  We develop a new algorithm to compute determinants of all possible Hankel
matrices made up from a given finite length sequence over a finite field. Our
algorithm fits within the dynamic programming paradigm by exploiting new
recursive relations on the determinants of Hankel matrices together with new
observations concerning the distribution of zero determinants among the
possible matrix sizes allowed by the length of the original sequence. The
algorithm can be used to isolate \emph{very} efficiently linear shift feedback
registers hidden in strings with random prefix and random postfix for instance
and, therefore, recovering the shortest generating vector. Our new mathematical
identities can be used also in any other situations involving determinants of
Hankel matrices. We also implement a parallel version of our algorithm. We
compare our results empirically with the trivial algorithm which consists of
computing determinants for each possible Hankel matrices made up from a given
finite length sequence. Our new accelerated approach on a single processor is
faster than the trivial algorithm on 160 processors for input sequences of
length 16384 for instance.
