Key Pre-Distribution Technique Using Shamir’s Secret Sharing Scheme

In [1], two new approaches to key pre-distribution based on an ideal additive homomorphic secret sharing scheme (SSS) are proposed. However, it has not been possible to prove their security against insider attacks in the general case. In this study, a simple method for distributing shares, corresponding to the first approach in [1], is proposed and analyzed using Shamir’s SSS. The problem considered is the distribution of 2n shares among n participants in such a way that each participant holds two shares, and every pair of participants corresponds to a (3,4)-threshold scheme, while the overall threshold can be arbitrary. It should be noted that this is the first time such a problem is solved in the theory of secret sharing. The analysis shows that the key agreement protocol based on the proposed technique of shares pre-distribution is not resistant to insider attacks. A general necessary condition for the security of a key agreement protocol in the internal adversary model is obtained.