A NEW CLASS OF NONINTERACTIVE ID-BASED KEY SHARING SCHEMES AND ITS PERFORMANCES

In this paper, we propose a new class of ID-based non-interactive key sharing scheme with a trusted center which generate a common key on th e basis of a linear combination of the center secrets. We also discuss the security of the proposed schemes, and show that the proposed sche mes prevent the conventional collusion attack, by adding another rando m integers unique to each user, on the secret vector that is assigned to the user. Furthermore, we present a new type of a statistical collu sion attack which is more suitable for the proposed schemes. We also p resent the lower bound of the threshold of the statistical collusion a ttack on the proposed schemes. The proposed schemes can be easily impl emented compared with other schemes as they require only computing of the inner product of two vectors over finite ring (including finite fi eld) and an Euclidean quotient, for generating the common key. Our pro posed schemes can be regarded as modified versions of the Blom's origi nal scheme. However our proposed schemes are secure against our new ty pe of the attack, as well as the collusion attack based on the solving of the linear equations, although Blom's scheme is insecure against b oth of these collusion attacks.