Patent ID: 7804962

Claim:
A method executed on a computer for designing a wireless sensor network topography comprising: assessing a degree of security of the wireless sensor network against a security threat to the wireless sensor network; and, estimating network design parameters for a design of the wireless sensor network topography as a function of the degree of security, wherein the design parameters comprise at least one of N and d, wherein N is a number of nodes, and wherein d is based on a reach of each node in the network, wherein the assessing of a degree of security further comprises assessing a tolerance to the security threat, wherein the tolerance is denoted as ∈, wherein the design parameters are arbitrated according to the following function: f ⁡ ( N , d , ɛ ) ⁢ = △ ⁢ p d 0 ( 1 - p d 0 ) ⁡ [ 1 2 ⁢ ( N - 1 ) ⁢ ( 1 - p d 0 ) ⁢ ( 1 - p ) ⁢ ( 1 + p d ⁡ ( 2 - p ) d ) ] κ - ɛ = 0 wherein κ is a polynomial in N, wherein M is a number of authentication tags used by the nodes during identity authentication, wherein p d 0 =1/M, wherein p is the probability that two of the nodes in the network do not share a common key and is given by the following equation: p = ⁢ ( s s ′ ) ( s s ′ ) × ( s - s ′ s ′ ) ( s s ′ ) = ( ( s - s ′ ) ! ) 2 ( s - 2 ⁢ s ′ ) ! ⁢ s ! = ⁢ ( 1 - s ′ s ) ⁢ ( 1 - s ′ s - 1 ) ⁢ ⁢ ⋯ ⁢ ⁢ ( 1 - s ′ s - s ′ + 1 ) wherein s is a number of keys in a pool from which keys to be assigned to each of the nodes are chosen, and wherein s′ is a number of keys assigned to each of the nodes.