Noisy channels are a powerful resource for cryptography as they can be used
to obtain information-theoretically secure key agreement, commitment and
oblivious transfer protocols, among others. Oblivious transfer (OT) is a
fundamental primitive since it is complete for secure multi-party computation,
and the OT capacity characterizes how efficiently a channel can be used for
obtaining string oblivious transfer. Ahlswede and Csisz\'{a}r (\emph{ISIT'07})
presented upper and lower bounds on the OT capacity of generalized erasure
channels (GEC) against passive adversaries. In the case of GEC with erasure
probability at least 1/2, the upper and lower bounds match and therefore the OT
capacity was determined. It was later proved by Pinto et al. (\emph{IEEE Trans.
Inf. Theory 57(8)}) that in this case there is also a protocol against
malicious adversaries achieving the same lower bound, and hence the OT capacity
is identical for passive and malicious adversaries. In the case of GEC with
erasure probability smaller than 1/2, the known lower bound against passive
adversaries that was established by Ahlswede and Csisz\'{a}r does not match
their upper bound and it was unknown whether this OT rate could be achieved
against malicious adversaries as well. In this work we show that there is a
protocol against malicious adversaries achieving the same OT rate that was
obtained against passive adversaries.
In order to obtain our results we introduce a novel use of interactive
hashing that is suitable for dealing with the case of low erasure probability
(p∗<1/2)