Towards a Group Theoretic Quantum Encryption Scheme Based on Generalized Hidden Subgroup Problem

Abstract

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.

8 pages, work of undergraduate students

References in corpus (4)

• Quantum factoring, discrete logarithms and the hidden subgroup problem
• Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of non-abelian Groups
• The Hidden Subgroup Problem - Review and Open Problems
• A QKD Protocol Extendable to Support Entanglement and Reduce Unauthorized Information Gain by Randomizing the Bases Lists with Key Values and Invalidate Explicit Privacy Amplification