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Workshop on Physics and Computation (PhysComp)

Cryptographic Primitives And Quantum Theory

Claude Crépeau

Published Aug 24, 2005• 5 citations
Publisher

Abstract

This paper summarizes the current knowledge in the field of two-party cryptographic protocols devised from quantum systems. We introduce the reader to the notion of cryptographic protocols and describe a number of simple building blocks to achieve them. We also give pointers for the reader who is interested to the quantum implementation of these building blocks. 1 Introduction Since the 1970's the science of secret writing, cryptography, has changed substantially due to the introduction of "public key cryptosystems" [26, 41]. The many properties of certain instances of these systems have open the door to several new applications (consult [42, 25, 29, 44, 34, 28, 7, 30, 36, 32, 11, 19, 33] for instance, to mention just a few). The initial goal of cryptography, to provide secure communications, has evolved into a variety of tasks involving secret data. The scenario in which such tasks take place involves two participants (say Alice and Bob) who wish to perform some computation involving ...

DOI
10.1109/phycmp.1992.615540

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This paper summarizes the current knowledge in the field of two-party cryptographic protocols devised from quantum systems. We introduce the reader to the notion of cryptographic protocols and describe a number of simple building blocks to achieve them. We also give pointers for the reader who is interested to the quantum implementation of these building blocks. 1 Introduction Since the 1970's the science of secret writing, cryptography, has changed substantially due to the introduction of "public key cryptosystems" [26, 41]. The many properties of certain instances of these systems have open the door to several new applications (consult [42, 25, 29, 44, 34, 28, 7, 30, 36, 32, 11, 19, 33] for instance, to mention just a few). The initial goal of cryptography, to provide secure communications, has evolved into a variety of tasks involving secret data. The scenario in which such tasks take place involves two participants (say Alice and Bob) who wish to perform some computation involving ...
Broadly speaking, cryptography is the problem of doing communication or computation involving two or more parties who may not trust one another. The best known cryptographic problem is the transmission of secret messages. Suppose wish to communicate in secret. For example, you may wish to give your credit card number to a merchant in exchange for goods, hopefully without any malevolent third party intercepting your credit card number. The way this is done is to use a cryptographic protocol. The most important distinction is between private key cryptosystems and public key cryptosystems.
Quantum cryptography lies at the intersection of information theory and quantum mechanics. Cryptosystems come in two major classes depending on whether the key is shared in public or in secret. Public key cryptosystems are special in that they allow two people, who have not yet met, to communicate securely by looking-up encryption methods in a public directory. In quantum cryptography, the sender and receiver have two types of communication channels: a classical public channel and a quantum channel. The best application of cryptography is to allow a secure communication. In the near future, quantum cryptography may be used in top-secret applications in the military, for example, as the basis of communication links. The first protocol for quantum cryptography was proposed in 1984 by C. H. Bennett and G. Brassard. Some of the basic quantum cryptographic systems are: four-states protocol, two-states protocol, 4+2 protocol and multi-photon and multi-stage protocol.
Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to communication. The cryptographic systems which perform these tasks are designed to keep the key secret while assuming that the algorithm used for encryption and decryption is public. Thus key exchange is a very sensitive issue. In modern cryptographic algorithms this security is based on the mathematical complexity of the algorithm. But quantum computation is expected to revolutionize computing paradigm in near future. This presents a challenge amongst the researchers to develop new cryptographic techniques that can survive th
This book offers an accessible and engaging introduction to quantum cryptography, assuming no prior knowledge in quantum computing. Essential background theory and mathematical techniques are introduced and applied in the analysis and design of quantum cryptographic protocols. The title explores several important applications such as quantum key distribution, quantum money, and delegated quantum computation, while also serving as a self-contained introduction to the field of quantum computing. With frequent illustrations and simple examples relevant to quantum cryptography, this title focuses on building intuition and challenges readers to understand the basis of cryptographic security. Frequent worked examples and mid-chapter exercises allow readers to extend their understanding, and in-text quizzes, end-of-chapter homework problems, and recommended further reading reinforce and broaden understanding. Online resources available to instructors include interactive computational problems in Julia, videos, lecture slides, and a fully worked solutions manual.
We call quantum security the area of IT security dealing with scenarios where one or more parties have access to quantum hardware. This encompasses both the fields of post-quantum cryptography (that is, traditional cryptography engineered to be resistant against quantum adversaries), and quantum cryptography (that is, security protocols designed to be natively run on a quantum infrastructure, such as quantum key distribution). Moreover, there exist also hybrid models, where traditional cryptographic schemes are somehow `mixed' with quantum operations in certain scenarios. Even if a fully-fledged, scalable quantum computer has yet to be built, recent results and the pace of research in its realization call for attention, lest we suddenly find ourselves one day with an obsolete security infrastructure. For this reason, in the last two decades research in quantum security has experienced an exponential growth in interest and investments. In this work, we propose the first systematic classification of quantum security scenarios, and for each of them we recall the main tools and results, as well as presenting new ones. We achieve this goal by identifying four distinct quantum security classes, or domains, each of them encompassing the security notions and constructions related to a particular scenario. We start with the class QS0, which is `classical cryptography' (meaning that no quantum scenario is considered), where we present some classical constructions and results as a preliminary step. Regarding post-quantum cryptography, we introduce the class QS1, where we discuss in detail the problems arising when designing a classical cryptographic object meant to be resistant against adversaries with local quantum computing power, and we provide a classification of the possible quantum security reductions in this scenario when considering provable security. Moreover, we present results about the quantum security and insecurity of the Fiat-Shamir transformation (a useful tool used to turn interactive identification schemes into digital signatures), and ORAMs (protocols used to outsource a database in a private way). In respect to hybrid classical-quantum models, in the security class QS2 we discuss in detail the possible scenarios where these scenarios arise, and what a correct formalization should be in terms of quantum oracle access. We also provide a novel framework for the quantum security (both in terms of indistinguishability and semantic security) of secret-key encryption schemes, and we give explicit secure constructions, as well as impossibility results. Finally, in the class QS3 we consider all those cryptographic constructions designed to run natively on quantum hardware. We give constructions for quantum encryption schemes (both in the secret- and public-key scenario), and we introduce transformations for obtaining such schemes by conceptually simpler schemes from the class QS2. Moreover, we introduce a quantum version of ORAM, called quantum ORAM (QORAM), aimed at outsourcing in a private way a database composed of quantum data. In proposing a suitable security model and an explicit construction for QORAMs, we also introduce a technique of independent interest which models a quantum adversary able to extract information from a quantum system without disturbing it `too much'. We believe that the framework we introduce in this work will be a valuable tool for the scientific community in addressing the challenges arising when formalizing sound constructions and notions of security in the quantum world.
Quantum computing and quantum cryptography are two areas of research that have the potential to transform modern computing and communication. Quantum computing promises to solve computational problems that are beyond the reach of classical computers, while quantum cryptography provides a way to secure communication channels that is immune to eavesdropping. Quantum cryptography is one of the emerging topics in the field of computer industry. This article focuses on quantum cryptography and how this technology makes a valuable contribution to an intensive defense strategy of completely secure key distribution. The scope of this article covers the weaknesses of modern digital cryptographic systems, the basic concepts of quantum cryptography, the practical implementations of this technology, and its limitations. , and finally the future direction that quantum cryptography is headed. We describe the result of an apparatus and protocol designed to perform quantum key distribution, whereby two users do not share any secret information (no private or public keys are known). previously known) initially exchanges a random quantum transmission consisting of veryweakly polarized light rays. In particular, readers can explore the following topics in depth: current cryptographic schemes (symmetric and asymmetric), the difference between quantum and classical computing, challenges of quantum computing, quantum algorithms (Shor and Grover), public key cryptographic schemes affected, symmetry affected schemes, impact on hash functions and post-quantum cryptography