Quantum Informational Divergence in Quantum Channel Security Analysis
László Gyöngyösi, Sándor Imre · International journal of network security · 2011
Abstract Computational Geometry is the art of designing efficientalgorithms for answering geometric questions. Computa-tional Geometry involves efficient and elegant solutionsfor difficult algorithmic problems and plays a central rolein many different areas of computer science. Quantumcloning-based attacks have deep relevance to quantumcryptography. In this paper we use the results of clas-sical Computational Geometry to analyze the security ofa quantum channel using current classical computer ar-chitectures. To analyze a quantum channel for a largenumber of input quantum states with classical computerarchitectures, very fast and effective algorithms are re-quired.Keywords: Quantum communication, quantum cryptogra-phy, quantum informational distance 1 Introduction In today’s communication networks, the widespread useof optical fiber and passive optical elements allows to usequantum cryptography in the current standard opticalnetwork infrastructure. In the past few years, quantumkey distribution schemes have attracted much study. Thesecurity of modern cryptographic methods, like asymmet-ric cryptography, relies heavily on the problem of factor-ing large integers [7]. In the future, if quantum computersbecome reality, any information exchange using currentclassical cryptographic schemes will be immediately inse-cure [11, 13]. Current classical cryptographic methods arenot able to guarantee long-term security. Other crypto-graphic methods, with absolute security must be appliedin the future. Cryptography based on the principles ofquantum theory is known as quantum cryptography. Us-ing current network technology, in order to spread quan-tum cryptography, interfaces must be implemented thatare able to manage together the quantum and classicalchannels [10].Many challenging hard algorithmic problems can bestudied with computational geometry and, at present,there exist many geometric algorithms that offer an effi-cient and well implementable solution for hard computa-tional problems. Computational Geometry was originallyfocused on the construction of efficient algorithms and itprovides a very valuable and efficient tool for computinghard tasks [8]. In many cases, the traditional linear pro-gramming methods are not very efficient. The computa-tion of the convex hull between quantum states cannot becomputed efficiently by linear programming, however themethods of computational geometry are better at solvingthese kinds of hard problems [18, 3, 8]. ComputationalGeometry uses the results of classical geometry and thepower of computing. In Figure 1, we illustrate the logicalstructure of the analysis and the cooperation of classi-cal and quantum systems. To this day, the most efficientclassical algorithms for this purpose are computationalgeometric methods. We use these classical computationalgeometrictoolsto analyzethe securityofa quantum chan-nel.