  Aggregate signatures are used to create one short proof of authenticity and
integrity from a set of digital signatures. However, one invalid signature in
the set invalidates the entire aggregate, giving no information on which
signatures are valid. Hartung et al. (2016) propose a fault-tolerant aggregate
signature scheme based on combinatorial group testing. Given a bound $d$ on the
number of invalid signatures among $n$ signatures to be aggregated, this scheme
uses $d$-cover-free families to determine which signatures are invalid. These
combinatorial structures guarantee a moderate increase on the size of the
aggregate signature that can reach the best possible compression ratio of
$O(\frac{n}{\log n})$, for fixed $d$, coming from an information theoretical
bound. The case where the total number of signatures grows dynamically
(unbounded scheme) was not satisfactorily solved in their original paper, since
explicit constructions had constant compression ratios. In the present paper,
we propose efficient solutions for the unbounded scheme, relying on sequences
of $d$-cover-free families that we call {\em nested families}. Some of our
constructions yield high compression ratio close to \rmv{the information
theoretical bound}\todo{the best known upper bound}. We also propose the use of
$(d,\lambda)$-cover-free families to support the loss of up to $\lambda-1$
parts of the aggregate.
