A New Class of Non-interactive ID-Based Key Sharing Schemes and Its Performances

Ryuichi SAKAI  Masao KASAHARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E78-A   No.1   pp.51-58
Publication Date: 1995/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
key sharing,  ID information,  common key,  cryptosystem,  information security,  

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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 the basis of a linear combination of the center secrets. We also discuss the security of the proposed schemes, and show that the proposed schemes prevent the conventional collusion attack, by adding another random integers unique to each user, on the secret vector that is assigned to the user. Furthermore, we present a new type of a statistical collusion attack which is more suitable for the proposed schemes. We also present the lower bound of the threshold of the statistical collusion attack on the proposed schemes. The proposed schemes can be easily implemented compared with other schemes as they require only computing of the inner product of two vectors over finite ring (including finite field) and an Euclidean quotient, for generating the common key. Our proposed schemes can be regarded as modified versions of the Blom's original scheme. However our proposed schemes are secure against our new type of the attack, as well as the collusion attack based on the solving of the linear equations, although Blom's scheme is insecure against both of these collusion attacks.