Computations in science and engineering have been becoming tough. Such computations are often outsourced to subcontractors so that users could concentrate on their main tasks (making models, discussion and so on). However, they must reveal important data to subcontractors. As a result, the data might be leaked. In order to prevent this security threat, many researchers have studied secure computation. It enables users to outsource without revealing important data. Fully homomorphic encryption (FHE) is a key technology to realize secure computation. This paper proposes a new extension of the IH method in FHE. The IH method is a method which enables users to encrypt data which is used for computing polynomial expressions by using a special matrix. While the usefulness of the IH method, its application is limited to polynomial expression: the case that the target computation is given as a polynomial expression. Now, this paper first proposes its extension to the case of rational expression. We find a newly revised matrix to be used in decryption even if the computation includes the operation of division and apply it to overcome the problem.
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