... In 2001, Li et al., [13] first proposed remote user authentication scheme for multi-server environment. Later many authentication protocols have been extensively proposed for multi-server architecture [13][14][15][16][17][18][19][20][21] with different security goals and properties based on dynamic identity, [19,20,21,25,27,34], password [12,13,[19][20][21][24][25][26][27][28][29][30][31][32], smart card [9][10][11][12][13][14][15][16][17][18][19][20][21][24][25][26][27][28][29][30][31][32], elliptic curve [26,31,32], biometric [29], and neural network [13,30]. However, most of these schemes have cryptanalyzed subsequently [8,11,12,20,23,27,33] In 2008, Lee et al., [14] proposed a password-based multi-server authentication scheme without using a smartcard based on the discrete logarithm problem (DLP), a symmetric cryptosystem, and a one-way hash function. ...