Random number space Z*N includes the following subgroups: quadratic residue group QRN and group ?1
. Elements included in quadratic residue group QRN are elements that are in random number space Z*N and raised to the power of 2, in other words, QRN={y2 mod N|y∈Z*N}, and a size of quadratic residue group QRN is (P?1)(Q?1)/4. Group 
?1
 is a second-order cyclic group generated by element (?1 mod N), group 
?1
 includes elements {?1 mod N, 1 mod N}, in other words, a size of group 
?1
 is 2.