I was reading PBC and its implementations for finding pairing parameters. I am particularly interested in implementing a BLS signature scheme with 20-byte (160-bit) signatures ("short signatures"). So, I concluded that (for my app to have enough security) type G pairings are the best. However, it is really hard to find a type G pairing that produces signatures of 160-bit, but I noticed that "bits of q" in listfreeman.exe (to find appropriate discriminants that will then be passed to gengparam.exe) should be a number close to 160 for short signatures (with enough strength of course) to exist. So, I now run listfreeman.exe recording discriminant values with bits of q close to 160.
However, this process is taking forever and I was wondering whether I can find type G pairings producing 160-bit signatures with a faster way than by searching all discriminants?