Quantum entropy expansion using n-qubit permutation matrices in Galois field

TL;DR

This paper introduces a quantum-based method using n-qubit permutation matrices to increase the entropy of various data formats, enhancing security without enlarging data size.

Contribution

It presents a novel entropy expansion technique leveraging n-qubit permutation matrices in Galois fields for different data types.

Findings

Entropy of English text increased from 4-5 to over 7.9 bits per byte.

Effective entropy expansion observed in image and audio data.

Method works with n-qubits up to 15, demonstrating versatility.

Abstract

Random numbers are critical for any cryptographic application. However, the data that is flowing through the internet is not secure because of entropy deprived pseudo random number generators and unencrypted IoTs. In this work, we address the issue of lesser entropy of several data formats. Specifically, we use the large information space associated with the n-qubit permutation matrices to expand the entropy of any data without increasing the size of the data. We take English text with the entropy in the range 4 - 5 bits per byte. We manipulate the data using a set of n-qubit (n $\leq$ 10) permutation matrices and observe the expansion of the entropy in the manipulated data (to more than 7.9 bits per byte). We also observe similar behaviour with other data formats like image, audio etc. (n $\leq$ 15).