Abstract-We consider a network where users can issue certificates that identify the public keys of other users in the network. The issued certificates in a network constitute a set of certificate chains between users. A user u can obtain the public key of another user v from a certificate chain from u to v in the network. For the certificate chain from u to v, u is called the source of the chain and v is called the destination of the chain. Certificates in each chain are dispersed between the source and destination of the chain such that the following condition holds. If any user u needs to securely send messages to any other user v in the network, then u can use the certificates stored in u and v to obtain the public key of v (then u can use the public key of v to set up a shared key with v to securely send messages to v). The cost of dispersing certificates in a set of chains among the source and destination users in a network is measured by the total number of certificates that need to be stored in all users. A dispersal of a set of certificate chains in a network is optimal if no other dispersal of the same chain set has a strictly lower cost. In this paper, we show that the problem of computing optimal dispersal of a given chain set is NP-complete. Thus, minimizing the total number of certificates stored in all users is NP-complete. We identify three special classes of chain sets that are of practical interests and devise three polynomial-time algorithms that compute optimal dispersals for each class. We also present two polynomial-time extensions of these algorithms for more general classes of chain sets.
Jung, Elmallah, and Gouda REF proves that computing a dispersal with minimal average number of certificates is in general NP-Complete, and presented three algorithms to compute optimal dispersal for classes of certificate graphs.
Optimal Dispersal of Certificate Chains
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
Computer Science Geography