the present invention proposes a continuous multi - parameter version of diffie - hellman protocol based on matrices over topological monoids . in its turn , based on this continuous protocol , a method for public establishment and distribution of keys for encryption systems is implemented . an embodiment of the method , while providing a high security level , is several orders of magnitude faster than the existing key establishment systems . the present invention is a further development of the method of the geometric key establishment first proposed in u . s . patent application ser . no . 10 / 708 , 197 by a . berenstein and l . chernyak .