Each of many sensor nodes are to be scattered throughout a region. The nodes are to communicate securely. Explain the problem of key distribution and outline a probabilistic strategy for distributing keys.

What will be an ideal response?

The nodes may have sufficient computational power to perform only secret-key encryption. If the nodes all share the same key then an attacker could compromise the whole collection by tampering with one node. If the number of nodes is large, there may be insufficient memory to store a pairwise key for each other node. A
compromise position is for nodes to share keys only with their nearest neighbours, and to rely on chains of mutually trusting nodes that encrypt messages hop-by-hop, rather than using end-to-end encryption.
But which keys should each node possess, if it is not known in advance which will be the node’s neighbours? One approach is to distribute keys probabilistically. Each node gets a random set of keys drawn from a distribution which makes the probability of it sharing a key withsufficiently many neighbours high enough so that a fully connected, secure netwrok can probably be constructed. Nodes can test for keys in common by exchanging messages with encrypted intelligible text as a challenge.