Murakami-Kasahara ID-based Key Sharing Scheme Revisited -- In Comparison With Maurer-Yacobi Scheme

In Sept. 1990, the present authors firstly discussed DLP over composite number and presented an ID-based Key Sharing Scheme referred to as MK1. In 1991, Maurer and Yacobi presented a scheme, referred to as MY, which is similar to our scheme, MK1. Unfortunately the schemes MK1 and MY are not secure. In Dec. 1990, the present authors presented a secure ID-based key sharing scheme referred to as MK2. With a rapid progress of computer power for the last 15 years, our proposed scheme would have more chance to be applied practically. Regrettably, it has not been widely known that (i) the schemes MY and MK1 are not secure, (ii) there exists a secure scheme, MK2. In this paper, we shall review MK2 and clarify the difference between MK2 and other schemes from the standpoint of security.