Factorization in Cybersecurity: a Dual Role of Defense and Vulnerability in the Age of Quantum Computing

One of the most critical components of modern cryptography and thus cybersecurity is the ability to factor large integers quickly and efficiently. RSA encryption, one of the most used types, is based largely on the assumption that factoring for large numbers is computationally infeasible for humans and computers alike. However, with quantum computers, people can use an algorithm like Shor’s algorithm to perform the same task exponentially faster than any normal device ever could. This investigation will go into the strength and vulnerability of RSA encryption using the power of factorization in an age of quantum computers.We start by looking at the foundations of both classical and quantum factoring with greater detail at number field sieve (NFS) and Shor’s. We examine the mathematical background of each topic and the associated algorithms. We conclude with theoretical analysis and experimental simulations that address the difficulty and implications of the above-mentioned algorithms in cryptography. The final thing that I will be discussing is where quantum computing is at present and how this could pose a threat to the current type of cryptographic systems, we use every day. I will be mentioning how we need post-quantum cryptography and how people are currently creating algorithms that are designed to be attack-resistant even to large-scale quantum computers. This investigation has shown the changing dynamics of cybersecurity in the quantum era and helps us understand the challenges and the need to innovate the current cryptographic systems

Quantum Cyber-Attack on Blockchain-based VANET

Blockchain-based Vehicular Ad-hoc Network (VANET) is widely considered as secure communication architecture for a connected transportation system. With the advent of quantum computing, there are concerns regarding the vulnerability of this architecture against cyber-attacks. In this study, a potential threat is investigated in a blockchain-based VANET, and a corresponding quantum cyber-attack is developed. Specifically, a quantum impersonation attack using Quantum-Shor algorithm is developed to break the Rivest-Shamir-Adleman (RSA) encrypted digital signatures of VANET and thus create a threat for the trust-based blockchain scheme of VANET. A blockchain-based VANET, vehicle-to-everything (V2X) communication, and vehicular mobility are simulated using OMNET++, the extended INET library, and vehicles-in-network simulation (VEINS) along with simulation of urban mobility (SUMO), respectively. A small key RSA based message encryption is implemented using IBM Qiskit, which is an open-source quantum software development kit. The findings reveal that the quantum cyber-attack, example, impersonation attack is able to successfully break the trust chain of a blockchain-based VANET. This highlights the need for a quantum secured blockchain.Comment: This paper consists of 10 pages with 7 figures. It has been submitted to IEEE Internet of Things Journa

A historical and practical survey of quantum computing using QISKit

Quantum Computing has been a part of computer science literature since the 1960s, but the call for quantum mechanical-based computation came when renowned theoretical physicist Richard Feynman said, “… nature isn\u27t classical, dammit, and if you want to make a simulation of nature, you\u27d better make it quantum mechanical, and by golly it\u27s a wonderful problem, because it doesn\u27t look so easy.” (Feynman, 486) His words inspired people to begin work on the project immediately. Although the best ideas have not yet been found, there is much active research and experimentation going on to learn how best to use these new quantum systems. The more computer scientists understand quantum computing, the better the algorithms become, although they have yet to create numerous future applications. How did quantum computing develop? A related question is, How do people use quantum computing in practical applications? Research suggests quantum computing developed in the early 1980s after the call came from Richard Feynman, and numerous researchers such as David Deutsch, Peter Shor, and Lov Grover outlined theoretical aspects of the field, defined fundamental algorithms, and predicted a quantum advantage providing exponential speedup over classical algorithms. This project provides historical context and pertinent background information. Computer scientists can use quantum computing for their own research and to extend the range of quantum computing itself. An experiment performed with the IBM resource known as QISKit shows how members of the public can perform their own practical applications of quantum computing, while also illustrating limitations that exist in the field of quantum computers

Quantum Multiplier Based on Exponent Adder

Quantum multiplication is a fundamental operation in quantum computing. Most existing quantum multipliers require $O(n)$ qubits to multiply two $n$-bit integer numbers, limiting their applicability to multiply large integer numbers using near-term quantum computers. In this paper, we propose the Quantum Multiplier Based on Exponent Adder (QMbead), a new approach that addresses this limitation by requiring just $\log_2(n)$ qubits to multiply two $n$-bit integer numbers. QMbead uses a so-called exponent encoding to represent two multiplicands as two superposition states, respectively, and then employs a quantum adder to obtain the sum of these two superposition states, and subsequently measures the outputs of the quantum adder to calculate the product of the multiplicands. This paper presents two types of quantum adders based on the quantum Fourier transform (QFT) for use in QMbead. The circuit depth of QMbead is determined by the chosen quantum adder, being $O(\log^2 n)$ when using the two QFT-based adders. If leveraging a logarithmic-depth quantum adder, the time complexity of QMbead is $O(n \log n)$, identical to that of the fastest classical multiplication algorithm, Harvey-Hoeven algorithm. Interestingly, QMbead maintains an advantage over the Harvey-Hoeven algorithm, given that the latter is only suitable for excessively large numbers, whereas QMbead is valid for both small and large numbers. The multiplicand can be either an integer or a decimal number. QMbead has been successfully implemented on quantum simulators to compute products with a bit length of up to 273 bits using only 17 qubits. This establishes QMbead as an efficient solution for multiplying large integer or decimal numbers with many bits.Comment: 12 pages, 7 figure

Quantum gates, sensors, and systems with trapped ions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 203-218).Quantum information science promises a host of new and useful applications in communication, simulation, and computational algorithms. Trapped atomic ions are one of the leading physical systems with potential to implement a large-scale quantum information system, but many challenges still remain. This thesis describes some experimental approaches to address several such challenges broadly organized under three themes: gates, sensors, and systems. Quantum logic gates are the fundamental building blocks for quantum algorithms. Although they have been demonstrated with trapped ions previously, scalability requires miniaturizing ion traps by using a surface-electrode geometry. Using a single ion in a surface-electrode trap, we perform a two-qubit entangling gate and fully characterize it via quantum process tomography, as an initial validation of surface-electrode ion traps for quantum information processing. Good logic gates are often good sensors for fast fluctuations and energy changes in their environment. Trapped ions are sensitive to fluctuating and static charges, leading to motional state decoherence (heating) and instabilities, problems exacerbated by the surface-electrode geometry. We investigate the material dependence of heating, specifically with aluminum and superconducting traps, to elucidate the physical origin of these fluctuating charges. Static charging is hypothesized to be caused by the trapping and cooling lasers due to the photoelectric effect. We perform systematic experiments with aluminum, gold, and copper traps with lasers at various wavelengths to validate this hypothesis. Realizing quantum processors at the system level requires models and tools for predicting system performance, demonstration of good classical and quantum control, and techniques for integrating different quantum systems. We develop a modeling system for trapped ion quantum computing experiments and simulate the effect of physical and technical noise sources on practical realizations of quantum algorithms in a trapped ion system. We experimentally demonstrate several such algorithms, including the quantum Fourier transform, order-finding, and Shor's algorithm on up to 5 ions. These experiments highlight several unique advantages of ion trap systems and help identify needs for further development. Finally, we explore the integration of ion traps with optical elements including mirrors and photon detectors as key elements in creating future hybrid quantum systems.by Shannon Xuanyue Wang.Ph.D

Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post‐Quantum Cryptography

In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future

Models of computation: A numeric analysis and performance evaluation

This research seeks to better understand what drives performance in computation. To develop this understanding the researcher investigates the literature on computational performance within the classical and quantum paradigm for both binary and multi-value logic. Based on the findings of the literature the researcher evaluates through an experiment of addition what drives performance and how performance can be improved. For the evaluation of this research, a realist research paradigm employs two research methods. The first is an automaton model of computation to model each of the computing paradigms and computational logic. The second is computational complexity theory for measuring the performance of addition. Through this evaluation the researcher seeks to gain a better understanding of what drives computational performance and how addition can be performed more efficiently. The results of the research lead the researcher to conclude that modernisation of machinery caused the birth start of automated computing and the binary number system in computers. As this research indicated that computation through increasing the radix can improve performance of computation for addition. Based on reported findings in the science of quantum mechanics research, it would be possible to implement a model of computation with increased radix. Through embracing state discrimination/ distinguishability this research calls to review the current quantum computing paradigm based on state duality

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma