Approach to Pairing Inversions Without Solving Miller Inversion

In the present paper, we show that the pairing inversion problem of Atei pairing can be solved under the assumption that we have a generic algorithm for solving “exponentiation inversion” problem. With such an algorithm, the inversion problem of Atei pairing can be solved without solving the Miller inversion. Thus, the pairing inversion problem of Atei pairing is reduced to the exponentiation inversion problem.