Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol

Table 1

Some of the notations used in Chen et al.'s protocol.

Symbol	Definition
ID𝐴,ID𝐵	Identities of users 𝐴 and 𝐵, respectively
ID𝑆	Identity of the authentication server 𝑆
𝑝,𝑞,𝑔	The large primes 𝑝 and 𝑞, a generator 𝑔 of group 𝐺 with the order 𝑞
𝑥,𝑦	The long-term key of 𝑆, and 𝑦=𝑔^𝑥mod𝑝
𝛿𝐴,𝛿𝐵	Components of authentication information 𝑉𝐴 and 𝑉𝐵
𝑎,𝑏	Random number privately chosen by 𝐴 and 𝐵, respectively
𝑅𝐴,𝑅𝐵	Components of session key, where 𝑅𝐴=𝑔^𝑎mod𝑝 and 𝑅𝐵=𝑔^𝑏mod𝑝
ℎ(⋅)	Collision-free one-way hash function
𝐶𝑋𝑌	Evidence generated by user 𝑋 for user 𝑌