Speeding up the Final Exponentiation in Pairing Computation

In this paper we propose efficient and general method to accelerate the final exponentiation in pairing computation. For an elliptic curve over a prime field Fp, our approach is to adjust the greatest coefficient of the final exponent in p-ary representation to be minimized by multiplying the original final exponent by a suitable integer. Since our method does not exploit the structure of parameters of elliptic curves, it is applicable to any curve with small embedding degree k, which is small enough to solve the shortest vector problem in a φ(k)-dimensional lattice easily. On average our method reduces the number of multiplications and squarings required to perform the final exponentiation by (1 − 1 φ(k) ) if k 6= 2.