Protocol Family for Optimal and Deterministic Symmetric Key Assignment

Secure pairwise communications for a group of N nodes can require a large number of keys, O(N ²) in the worst case. This work proposes a two-part algorithm for large-scale symmetric key pre-distribution: a key assignment algorithm deterministically assigning O(log₂ N) keys to each node, and a key discovery algorithm requiring O(log_q N) computations and inter-node messages to find the appropriate secure keys for a pair-wise communication. The lower bound of O(log N) complexity is achieved by novel applications of the Maximum-Distance Separable (MDS) codes. Compare to previous works, our scheme is deterministic, efficient, and has good security properties against collusion. Using (n,k)_q Reed-Solomon codes as the MDS codes, we show by analysis that (1) in all practical cases, the lower bound of c log₂ N keys per node can be reached within 2 levels of recursions with a multiplicative constant c less than 8; (2) channel resilience against r-collusion is roughly 1 -Rd ^min, with R = 1 (1 - 1/q)^2r and d _min = n - k + 1.