On: Basic Intro to Elliptic Curve Cryptography (2019)

[staycoolboy]

Very cool. I would love an ELI5 why some curves are more or less secure than others (e.g. p256r1 is the hot curve now, but why?)

[john_alan → staycoolboy]

When you say p-256r1 are you talking about secp256r1 or Brainpool?

The security of a curve is defined by p, the prime field over which it is defined, a and b the curve co-efficient.

There exists attacks against curves in various ways, composite order attacks, anomalous curves (where the curve order === field order).

[staycoolboy → john_alan]

secp256r1

> There exists attacks against curves in various ways, composite order attacks, anomalous curves (where the curve order === field order).

This is where I need the ELI5 part. :) But I realize some things just require hard work to understand... like ECC theory.

[john_alan → staycoolboy]

Haha, well I guess.

To start you off:

Composite order attacks: things that are prime tend to be hard to attack. If your curve doesn’t use prime stuff then you can take the factors of the thing and attack it in little groups.

Anomalous curves: elliptic curves have a total number of points. We call that the order. So does the “field” (kinda like a box) that the curve lives in. If the number of elements in the field and the number of elements in the curve are the same, you can kinda “lift” the curve out of its box and put it in another box that’s easier to smash it in. :)

[staycoolboy → john_alan]

Thanks, this answer is helpful for focusing my search terms!