | added | fkraiem | The integers that occur in ECDLP-based cryptography are typically small enough to be factored efficiently. Moreover, if $n$ is prime it is of course trivial to find the largest prime factor of $n$: that is $n$ itself. | |
| Jun 23, 2019 at 16:23 | comment | added | THG | Not really. It does tell me how to find the order of the curve $\#E(\mathbb{F}_p)$ using Schoof's algorithm but not how to find the generator point $(x_g, y_g)$ or the order of the generator. In the answer it says "Factor $n$ to determine its largest prime factor $l$", but that seems unacceptable especially for large values of $n$ because that's essentially the prime factorization problem. What if $n$ is prime? | |
| Jun 22, 2019 at 20:22 | comment | added | kelalaka | Does How to find the order of a generator on an elliptic curve? satisfies you? | |
| Jun 22, 2019 at 19:33 | history | asked | THG | CC BY-SA 4.0 |