  How secure automatic speaker verification (ASV) technology is? More
concretely, given a specific target speaker, how likely is it to find another
person who gets falsely accepted as that target? This question may be addressed
empirically by studying naturally confusable pairs of speakers within a large
enough corpus. To this end, one might expect to find at least some speaker
pairs that are indistinguishable from each other in terms of ASV. To a certain
extent, such aim is mirrored in the standardized ASV evaluation benchmarks.
However, the number of speakers in such evaluation benchmarks represents only a
small fraction of all possible human voices, making it challenging to
extrapolate performance beyond a given corpus. Furthermore, the impostors used
in performance evaluation are usually selected randomly. A potentially more
meaningful definition of an impostor - at least in the context of
security-driven ASV applications - would be closest (most confusable) other
speaker to a given target.
  We put forward a novel performance assessment framework to address both the
inadequacy of the random-impostor evaluation model and the size limitation of
evaluation corpora by addressing ASV security against closest impostors on
arbitrarily large datasets. The framework allows one to make a prediction of
the safety of given ASV technology, in its current state, for arbitrarily large
speaker database size consisting of virtual (sampled) speakers. As a
proof-of-concept, we analyze the performance of two state-of-the-art ASV
systems, based on i-vector and x-vector speaker embeddings (as implemented in
the popular Kaldi toolkit), on the recent VoxCeleb 1 & 2 corpora. We found that
neither the i-vector or x-vector system is immune to increased false alarm rate
at increased impostor database size.
