System and method for generating a server-assisted strong password from a weak secret

A system comprising:

• a generating computer client and/or recovery computer client in operative communication with a user;
• where the user provides a password to the generating computer client and/or recovery computer client;
• and
• a computer server;
• where the computer server is in operative communication with the generating computer client and/or recovery computer client;
• and
• where the generating computer client and/or recovery computer client:
• generates a RSA-key pair (d, (N, e)), where d, N and e represent integers and where the relationship between d, N and e is given by equation (1):
• (d)e≡1 mod φ(N) (1),
• splits up the integer d into a plurality of key-shares;
• assigns a portion of each key-pair share di to the one or more computer servers as seen in the Equation (2);
• where n is an integer that represents a number of computer servers;
• (d1d2d3 . . . dn)e≡1 mod φ(N) (2),
• where di is a share of the ith computer server;
• where n is an integer that represents the number of computer servers;
• sends initial data that is derived from the low entropy password PW, the RSA-key pair, a salt k, and an optional “id” from the generating computer client and/or recovery computer client to the one or more computer servers;
• where initial data is represented by Equation (3)
• id,h1=H(k,PW,S1)d1,N (3), and
• computes a bit string (N, e, di, id) which provides the high entropy password;
• where the bit string is computed by the at least n computer servers, or a combination of the one or more of the at least n computer servers and the generating computer client.