The map
modulo
is related to a variation of the ElGamal digital signature scheme in a similar way as
the discrete exponentiation map, but it has received much less study. We explore the
number of fixed points of this map by a statistical analysis of experimental data. In
particular, the number of fixed points can in many cases be modeled by
a binomial distribution. We discuss the many cases where this has been
successful, and also the cases where a good model may not yet have been
found.
Keywords
self-power map, exponential equation, ElGamal digital
signatures, fixed point, random map, number theory