Patent ID: 8225095

Claim:
A method of communicating between at least a first network device and a separate, second network device residing on a communications network, the method comprising: encrypting on the first network device, using a first password-based key derived from a password, a first exchange key defined in accordance with a key-exchange algorithm to produce an encrypted first exchange key; transmitting, from the first network device to the second network device, a communication including at least the encrypted first exchange key; decrypting the encrypted first exchange key, on the second network device, using a second password-based key derived from the password and different than the first password-based key; computing on the first network device the first password-based key using a modulus, n, that is a product of three prime numbers; calculating the second password-based key by generating a hash value from the password using a hash function; calculating Euler's totient function, Φ(n), of the modulus n; and calculating the first password-based key as the inverse of the second password-based key modulo Φ(n).