In this paper, the authors describe and compares a variety of algorithms for secure transmission of information via open communication channels based on the discrete logarithm problem that do not require search for a generator (primitive element). Modifications that simplify the cryptosystem are proposed, and, as a result, accelerate its performance. It is shown that hiding information via exponentiation is more efficient than other seemingly simpler protocols. Some of these protocols also provide digital signature/sender identification. Numeric illustrations are provided.