Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol

Table 2

Some of the notations used in our paper.

Symbol	Definition
ID𝐴,ID𝐵	Identities of users 𝐴 and 𝐵, respectively
ID𝑆	Identity of the authentication server 𝑆
𝑁	The large prime 𝑁
𝑥1,𝑦,𝑛	The long-term key of 𝑆, and 𝑦=𝑇𝑥1(𝑥)
𝑥	𝑥 is the seed of the enhanced Chebyshev polynomial
𝑃𝐴,𝑃𝐵	Passwords of 𝐴 and 𝐵, respectively
𝑎,𝑏	Random large integer number chosen by 𝐴 and 𝐵, respectively
𝑅𝐴,𝑅𝐵	Components of session key, where 𝑅𝐴=𝑇𝑎(𝑥) and 𝑅𝐵=𝑇𝑏(𝑥)
𝐻(⋅)	Collision resistant secure one-way chaotic hash function
𝐶𝑋𝑌	Evidence generated by user 𝑋 for user 𝑌