Privacy-preserving distributed clustering

EURASIP Journal on Information Security

Table 1 List of symbols

Symbol	Description
M	Number of groups created by the service provider
N _u	Total number of users in the social network
K	Number of clusters
P _i	Preference set of user i
${\tilde{P}}_{Σ_{(m, r)}}$	Packed sum of preferences of users in G_m
p _(i,r)	r th coordinate of P_i
c _(k,r)	r th coordinate of cluster k
${\tilde{P}}_{i}$	Packed preference of user i
${\tilde{C}}_{r}$	Packed centroid for dimension r
γ _(i,k)	Binary value for the k th cluster: 1 for the closest cluster,0 otherwise
${\tilde{Γ}}_{Σ_{m}}$	Packed total number of users in each cluster for G_m
w	Bit length of p_(i,r) and c_(j,r)
α,β,ϕ,ψ,ρ	Random values
[ [·] ]_H	Encryption of a plain text using the public key of H_m
${\tilde{S}}_{(i, r)}$	Packed partial input of user i for dimension r
N _g	Number of users in each group
R	Dimension of preferences
G _m	Group m
${\tilde{P}}_{i}$	Packed preferences of user i
${\tilde{P}}_{Σ_{r}}$	Packed sum of preferences of all users for dimension r
C _k	Cluster centroid k
D _(i,k)	Euclidean distance between P_i and C_k
${\tilde{D}}_{(i, k)}$	Packed Euclidean distance between P_i and C_j
Δ	Compartment size of ${\tilde{Γ}}_{i}$ in bits
${\tilde{Γ}}_{i}$	Packed vector of γ’s for user i
${\tilde{Γ}}_{Σ}$	Packed total number of users in each cluster
σ	Statistical security parameter
H _m	Helper user of group m
n	Paillier modulus
ℓ	Compartment size of $\tilde{C}$ in bits