There is provided a computer-readable recording medium recording a program for encryption/decryption, an apparatus for encryption/decryption, an apparatus for multiplication in an extension field, that enable to perform high speed multiplication processing, while allowing the selection of arbitrary key lengths. In multiplying two elements A={a0, a1, a2, . . . , am−1} and B={b0, b1, b2, . . . , bm−1} in an extension field Fpm of extension degree m with a prime number p as characteristic, firstly, a positive integer k is determined such that km+1 is a prime number and p is a primitive element in Fkm+1. Next, two elements A and B are multiplied as two elements in extension field Fpkm of extension degree km with a prime number p as characteristic using the positive integer k. Lastly, using the result of such multiplication, a result of multiplication in an element in the extension field Fpm of extension degree m which is a subfield of Fpkm is obtained.