Quantum Computing and the Possible Effects on Modern Security Practices SE 4C03 Winter 2005 Kartik Sivaramakrishnan Researched by: Jeffery Lindner, 9904294 Due: April 04, 2005
Table of Contents Introduction... 1 The Age of Quantum Computing... 1 Impact on Modern Security... 2 Are we there yet?... 3 Conclusions... 3 References... 4
Introduction Security plays a massive role in today s computing world. With further dependence being placed on technology, one must always be knowledgeable of new issues and findings in order to always keep oneself protected. While today s methods for network security seem reliable and safe, there is a new technology that is promising to be a great threat to the way current computing is done, and the security repercussions surrounding it. This technology, and how it relates to the computing world, is commonly referred to as quantum computing. In the following report, the reader will be introduced to quantum computing and how it differs from classical logic. The security implications will then be explored in order to show exactly how quantum computing may be able to undermine modern security practices. Finally, the current state of quantum computing will be described, in order to assert how imminent this threat really is. The Age of Quantum Computing Quantum computing has been a topic of research amongst physicist since the 1970 s; ever since the limitations of classical computing were first explored.[1] Before an introduction to quantum computing is given, it is best to start with a background on classical computing and the physics behind what sparked quantum theory. The basic unit in classical computing is known as the bit. Bits can be in either of two values: 1, or 0, and represent the fundamental idea of state. Multiple bits form the basis for any modern computer, and subsequently, since bits can only hold one state at a time, computers are bound by this same limitation. Modern computers are built entirely upon this fundamental way of thinking; however some scientists have recently thought that other possibilities may exist. Moore s law states that data density has doubled roughly every year since the advent of integrated circuits. This trend is expected to continue, however researchers acknowledge that this law will eventually reach a physical limit in which components will eventually reach the size of atoms themselves.[2] At the atomic level, laws of classical physics break down, and quantum mechanics takes over. Scientists believed that inherent in this fact, may lie a different way of computing. This gave birth to the idea of quantum computing.[1] 1
Quantum computing abolishes the aspect that bits can only have two states, and this is the key element that makes quantum theory such a threat. Unlike classical computing, the fundamental unit of information in quantum theory is the qubit. A qubit has the potential of being quaternary, and greatly differs from the binary notional that has governed modern computing for decades.[1] Quantum theory makes use of the rule of superposition, in which a qubit can be 0, 1 or both. The details of this idea is outside the scope of this report, however this principal reveals that the number of stored values can greatly increase as the number of qubits increase. A computer using L qubits can store 2 L values at one time.[3] For example, a machine with 200 qubits, could potentially operate on not just one state during one clock tick, but rather 2 500 states! This is where the power of quantum computing lies: the ability for multiple state transitions during a cycle, which is commonly referred to as quantum parallelism.[1] Impact on Modern Security Now that quantum theory has been introduced, it is important to understand the repercussions this computing power may have on current security practices. RSA is one of the most secure and commonly known cryptographic algorithms. Founded in 1977, it still remains used today and is centered around the idea of public and private keys for authentication. Key generation is simple and is based on the multiplication of two, very large, prime numbers. To date, no one has been able to effectively decode the RSA algorithm.[4] What makes the RSA algorithm so secure is the fact that there is no efficient way to factor a large composite number into its two prime factors. Conventional computing is still slow in terms of factoring. Currently, the fastest way is through the use of a number field sieve in which a 512 RSA modulus was last factored in 8,400 million instructions per second (MIPS) years.[5] As factoring techniques become more efficient, users will be able to increase the size of the modulus to compensate. It is estimated that a modulus size of 2048 will be sufficient for permanent usage and security.[5] However, through the use of quantum computing, it is predicted that factoring of such large numbers can be done in polynomial time. Invented by Peter Shor, the first algorithm designed for quantum 2
computing (commonly called: Shor s algorithm) boasts an incredible power, and is theorized to be able to factor numbers in the magnitudes of 100 200 digits or greater in a matter of seconds![1] Should quantum computers become realizable, this would prevent RSA from being an option for cryptography and computer security. Are we there yet? Quantum computing still has a long way to go in terms of research and development. Phenomena such as decoherency still plagues physicists trying to develop quantum theory. Decoherency is where qubits decay and lose their state over time. This sort of behavior is unavoidable, and is one of the major problems in implementing quantum theory.[1] So far, scientists at the IBM-Almaden Research Center have been able to construct a 7-qubit quantum computer, and have successfully been able to factor the number 15 into its two factors: 3 and 5.[6] Obviously this type of calculation can be done by any normal conventional computer, however it does mark progress in the quantum field. It is undetermined as to when technology will advance to the point where quantum computers can be used to decipher some of the more complex security algorithms used today; however it is on the horizon. Conclusions As one can see, a great power lies in the practical implementation of quantum computing. As researchers move closer to developing stable quantum machines, current security procedures and algorithms must adapt. Quantum computing is on the forefront of technology, and rather than deal with the ramifications once implemented, forethought should be used to anticipate its impact. The nineteenth century was known as the machine age, the twentieth century will go down in history as the information age. I believe the twenty-first century will be the quantum age. [7] Paul Davies, leading researcher in quantum physics 3
References [1] J. West, The Quantum Computer (April 28, 2000), accessed on March 26 th, 2005: http://www.cs.caltech.edu/~westside/quantum-intro.html [2] Moore's Law (n.d.), accessed on March 26 th, 2005: http://www.webopedia.com/term/m/moores_law.html [3] A. Barenco, A Short Introduction to Quantum Computation (n. d.), accessed on March 26 th, 2005: http://www.qubit.org/library/intros/comp/comp.html [4] C. Kaufman, Network Security (2002) [5] E. Landquist, The Quadratic Sieve Factoring Algorithm (December 14, 2001), accessed on March, 27 th, 2005: http://www.math.uiuc.edu/~landquis/quadsieve.pdf [6] IBM's Test-Tube Quantum Computer Makes History (December 19 th, 2001), accessed on March, 24 th, 2005: http://domino.research.ibm.com/comm/pr.nsf/pages/news.20011219_qu antum.html?open&printable [7] W. Chen, Quantum Computing (n.d.), accessed on March, 22 nd, 2005: http://www.uhisrc.com/ftb/quantum/quantumcomputing.pdf 4