We try to use a computer algebra system Mathematica as a test case generation system. In test case generation, we generally need to solve equations and inequalities. The main reason why we take Mathematica is because it has a built-in function to solve equations and inequalities. In this paper, we deal with both black-box testing and white-box testing. First, we show two black-box test case generation procedures described in Mathematica. The first one is based on equivalence partitioning. Mathematica explicitly shows a case that test cases do no exist. This is an advantage in using Mathematica. The second procedure is a modification of the first one adopting boundary value analysis. For implementation of boundary value analysis, we give a formalization for it. Next, we show a white-box test case generation procedure. For this purpose, we also give a model for source programs. It is like a control flow graph model. The proposed procedure analyzes a model description of a program.

We introduce an efficient interpolation attack which gives the tighter upper bound of the complexity and the number of pairs of plaintexts and ciphertexts required for the attack. In the previously known interpolation attack there is a problem in that the required complexity for the attack can be overestimated. We solve this problem by first, finding the actual number of coefficients in the polynomial used in the attack by using a computer algebra system, and second, by finding the polynomial with fewer coefficients by choosing the plaintexts. We apply this interpolation attack to the block cipher SNAKE and succeeded in attacking many ciphers in the SNAKE family. When we evaluate the resistance of a block cipher to interpolation attack, it is necessary to apply the interpolation attack described in this paper.