Applying LU Decomposition of Matrices to Design Anonymity Bilateral Remote User Authentication Scheme

Table 1

Notations used in this paper.

𝑆	The server
𝑈𝑖	User 𝑖
ID𝑖	The identity of user 𝑈𝑖
PW𝑖	The password of user 𝑈𝑖
𝐾𝑆	The server's secret key
AK𝑖	The authenticated session key shared between the server and 𝑈𝑖
𝑛	The number of users that could be supported by the system
𝐴	A secret 𝑛×𝑛 symmetric matrix with LU decomposition generated by the server
𝐿,𝑈	Matrix 𝐴's LU decomposition such that 𝐴=𝐿𝑈
𝑇	The timestamp
Δ𝑇	The expected time interval for transmission delay
ℎ(⋅)	One-way hash function
𝑝,𝑞	Two big prime numbers generated according to the requirement as in Section 2.2
𝑔	A generator of order 𝑞