A fast encryption method particularly useful for long message lengths is provided. A message m is encrypted using a transmitter secret key z to form a quantity E. A transmitter processor prepares a quadruplet (a_new, b_new,s_new, E) where:

As in previous embodiments y=g^xmodulo p is the public key and x is the receiver secret key. The parameters g, x, and p according to methods known to a person skilled in the art and the parameter g is a generator of the group G_p. The parameter c is a random number. The transmitter processor sends the quadruplet (a_new, b_new,s_new, E) to a receiver processor. The receiver processor verifies the signature on s_new using methods known in the art. The receiver processor then decrypts a_new and b_new using the receiver secret key x to get the transmitter secret key z, i.e. in the following manner z=a_new/b_new^x. The receiver processor uses the transmitter secret key z to decrypt E to get the message M.