For my research, I would like to compare the efficiency of a scheme when instantiated with Elliptic curves and RSA. So, I would like to know a "latest" comparison (as of 2018) on what group sizes of ECC and RSA provide equal amount of security. I found some references online, but they are really outdated and I would like to have a latest comparison on their security.
For example, I would like to have a table of the form for each of the 15 NIST curves.
2048 bit RSA - 224 bit ECC curve - xx bit security.
1024 bit RSA - 160 bit ECC curve - xx bit security.
What are the time complexities of best attacks in each case? Does the comparison matter whether the group is being used for encryption or signatures? It would be helpful to provide an explanation on why those groups provide the corresponding amount of security.