Quantum Computing and Encryption

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Since Charles Babbage attempted to invent an analytical engine in the1830s, there have been continuous developments in computer science.In the past 75 years, remarkable developments have been realized inform of “the first integrated circuit computer, the firstelectronic programmable computer, and the first microprocessor”(Anthony 1). Richard Feynman, a Nobel Laureate challenged scientiststo create a new breed of computers, which would be founded on quantumphysics, in 1981 during a physics conference. From then, scientistshave been working on the invention of a quantum computer. In thefollowing discussion, the research paper explain what quantumcomputing is, how it is coming along, the safety of encryption thatis linked to quantum computers and recommendations for betterencryption against quantum computing.

Quantum Computing

Quantum computing refers to the application of quantum physics, ormechanics to perform calculations in an approach that is completelydissimilar to traditional computation models (IBM QuantumComputing 1). Quantum mechanics ensures that the computing,communication and sensing applications are effective and accurate.Computing is the handling and storing of information. Communicationis related to the transmission of information. Sensing is associatedwith detecting signals. Hence, quantum computing pertains to theimprovement of these quantum mechanics laws to process information.

It is a technology that analyzes how effectively nature makes itpossible for people to compute. The common computation model is basedon classical mechanics, which is the Turing machine. However,scientists have realized that the model places avoidable restrictionson computation, resulting in the need for a better computationalmodel, which has in turn resulted in the development of quantumcomputing.

This type of computing is founded on logic, and is not restrictedonly to true-or-false, on-or-off settings. Similar to conventionalcomputers, quantum computing comprises of bits. The difference isthat in place of “ones and zeros, quantum computing has quantumbits or qubits, which can represent a one, a zero, or both at once, aphenomenon known as superposition” (IBM Quantum Computing 1).The superposition apparent in the quantum computer is exceptional tothat occurring in classical systems. This is because, it allows twoof the qubits to perform in manners that are not possible to explainthrough individual components, a process referred to as entanglement.

In conventional computing, 0s or 1s are used to represent numbers. Inaddition, calculations are performed depending on the instructions ofan algorithm. The instructions manipulate the 0s and 1s, in theprocess converting the input to an output. Contrary, “quantumcomputing relies on atomic-scale units or qubits that can besimultaneously 0 and 1. In this state, a single qubit can essentiallycarry out two separate streams of calculations in parallel” (Chu1). This makes computation using quantum computing more effective ascompared to the everyday computer.

The fundamental paradigm for quantum computing is the quantum circuitmodel that is made up of qubits, quantum gates and quantum circuits.The qubit “is the quantum analogue of the bit, the classicalfundamental unit of information” (Hagar and Cuffaro 1). It refersto a mathematical object comprising of particular properties, whichare realized physically via diverse ways as a precise physicalstructure. In the same way the conventional bit has a 0 or 1 statequbits as well have a state. However, contrary to the state apparentin the classical bit, 0 and 1 are only possible qubit states. Thismeans that any linear combination or superposition is as wellphysically probable (Hagar and Cuffaro 1).

Hence, “the physical state of a qubit is the superposition ∣ψ⟩= α∣0⟩ + β∣1⟩(where&nbspα&nbspand&nbspβ&nbsparecomplex numbers)” (Hagar and Cuffaro 1). The qubit’s state isdefined as a vector within a two-dimensional Hilbert space, or anintricate vector space. The states 0 and 1 are referred to as thecomputational basis state, which act as the foundation for the vectorspace. Theoretically, one qubit is capable of storing an incalculableamount of information. However, when measured, the results obtainedare the classical 0 or 1 with specific possibilities, defined by thequantum state. This means that the measurement alters the qubitstate. Important to note is that unless a measurement of the qubit isconducted, the hidden information stored is preserved as its dynamicevolution. As a result it becomes possible to control the informationthat is stored in unmeasured qubits using quantum gates, which is amajor advantage of quantum computing.

Quantum gates are responsible for manipulating the information keptin bits. The gates are represented through matrices in quantumcomputing (Hagar and Cuffaro 1). The representation implies thatquantum gates act as unitary operators, meaning that they are capableof preserving the norm of the quantum state. Similar to classicalcomputing that has a universal gate, in quantum computing it ispossible to compose a qubit logic gate from the quantum gate.Nevertheless, quantum gates are distinguished from classical gates bythe fact that they can be reversed. “The inverse of a unitarymatrix is also a unitary matrix”, and as a result a quantum gatecan be inverted using a different quantum gate (Hagar and Cuffaro 1).

Quantum circuits can be compared to conventional computer circuitsbased on the fact that they comprise of wires as well as logicalgates. The significance of the wires is that they convey information,whereas the gates are used for manipulating the information.Traditionally, the quantum circuit input is presumed to be incomputational state, the state that consists of all 0. The outputcircuit state is calculated using the computational basis.

There are three types of quantum computing. These are the universalquantum, analog quantum and quantum annealer. Universal quantumcomputing is highly effective, but the hardest to create. It isestimated that the computer might be made of more than 100,000physical qubits (IBM Quantum Computing 1). The analog quantumis developed to stimulate difficult quantum interactions, which haveproven to be difficult for current conventional machines, while thequantum annealer is easy to build, but its limitation is that it onlyperforms a single function of problems optimization (IBM QuantumComputing1).

Development of Quantum Computing

Scientists and physicians began to explore the concept of acomputational device founded on quantum mechanics as early as the1970s. In 1969, Steven Wiesner had earlier suggested quantumcomputing as an advanced method of completing cryptologic tasks.However, the well known contributions in quantum mechanics were madeby “Charles H. Bennett of the IBMThomas J. Watson Research Center, Paul A. Benioff of Argonne NationalLaboratory in Illinois, David Deutsch of the University of Oxford,and the late Richard P. Feynman of the California Institute ofTechnology” (Hagar and Cuffaro 1).The idea came up at a time when scientists were exploring the basicphysical restrictions of computation.

Feynman was among the firstscientists to create an abstract quantum computing model. Hedemonstrated how the quantum system could be employed in computation.In addition, the scientists explained that a quantum computer couldbe capable of acting as a simulator for quantum physics. Heconceptualized how speed could be improved using a quantum computer(Anthony 1). David Albert later demonstrated how a quantum mechanicalautomation acts remarkably different from the traditional automation.This idea was followed by David Deutsch’s proposal of the firstquantum Turing machine in 1985. His proposal paved way to theinvention of the quantum circuit model. Deutsch introduced the firstquantum algorithms, which was “later generalized to theDeutsch-Jozsa algorithm” (Rieffel 5). The algorithms were capableof solving problems effectively with assurance, something thatclassical methods are able to solve but with no assurance.

In 1990, Pitowsky Itamarquestioned how the superposition theory would make it possible forquantum computers to work out computational decision problems.However, the scientists noted that it was not possible to efficientlyretrieve information using quantum computing (Hagar andCuffaro 1). Further developments inquantum computing were evident in the 1990s. In specific was “PeterShor’s 1994 polynomial-time quantum algorithm for factoringintegers. This result provided a solution to a well-studied problemof practical interest” (Rieffel 5). Shor’s algorithm implies thatwhen a large quantum computer is created, “all standard public keyencryption algorithms will be completely insecure” (Rieffel 5). Hisdiscovery sparked more concentration in the field.

Later, Lov Grover came up with the“quantum search algorithm which yields a quadratic speed-upcompared to its classical counterpart” in 1996 (Hagar and Cuffaro1). This was followed by the initial NMR model of quantum computingproposal in 1997, founded on nuclear magnetic resonance methods. Themodel was later improved in 2000 by increasing the qubits scale. From2000’s quantum computing has grown tremendously. Advent paradigmshave been invented, like the “adiabatic algorithms,measurement-based algorithms, and topological quantum field theorybased algorithms, as well as new physical models for realizing alarge scale quantum computer with cold ion traps, quantum optics,condensed matter systems and solid state physics” (Hagar andCuffaro 1).

In 2001, Isaac Chuang, who is theprofessor of physics as well as computer science and electricalengineering at the “Massachusetts Institute of Technology”,invented a quantum computer using a single molecule, which would beheld in superposition. The computer could also be manipulated usingnuclear magnetic resonance (Chu 1). Chuang’s invention acted as thefirst experiment to make Shor’s algorithm a reality. However, thequantum computer system was not scalable, resulting in morecomplexity in regulating the system. The system was made up of moreatoms, and with many atoms it became impossible to regulate a singleatom from the next. Chuang explained that the intricacy in inventinga quantum computer derives from the inability to implement Shor’salgorithm in an adequately isolated system, to the extent that itremains mechanical for a period that makes it possible to calculatethe entire algorithm (Chu 1).

Chuang, together with fellowscientists, have invented another scalable quantum system, which isaimed at factoring numbers in a more effective way. Basically, 12qubits are required to factor number 15. However, the researchershave invented how to reduce the qubits to 5, each represented by oneatom. With the new quantum computer, it is possible for every atom to“be held in a superposition of two different energy statessimultaneously. The researchers use laser pulses to perform logicgates or components of Shor’s algorithm, on four of the five atoms”(Chu 1). The results obtained are recorded, sent, obtained andrecycled through the fifth atom. As a result, Shor’s algorithm isconducted in parallel since lesser qubits are needed. However,Anthony (1) notes that currently, quantum computing is largelytheoretical and a lot of developments still need to be done in thefield.

It is anticipated that quantumcomputing will bring about the breakthrough needed in ensuring that“machines think with the nuance and interpretative skill of humans”(Anthony 1). Particular areas will be transformed by quantumcomputing. They include cryptography, machine learning, medicine andmaterials, and searching big data (IBM Quantum Computing1). In cryptography, quantumcomputing is recognized for breaking codes. However, its actualpotential lies in ensuring that cloud computing becomes more secure.Founded on the laws of physics, the computers are able to ensure thatpersonal data is not accessed by hackers regardless of its locationin the computer (IBM Quantum Computing 1).

Machine learning is an advent areaof study that is possible through quantum computing.

Using quantum computers, it willbecome possible to improve machine learning as well as dataevaluation tasks (IBM Quantum Computing 1).In medicine and materials, the quantum computer emulates nature’scomputing method, making it possible to copy, comprehend as well asenhance natural things, such as molecules, in more advanced ways ascompared to an everyday computer. This could result in advent medicaldevelopments as well as discovery of new medical materials. Quantumcomputing is anticipated to facilitate the search for big data. Datacontinues to grow on a daily basis. This means that people will needcomputers that can search for data from numerous sources and locateimportant connections at a fast rate, something that is not possiblewhen using conventional computers (IBM Quantum Computing1).

Quantum computers are made of newproperties, which researchers not can be improved to ensure that thecomputers are able to work more effectively than traditionalcomputers, currently in use. The use of the new quantum properties,implies that the quantum computer is capable of solving specificissues such as factoring at a greater speed than an everyday computerwould. The quantum computers employ the best algorithms is solvingproblems.

Safety of Encryption with QuantumComputing

Despite the advantages associatedwith quantum computing, its safety issues cannot be disregarded. Thistype of computing has a negative impact on cryptography, which inturn negatively influences the level of security. Cryptography isvery significant when using computers, in specific, when exchanginginformation electronically to different people. It guarantees thatjust the intended message recipients are able to receive exchangedmessages. Quantum computing poses a threat to the role of ensuringthat electronic communication is secure and accurate. This is becausethe technology has the capability to complete specific types ofcomputations, which cannot be completed when using conventionalcomputers.

Quantum computing results in thebreaking of cryptographic keys at a fast rate. As a result, otherpeople are able to listen to communications not intended for them. Italso creates the possibility that an individual could pretend to besomebody they are not, and as a result receive personal informationnot intended for them. With quantum computing, computers guessprivate cryptographic keys or make quick reverses to calculation, atask that is impossible when using traditional computers.

The social, political as well aseconomic development of people and nations relies on theconfidentiality, accuracy and integrity of private information thatis sent using computers. Organizations and governments are taskedwith the duty of ensuring that they preserve the privacy of sensitiveinformation that both parties exchange. For instance, informationsuch as military communications, confidential governmentpublications, medical reports and financial records, should beprivate. However, when using quantum computers, it is highly likelythat the information could be leaked out to unintended parties.

In the past, information wasregarded a secure provided it was encrypted via the use of anunbroken cryptosystem. Such a system was part of a significantsecurity framework for all information that would be exchangedonline. Quantum computing challenges the presumption that providedthe system is unbroken, information is secure. The new computingtechnology provides an advent as well as dominant group of tools,which enhances the possibility that the cryptosystems may collapse.This has been proven practically, because most ciphersuites havedepicted a level of insecurity when exposed to quantum computing.

Any information, which isencrypted through the use of many cryptosystems, and whose securitywas founded “on the computational intractability of the so-calledhard problems of discrete log and integer factorization in underthreat of both eavesdropping and attack by future adversaries inpossession of quantum computers” (Campagna et al. 12). This impliesthat in the absence of “quantum-safe encryption” all theinformation that is exchanged via an observable network issusceptible to being received by unintended recipients, or can easilybe accessed by hackers. The safety issue does not merely refer toinformation stored, but also information that could be encrypted inthe similar manner in prospect.

It is important that forindividuals to ensure their data is secure from unintended parties,to consider comprehending the use of quantum computers. Theindividuals ought to think about how long they intend to ensure thattheir information remains secure, or how to ensure that they arequantum-safe. Considering that many people are not technologicallysavvy, it can only mean that with quantum computing more people areexposed to the risk of exchanging unsecure informationelectronically. For instance, assuming that the personal informationof individuals becomes public, they are exposed to issues such asidentity theft.

Nevertheless, research indicatesthat “not all security protocols and cryptographic algorithms arevulnerable to quantum attacks some are believed to be safe fromquantum attacks, while some are known to be vulnerable” (Campagnaet al. 13). In addition, security controls that could be currentlyeffective in ensuring data safety may eventually be proven to beineffective in ensuring quantum safety. When there is no evidence“that an algorithm is vulnerable to a quantum attack, acryptographic primitive and the protocols that use it are presumed tobe quantum-safe if they are well studied and resists attacks usingall known quantum algorithms” (Campagna et al. 13).

The security controls, which arehighly susceptible to being broken down by quantum computing include,all cryptosystems that are created based on the “mathematicalcomplexities of Integer Factoring and Discrete Logarithms”. Theseare “RSA, DSA, DH, ECDH, and ECDSA” as well as different types ofthe similar cipher (Campagna et al. 13). Other vulnerable controlsare security protocols, whose security originates from the identifiedciphers and security structures, whose security emanates fromcryptography security protocols.

There are some controls susceptibleto quantum attack, yet are possible to repair such as the AES. Theyare regarded as quantum safe since their ciphers are capable ofadapting to any attack. This is achieved by enhancing their size tocorrect a threat emerging from quantum computing. However, ciphersthat are incapable of altering their sizes are unsafe. In addition,any protocol that depends solely on ciphers cannot be protected fromquantum attack. On the other hand, a protocol, which does not solelydepend on ciphers, can adjust to become quantum safe.

While it is important that we shiftfrom the use of conventional computers to using quantum computers,the safety issue cannot be disregarded. The quantum computers willprovide the speed of computing needed in computations. At the sametime, they expose computer users to the risk of having theirinformation leaked out to other parties. The new technology must beapproached with caution, to ensure that all security measures are putinto consideration prior to shifting from conventional to quantumcomputers.

Recommendations

Quantum computers have for a longperiod been regarded as a theoretical possibility. However, it is nowanticipated that in the next 5 to 30 years, people, organizations andinstitutions could be using the computers. But bearing in mind thehigh possibility that the systems could decrypt majority of theglobe’s secure information, recommendations are required on thepossibility of having a better encryption against quantum computing.

One such recommendation is todesign schemes that are quantum resistant. The schemes should bedifferent to those used in conventional computers. In addition, theyshould be founded “on the mathematics of lattices –multidimensional, repeating grids of points” (Wolchover 1). Theschemes are reliant on the intricacy associated with findinginformation, which is concealed in a network that is made up of manyspatial dimensions. The only way individuals can exchange informationusing such a scheme is when an individual is aware of the secretroute.

Another recommendation is to stopdepending on factoring large figures. Instead, a cryptosystem thathides information through wrapping it via the use of error-correctingcode (ECC) should be devised. In addition, noise should be added tothe code. The rationale is that quantum computing is not applicablewhen computing some kinds of ECCs. The ECC should be created using acode that is easily reversible, converted to one that is difficult tosolve and the matrices multiplied. The matrices that make the changesfrom a challenging problem to one that is easy and vice versa, shouldact as the secret key. Hence, error correction and noise are added todata, but eliminating the noise is make complex, which acts as thepassword.

Works Cited

Anthony, Andrew. Has the Age ofQuantum Computing Arrived? TheGuardian 22 May. 2016.Web. 25 Jul. 2016.https://www.theguardian.com/technology/2016/may/22/age-of-quantum-computing-d-wave

Campagna, Matthew et al. QuantumSafe Cryptography and Security: An Introduction, Benefits, Enablersand Challenges. EuropeanTelecommunications Standards Institute(2015): 1-62.

Chu, Jennifer. The Beginning of theEnd for Encryption Schemes? MassachusettsInstitute of Technology News3 Mar. 2016. Web. 25 Jul. 2016.http://news.mit.edu/2016/quantum-computer-end-encryption-schemes-0303

Hagar, Amit and Cuffaro, Michael.Quantum Computing. StanfordEncyclopedia of Philosophy,2015. Web. 25 Jul. 2016.http://plato.stanford.edu/entries/qt-quantcomp/#Qub

IBM Quantum Computing.A Primer on Quantum Computing 2016. Web. 25 Jul. 2016.https://www.research.ibm.com/quantum/expertise.html

Rieffel, Eleanor. QuantumComputing. FX Palo AltoLaboratoty (n.d): 3-30.

Wolchover, Natalie. The TrickyEncryption that Could Stump Quantum Computers. Science 19 Sept. 2015.Web. 25 Jul. 2016.http://www.wired.com/2015/09/tricky-encryption-stump-quantum-computers/