  Recent years have seen growing efforts to develop spoofing countermeasures
(CMs) to protect automatic speaker verification (ASV) systems from being
deceived by manipulated or artificial inputs. The reliability of spoofing CMs
is typically gauged using the equal error rate (EER) metric. The primitive EER
fails to reflect application requirements and the impact of spoofing and CMs
upon ASV and its use as a primary metric in traditional ASV research has long
been abandoned in favour of risk-based approaches to assessment. This paper
presents several new extensions to the tandem detection cost function (t-DCF),
a recent risk-based approach to assess the reliability of spoofing CMs deployed
in tandem with an ASV system. Extensions include a simplified version of the
t-DCF with fewer parameters, an analysis of a special case for a fixed ASV
system, simulations which give original insights into its interpretation and
new analyses using the ASVspoof 2019 database. It is hoped that adoption of the
t-DCF for the CM assessment will help to foster closer collaboration between
the anti-spoofing and ASV research communities.
