In 1994 Boo Barkee and others have written a paper ``\emph{Why you
 cannot even hope to use Gr\"obner Bases in Public Key Cryptography: an
 open letter to a scientist who failed and a challenge to those who
 have not yet failed.}'' Since 1994, further attempts have been made,
 that gave rise to several cryptosystems now known as Polly Cracker
 systems. None of these proposals have been successful, and while
 Gr\"obner Bases are now an established tool for cryptoanalysis, the
 challenge of Boo Barkee still stands w.r.t. the design point of
 view. We outline a description on how all these attempts have failed.
 
 The analysis shows that the only possibility of a successful Polly
 Cracker can be one with binomial ideals, toric ideals in particular.
 But the correspondence of toric ideals with lattices brings the
 possibility of redefining some known lattice cryptosystems as Polly
 Cracker systems; whether this will result in breaking these
 cryptosystems, (those that still stand) or if the introduction of
 Gr\"obner basis methods will result in stronger lattice cryptosystems
 is too early to say. We will in particular discuss some experiences on
 the cooperation of Gr\"obner basis methods (Buchberger algorithm) and
 lattice methods (LLL algorithm) to solve toric ideals/lattices.