Key-exchange protocol using a password-derived prime

A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for using a password-derived prime number to facilitate a secure key exchange between a client and a server across a network, the method comprising:

• receiving a password from a user at the client;
• using the password to determine a prime number P associated with the password;
• using the prime number P to determine a generator g associated with P;
• calculating X=gx mod P, wherein x is a random number generated by the client;
• sending X to the server;
• receiving Y=gy mod P from the server, wherein y is a random number generated by the server;
• and
• computing a secret key Ks=Yx mod p at the client, which the server can similarly obtain by computing Ks=Xy mod p, whereby the client and the server can both obtain the same secret key Ks through insecure communications over the network.

An apparatus that uses a password-derived prime number to facilitate a secure key exchange between a client and a server across a network, comprising:

• a receiving mechanism at the client configured to receive a password from a user;
• a prime number determination mechanism at the client configured to use the password to determine a prime number P associated with the password;
• a generator determination mechanism at the client configured to use the prime number P to determine a generator g associated with P;
• and
• a key generation mechanism at the client configured to,
• calculate X=gx mod P, wherein x is a random number generated by the client,
• send X to the server,
• receive Y=gy mod P from the server, wherein y is a random number generated by the server, and to
• compute a secret key Ks=Yx mod p at the client, which the server can similarly obtain by computing Ks=Xy mod p, whereby the client and the server can both obtain the same secret key Ks through insecure communications over the network.