As a beginner in cryptography, I do not know anything about different pairing types more than their names. So far, I know these names: Ate pairing, tate pairing, eta pairing, and r-ate pairing.
I am curious whether I should care which type of pairing I am using in my implementations? Do they affect performance or security at all?
What should I know about these types?
So far, I think I've got these points:
- There is an obvious and serious difference between different types of "Curve Generation" in pairings. I mean, whether they are Super Singular, MNT curves, Cocks-Pinch, Barreto-Naehrig, etc is really important because it affects the "security multiplier" (i.e. embedding rate). And for a certain security parameter higher embedding rate means better performance and shorter representation of elements of $G_1$.
- Also it is important whether the curves are over "large prime fields" or over fields of "small characteristic" because recent research works in cryptanalysis of elliptic curves show that elliptic curves over fields of small characteristic are not secure anymore.