The Discrete Logarithm Problem is well-known among cryptographers, for its
computational hardness that grants security to some of the most commonly used
cryptosystems these days. Still, many of these are limited to a small number of
candidate algebraic structures which permit implementing the algorithms. In
order to extend the applicability of discrete-logarithm-based cryptosystems to
a much richer class of algebraic structures, we present a generalized form of
exponential function. Our extension relaxes some assumptions on the exponent,
which is no longer required to be an integer.