Constructing pairing-friendly elliptic curve

How to compute Tate pairing is a research focus in all kinds of applications of pairing-based cryptosystems (PBC). In the paper, the structure of Miller´s algorithm is firstly analyzed, which is used to implement Tate pairing. Based on the characteristics that Miller´s algorithm will be improved tremendous if the order of the subgroup of elliptic curve group is low hamming prime, a method of generating primes with low hamming is presented. Then, a new method for generating parameters for PBC is put forward, which enable it feasible that there is certain some subgroup of low hamming prime order in the elliptic curve group generated. Finally, the computation efficiency of Tate pairing using the new parameters for PBC is analyzed, which saves 25% of the time to compute the Tate pairing.