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Table 1 Table of notations

From: Location-sharing protocol for privacy protection in mobile online social networks

Notation Description
\(ID_i\) User i’s social network identifier
\(FID_i\leftarrow _R\{0,1\}^{k}\) A random bit-string \(FID_i\) selected from a set of k bit-string
\(S_{LS}\) Location server
\(S_{OSN}\) Social network server
(\(x_i\),\(y_i\)) User \(ID_i\)’s real location
\(df_{ID_i}\) User \(ID_i\)’s friend-case threshold distance
\(ds_{ID_i}\) User \(ID_i\)’s stranger-case threshold distance
G A social network graph stored in \(S_{OSN}\)
\((pk_{ID_i},sk_{ID_i})\) User \(ID_i\)’s public key and secret key pair
\((pk_{osn},sk_{osn})\) The public key and secret key pair of \(S_{OSN}\)
\((pk_{LS},sk_{LS})\) Location server’s public key and secret key pair
dist((\(x_1,y_1\)),(\(x_2,y_2\))) The function calculates the distance between \((x_1,y_1)\) and \((x_2,y_2)\)
min(x,y) The function that computes the minimum of x and y
\(s_{OSN}=Sig_{sk_{osn}}(FID_i,ts)\) A signature \(s_{OSN}\) generated with the user’s secret key \(sk_{osn}\) over (\(FID_i\),ts)
\(Ver_{pk_{osn}}(s_{OSN})\) Verify the correctness of the signature \(s_{OSN}\) with the user’s public key \(pk_{osn}\)