According to one embodiment, in an inverse element arithmetic apparatus, a word unit processing unit, as approximate calculation loop for extended binary GCD process, iterates a first loop in a case where a value of |r−s| is a subtraction threshold or more, and is capable of iterating a second loop instead of the first loop in a case where the value of |r−s| is smaller than the subtraction threshold. In the first loop, values of r, s, a, b, m, and n is updated and an update matrix M is generated or updated. In the second loop, the values of m and n are updated without updating the values of r, s, a, b and the update matrix M. The control unit terminates the loop of the inverse element arithmetic process in a case where a loop number of times of the inverse element arithmetic process reaches a number-of-times threshold.