An Authenticated Privacy-Preserving Mobile Matchmaking Protocol Based on Social Connections with Friendship Ownership

Table 1

Notations.

Notation	Meaning
pk𝐴	Public key of user 𝐴
𝑠𝑘𝐴	Private key of user 𝐴
id𝐴	Identity of user 𝐴
𝑠𝑛𝐴	A fixed sufficient long string chosen by user 𝐴
ℎ(⋅)	Cryptographic hash functions
sig𝑘(𝑚)	Signature of 𝑚 signed using private key 𝑘
ver𝑘(𝑚,𝑠)	True, if 𝑠 is a valid signature of message 𝑚 verified using public key 𝑘; else false
sig^𝐴𝐵	sig𝑠𝑘𝐵(ℎ(id𝐵)||pk𝐴)
𝑑𝑚(𝐴)	ℎ(id𝐴||𝑠𝑛𝐴)
𝑑𝑚(𝐴,𝑟)	ℎ(id𝐴||𝑠𝑛𝐴||𝑟)
𝐹(𝐴)	{𝑥|𝑥 is the friend of user 𝐴}
𝐹(𝐴∩𝐵)	𝐹(𝐴)∩𝐹(𝐵)={𝑥|𝑥∈𝐹(𝐴) and 𝑥∈𝐹(𝐵)}
𝐹(𝐴∪𝐵)	𝐹(𝐴)∪𝐹(𝐵)={𝑥|𝑥∈𝐹(𝐴) or 𝑥∈𝐹(𝐵)}
𝐹(𝐴−𝐵)	𝐹(𝐴)−𝐹(𝐵)={𝑥|𝑥∈𝐹(𝐴) and 𝑥∉𝐹(𝐵)}
𝐷𝑀(𝐴)	{𝑑𝑚(𝑥)|𝑥∈𝐹(𝐴)}
𝐷𝑀(𝐴,𝑟)	{𝑑𝑚(𝑥,𝑟)|𝑥∈𝐹(𝐴)}
𝐷𝑀(𝐴∩𝐵)	𝐷𝑀(𝐴)∩𝐷𝑀(𝐵)
𝐷𝑀(𝐴∩𝐵,𝑟)	𝐷𝑀(𝐴,𝑟)∩𝐷𝑀(𝐵,𝑟)
Enpk𝐴(𝑀)	Encrypt 𝑀 using public key pk𝐴
Desk𝐴(𝐶)	Decrypt 𝐶 using private key 𝑠𝑘𝐴
𝐸𝐾(𝑀)	Encrypt 𝑀 using symmetric key 𝐾
𝐷𝐾(𝐶)	Decrypt 𝐶 using symmetric key 𝐾
SIG^𝐴(𝐵)	{sig^𝐴𝑥|𝑥∈𝐹(𝐵)}
SIG^𝐴(𝐵∩𝐶)	{sig^𝐴𝑥|𝑥∈𝐹(𝐵) and 𝑥∈𝐹(𝐶)}
FCL𝐴	Friendship certificate list of user 𝐴
𝑀𝐻(𝑇,𝑃)	True, if ∀𝑇𝑖∈𝑇∃𝑝𝑗∈𝑃∋𝑝𝑗∈𝑇𝑖; false, else
	Where 𝑃= sets {𝑝𝑗},𝑇= sets {𝑇𝑖}.