Abstract. In this paper we give a function approximation formula using the Ganelius sampling points for analytic functions with end-point singularities. Then we show that it is more accurate than the SE-Sinc formula and that it is optimal.

Abstract. It is actively researched to exploit cryptosystems which prevent from attacks using quantum computer, where such cryptosystems are called post-quantum cryptosystems. Multivariate Public Key Cryptosystems are one candidate of the post-quantum cryptosystems. In this paper, I propose MPKCs using Multi-Layer Square+. Moreover, I analysis the security of Multi-Layer Square+ against some attacks and explain how to derive the recommended security parameters of MPKCs with layer structure.

Abstract. The exponential integrator is one of the powerful methods for solving systems of ordinary differential equations. In this method, the computation of certain matrix functions, usually called φ functions, is an important issue. For the efficient computations of these functions, the scaling and squaring technique based on rational approximations is used. There exist two rational approximation methods. For each of the two methods the computational cost is evaluated and compared. For the best method, a modified squaring technique is applied to reduce roundoff errors. Numerical experiments show that the modified technique improves the accuracy by about 2 decimal digits.