There is provided a pairing computation device, a pairing computation method and a recording medium recording a pairing computation program all enabling a pairing computation at high speed. In the case where the Ate pairing e(Q,P) is defined as in equation (1) and k is any one of even, a multiple of 3, a multiple of 4, and a multiple of 6, arithmetic operations of a rational function which is required to derive the Miller function fs,Q(P) are performed on the proper subfield specified by a twist curve using a quadratic and cubic non-residue v which becomes 1 when an exponentiation of this fs,Q(P) to the power of (qk−1)/r is performed.