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

TL;DR

This paper proposes a novel quantum encryption scheme leveraging group theory and the hidden subgroup problem, aiming to extend quantum cryptography beyond key distribution to direct data encryption.

Contribution

It introduces a new quantum encryption approach based on group theoretic principles and the hidden subgroup problem, with a model for quantum computations using group representations.

Findings

Initial model for quantum encryption using subgroup reconstruction

Non-constructive security proof outline

Discussion of challenges in quantum data encryption

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.