I'm currently testing one among those many interesting cryptographic protocols based on bilinear maps. It's quite hard to understand the underlying fundamentals, especially since there are several types of pairing and different underlying algorithms like Weil, Tate and Ate (again with subtypes?). Although I understand the properties
So I started with Ben Lynn's "On The Implementation of pairing based cryptosystems", which is relatively old. There he distinguishes between Type A-G curves and notes that Type3 curves are "susceptible to certain discrete log attacks". On the other hand, Steven Galbraith talks about "the death of Type 1 pairings" in his quite new blog entry and states that "Type 3 pairings are usally the most efficient" and Type 4 is rarly used. (Ben Lynn however seemed to have a little preference for the Type 4 pairing) Are those the same pairings as mentioned by Ben Lynn?
Can some of them been seen als secure enough for productive use? Are some of them seen to be more secure than others? What about the Ate-pairing which seems to be surprisingly fast?