Table 2. Computational basics for parameters.

Primitives			Properties and Components
Dimension	:	N	Prime, $d\approx N/3$
Mod	:	$q_1,q_2$	Twin primes $q_1+2=q_2$
Polynomial coefficients	:	$d_f=d_g=d$	$q_1>40d-18$
Message security	:	ms $={\log }_2\sqrt{\frac{N!}{d{!}^2(N-2d)!}}$ bit
Key security	:	ks $={\log }_2\sqrt{\frac{N!}{d!(d-1)!(N-2d+1)!}}$ bit
Security parameter	:	$\kappa =\lfloor \mathrm{m}\mathrm{i}\mathrm{n}\{ms,ks\}\rfloor$
Public key size	:	pk = $\frac{N({\log }_2{q}_1+{\log }_2{q}_2)}{8}$ byte	$h_1\in R_{q_1}$ $h_2\in R_{q_2}$
Private key size	:	sk = $\frac{2N{\log }_{2}p+N{\log }_2{q}_1}{8}$ byte	$f\in R_p$ $f_p^{-1}\in R_p$ $G\in R_{q_1}$
Packaged key pair size	:	ct = $\frac{N({\log }_2{q}_1+{\log }_2{q}_2+{\log }_{2}2)}{8}$ byte	$c_1\in R_{q_1}$ $c_2\in R_{q_2}$ $K\in R_2$