In [38, 39], each node among n nodes
stores a secret vector of length ?? + 1, where the secret vector is multiplied
to a publicly known (?? + 1) ?— n matrix to compute a symmetric key with
another node. Du et al. [18] adopt a similar method so that only O(??) keys
are needed per node. Note that the fully pairwise key scheme is a special case
of the ??-secure key scheme, where ?? = n. However, the number of keys saved
per node may be still large since ?? must increase with n, and if the number
415
of compromised nodes reach ??, the network is totally unsecured.
Xiaojiang Du and Yang Xiao
p-probabilistic Key Pre-distribution Scheme
Eschenauer and Gligor [11] present a p-probabilistic key pre-distribution
scheme in which m random keys out of a pool of total of M keys are stored in
a sensor node. All the sensor nodes choose keys from the same pool of the M
keys, and the pool of the M keys is designed in such a way that two random
subsets of size m in the pool at least have one key with probability p, which
should be chosen to be related to node density. Therefore, two sensor nodes
can share a common key to communicate with probability p after performing
a challenge-response key discovery.
The p-probabilistic key pre-distribution scheme is a trade-o?® scheme between
using a single key and using a large number of pairwise keys, i.e., a
tradeo?® of security and memory space. However, the p-probabilistic key predistribution
scheme may be di?±cult to provide guaranteed connectivity under
non-uniform/sparse deployment.
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