Construction of strongly aperiodic logarithmic signatures

The aim of the paper is to present a general construction of strongly aperiodic logarithmic signatures (SALS) for elementary abelian p-groups. Their existence significantly extends the classes of tame logarithmic signatures which are used for the cryptosystem MST3{\mathrm{MST}_{3}}. They have particular characteristics that do not share with the well-known classes of transversal or fused transversal logarithmic signatures, and therefore they will play a vital role for logarithmic signature based cryptosystems in practice. In theory, the construction of SALS is interesting in its own right as well.