ElGamal encryption is one of the best known public key encryption methods in use. Usually the encryption is carried out in an associative algebraic structure, such as a group. However, the ElGamal method can be formulated also in a more general structure without the associativity property. In this paper we study the discrete logarithm problem, exponentiation and ElGamal encryption in a Paige loop. We discuss the selection of the subgroup for the discrete logarithm problem and it is shown that the exponentiation can be completely carried out in the corresponding finite field. We also discuss the benefits, drawbacks and feasibility of this method.

non-associative, cryptrography, discrete logarithm problem.