Table 2: Some of the notations used in our paper.

Symbol Definition

Identities of users and , respectively
Identity of the authentication server
The large prime
The long-term key of , and
is the seed of the enhanced Chebyshev polynomial
Passwords of and , respectively
Random large integer number chosen by and , respectively
Components of session key, where and
Collision resistant secure one-way chaotic hash function
Evidence generated by user for user