Annotation: Two new approaches to key pre-distribution based on an ideal additive homomorphic secret sharing scheme were proposed in [1]. However, it was not possible to prove their security against insider attacks in the general case. In this paper, a simple method for distributing shares based on Shamir’s secret sharing scheme corresponding to the first approach in [1] is proposed and analyzed. Namely, the following problem is solved: it is necessary to distribute 2n shares among n participants in such a way that each participant keeps two shares, and any pair of participants corresponds to a (3,4)-threshold scheme, where the common threshold can be arbitrary. Note that such a problem is solved for the first time in the theory of secret sharing. Unfortunately, the analysis showed 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 the key agreement protocol in the inside adversary model is obtained

Keywords: key pre-distribution, Shamir’s secret sharing scheme, key agreement protocol, adversary model, lightweight cryptography