Notation	Definition
$I{D}_i$	Identification of $i$
$p{w}_i$	password of $i$
$sal{t}_i$	Salt value of $i$
$v_i$	Verification element of $i$
$S{K}_{ik}$	Session key of i and k
$h{k}_i$	Hash key of $i$
$h{p}_i$	Projection key of $i$
$h_i$	Hash function value of $i$
$h_i^{\prime }$	Projection function value of $i$
$p{k}_i$	Public key of $i$
$s{k}_i$	Private key of $i$
${\phi }_i$	Verifiable MAC value of $i$
${\chi }_{\beta }$	Discrete Gaussian distribution
$m_i$	The plaintext message sent by the communicating entity $i$
$C_i$	The ciphertext message sent by the communicating entity $i$
$ssi{d}_i$	Session id of $i$
$R_q$	Polynomial rings with integral coefficients modulo $q$
$i\left|\right|k$	$i$ and $k$ are connected bin series