Efficient Quantum Algorithm for Post Quantum Cryptography

Summary

This protocol describes the implementation of a "Code based Cryptography" with an explicit quantum circuit for efficient quantum cryptography with a large asymmetric key by utilizing quantum arithmetic with quantum Fourier transformation.

Abstract

The realization of Quantum computers could significantly affect society and global security in many ways. A considerable amount of research has been on quantum cryptography - machines that exploit quantum computerized sensations to solve mathematical problems inaccessible to conventional computers. The flourishing 6th generation of 'Quantum computing' can break and threaten much of the current established protection and digital economy, but may provide cryptographic alternatives. Thus, we are able to optimize various processes more effectively, improving efficiency and enabling faster quantum mechanical simulations for better drug and material design, among other applications. This research focuses on implementing a post-quantum cryptographic algorithm by connecting large-number Quantum multiplication with a quantum random number generator (QRNG). A code-based cryptographic approach using a Quantum Fourier Transformation (QFT) is taken with a giant asymmetric key in an explicit quantum circuit to establish a secure quantum communication system. In this research work, a 'plain text' (classical data) has been encrypted with QRNG using a Quantum multiplier with the aid of quantum arithmetic. Consequently, the resultant quantum data with QRNG data will be transmitted to the receiver end through the quantum channel, where the quantum divider decrypts the same. Furthermore, each intended component's IBM Qiskit simulation results and comparative analysis with previous works and algorithms suggest more robustness and reliability of the proposed quantum proof algorithm when considering large qubit quantum devices. The work provides a valuable direction for further developments in this domain and paves the way for future applications of quantum computing in post-quantum cryptography.

Introduction

Quantum computation is based on quantum bits (qubits), which differ fundamentally from classical bits. While a classical bit can exist only in the state 0 or 1, a qubit can represent 0, 1, or any linear superposition of both states simultaneously. This property enables quantum systems to store and process a vast number of values in parallel rather than sequentially. Upon measurement, the qubit collapses to a definite state, providing the computational result. The inherent parallelism of quantum processing offers a significant speed-up, with estimates suggesting that quantum computers may outperform classical systems by several orders of magnitude. Such advancements po....

Protocol

This article employs the algorithm, utilizing quantum arithmetic and Quantum Fast Fourier Transformation¹³, to decrypt the message by dividing the ciphertext by the symmetric key. The primary objective of this study is to demonstrate the quantum implementation of symmetric key-based cryptography by generating a random key, employing a large multiplication algorithm, and performing a large number of divisions on the IBMQ Environment v1.7.4. Figure 1 depicts the end-to-end process for implementing symmetric key-based encryption. It is assumed that the symmetric key and ciphertext are transferred from the source devic....

Results

All the components of the above-mentioned circuit (Figure 1) have been implemented using Python code (Supplementary Files 1-3) with IBM Qiskit and executed on a Local and IBMQ simulator. However, they are not able to execute on quantum devices due to the lack of freely available qubits in existing quantum devices. The histogram output in the Local and IBMQ simulators for all the key components is depicted below.

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Discussion

The success of the proposed quantum cryptography protocol relies on three critical stages: Quantum Random Number Generation (QRNG), Quantum Arithmetic Operations using Quantum Fast Fourier Transformation (QFFT and QIFFT), and Quantum Key Shuffling and Reshuffling. The QRNG stage establishes the foundation of security by generating truly random symmetric keys³. The arithmetic operations, executed using controlled QFFT and inverse QFFT gates, ensure accurate encryption and decryption, while the shuf.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
GPU A100	NVIDIA		80G GPU
ibm_brisbane	IBM	https://quantum.ibm.com/	The superconducting quantum computer in the IBM Quantum Eagle family.
python3.10	Python Software Foundation	https://www.python.org/downloads/release/python-3100/
Qiskit	IBM	https://www.ibm.com/quantum/qiskit	An open-source SDK for working with quantum computers at the level of extended quantum circuits, operators, and primitives.