A Fast Implementation of Diffie-Hellman Type ID-NIKS

In 1990, Murakami and Kasahara proposed a Diffie-Hellman type ID-based non-interactive key sharing scheme, referred to as MK. The applying the scheme MK to a practical use was considered difficult due to the lack of a computer power at that time. However, MK would have more chance to be applied practically because of a rapid progress of computer power for the last 15 years. In this paper, we shall propose a new special composite number of particular form for the purpose of a practical realization of MK and show the proposed numbers sufficiently exist. Moreover, we show the computing time of the discrete logarithms over the proposed composite number