A exponentiation calculation apparatus includes a dividing unit which divides an input value as an element of a torus T2(Fq^r) (r is an odd prime, q is a power of a prime) into first and second elements (of Fq^r), a first calculating unit which calculates some multiplications on a base field based on the first and second elements, a second calculating unit which calculates, when the (q+1)th power of the input value as an element of Fq^2r is divided into third and fourth elements (of Fq^r), the third element based on a result of the multiplications, a third calculating unit which calculates the fourth element by Fq^r multiplication based on the first and second elements, and a coupling unit which couples the third element with the fourth element to obtain the (q+1)th power of the input value.