Abstract: A data encryption method performed with ring arithmetic operations wherein a modulus C is be chosen of the form 2w?L, wherein C is a w-bit number and L is a low Hamming weight odd integer less than 2(w?1)/2. And in some of those embodiments, the residue mod C is calculated via several steps. P is split into 2 w-bit words H1 and L1. S1 is calculated as equal to L1+(H12x1)+(H12x2)+ . . . +(H12xk)+H1. S1 is split into two w-bit words H2 and L2. S2 is computed as being equal to L2+(H22x1)+(H22x2)+ . . . +(H22xk)+H2. S3 is computed as being equal to S2+(2x1+ . . . +2xk+1). And the residue is determined by comparing S3 to 2w. If S3<2w, then the residue equals S2. If S3?2w, then the residue equals S3?2w.

Abstract: A network system server that provides password composition checking for a plurality of clients is disclosed. The network system server includes a main data store, a security server, which is coupled to the main data store and the plurality of clients, a password synchronization server, which is coupled to the security server, a plurality of password strength servers, each of which is coupled to the password synchronization server, that provides password integrity among the plurality of clients so that each client maintains a password whose composition is consistent with the network server system. Each of the password strength servers is uniquely programmable with respect to performing password composition checking.