Symmetric vs non-symmetric pairing based crypto

Question

I am trying to find a comparison of how different pairing-friendly elliptic curves perform (in terms of security) in real world applications;

I am using PBC library, and it has type A curves and type D curves (also , i am having hard time understanding how pairing types depend on underlying curve types, and which of them have been broken/ or are considered insecure at the moment;

Type A

Type D

At first glance, there are 3 types of pairings, type 1(symmetric), type 2 (g1!=g2, g2->g1) and type 3; i understand that different algorithms require pairings to be either of type1 or type2 or type3;

I would also like to know more about why some algorithms are limited to certain pairing types. Any references would be greatly welcome

Answer 1

This lecture by Dan Boneh should answer all your questions and more:

https://www.youtube.com/watch?v=F4x2kQTKYFY

ps. I saw you also had a question about NIZK proofs, so you should check out the full list of videos

https://www.youtube.com/playlist?list=PLXF_IJaFk-9C4p3b2tK7H9a9axOm3EtjA

which has almost 3 hours of lectures on Groth-Sahai proofs by Jens Groth which might interest you.