  This paper introduces a completely new approach to encryption based on group
theoretic quantum framework. Quantum cryptography has essentially focused only
on key distribution and proceeded with classical encryption algorithm with the
generated key. Here, we present a first step towards a quantum encryption
scheme based on the solution for the hidden subgroup problem. The shared secret
key K from QKD evolves as a generator for a subgroup H of a group G, in
combination of the plain text data modeled as group elements. The key K helps
in regeneration of the plain data on the receiver's side based on subgroup
reconstruction. This paper models all quantum computations using group
representations. A non-constructive proof is attempted towards the security of
the encryption scheme. We also address the issues involved in a such a venture
into the realms of Quantum data encryption.
