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Alternative Approaches - Quantum Cryptography and Bounded Storage Model

Andreas Würfl

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Several encryption algorithms have been discussed in the course of this seminar. This paper will introduce two alternative approaches. A change in the concept of provable security leads to a cipher which is shown to be ”perfect with high probability”. Assuming that the memory capabilities of a potential adversary are limited a strongly-randomized cipher is devised which uses a publicly-accessible string of random bits. In this cipher the secret key is short but the plaintext can be very long. The second approach is based on quantum physics. Heisenberg’s uncertainty principle guarantees the security of quantum cryptography. The first experiment which demonstrated the practicability of the only known encryption unbreakable by law of nature was conducted in 1989. The physical and technical fundamentals are introduced as well as the Quantum Key Exchange (QKE) protocol. We will demonstrate the eects of attempted eavesdropping and its detection. Finally the rapid development of the last 15 years and the currently available implementations will be presented.

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Several encryption algorithms have been discussed in the course of this seminar. This paper will introduce two alternative approaches. A change in the concept of provable security leads to a cipher which is shown to be ”perfect with high probability”. Assuming that the memory capabilities of a potential adversary are limited a strongly-randomized cipher is devised which uses a publicly-accessible string of random bits. In this cipher the secret key is short but the plaintext can be very long. The second approach is based on quantum physics. Heisenberg’s uncertainty principle guarantees the security of quantum cryptography. The first experiment which demonstrated the practicability of the only known encryption unbreakable by law of nature was conducted in 1989. The physical and technical fundamentals are introduced as well as the Quantum Key Exchange (QKE) protocol. We will demonstrate the eects of attempted eavesdropping and its detection. Finally the rapid development of the last 15 years and the currently available implementations will be presented.
The peculiar properties of quantum mechanics enable possibilities not allowed by classical physics. In particular, two parties can generate a random, secret key at a distance, even though an eavesdropper can do anything permitted by the laws of physics. Measuring the quantum properties of the signals generating the key, would ultimately change them, and thus reveal the eavesdropper’s presence. This exchange of a random, secret key is known as quantum cryptography.\n\nQuantum cryptography can be, and has been proven unconditionally secure using perfect devices. However, when quantum cryptography is implemented, one must use components available with current technology. These are usually imperfect. Although the security of quantum cryptography has been proven for components with certain imperfections, the question remains: can quantum cryptography be implemented in a provable, unconditionally secure way, using components available with current technology? This thesis contains both a theoretical, and an experimental contribution to the answer of this question. On the experimental side, components used in, and complete quantum cryptography systems have been carefully examined for security loopholes. In particular, it turned out that two commercial quantum cryptography systems contained loopholes, which would allow an eavesdropper to capture the full secret key, without exposing her presence. Furthermore, this detector control attack could be implemented with current technology. The attack is applicable against a variety of quantum cryptography implementations and protocols.\n\nThe theoretical contribution consists of security proofs for quantum cryptography in a very general setting. Precisely, the security is proven with arbitrary individual imperfections in the source and detectors. These proofs should make it possible to use a wide array of imperfect devices in implementations of quantum cryptography.\n\nFinally, a secure detection scheme is proposed, immune to the detector control attack and compatible with those security proofs. Therefore, if this scheme is implemented correctly, it offers provable security.
The practical implementation of quantum information technologies requires, for the most part, highly advanced and currently experimental procedures. One exception is quantum cryptography, or quantum key distribution, which has been successfully demonstrated in many laboratories and has reached an advanced level of development. It will probably become the first commercial application of quantum information. In quantum key distribution, Alice and Bob exploit a quantum channel to create a secret shared key comprising a random string of binary digits. This key can then be used to protect a subsequent communication between them. The principal idea is that the secrecy of the key distribution is ensured by the laws of quantum physics. Proving security for practical communication systems is a challenging problem and requires techniques that are beyond the scope of this book. At a fundamental level, however, the ideas are simple and may readily be understood with the knowledge we have already acquired. Quantum cryptography is the latest idea in the long history of secure (and not so secure) communications and, if it is to develop, it will have to compete with existing technologies. For this reason we begin with a brief survey of the history and current state of the art in secure communications before turning to the possibilities offered by quantum communications. The history of cryptography is a long and fascinating one. As a consequence of the success or, more spectacularly, the failure of ciphers, wars have been fought, battles decided, kingdoms won, and heads lost. In the information age, ciphers and cryptosystems have become part of everyday life; we use them to protect our computers, to shop over the Internet, and to access our money via an ATM (automated teller machine). One of the oldest and simplest of all ciphers is the transposition or Caesarean cipher (attributed to Julius Caesar), in which the letters are shifted by a known (and secret) number of places in the alphabet. If the shift is 1, for example, then A is enciphered as B, B→C, · · ·, Y→Z, Z→A. A shift of five places leads us to make the replacements A→F, B→G, · · ·, Y→D, Z→E.
Quantum cryptography provides perfect secrecy if the key exchanged is used for one-time-pad encryption. However, this requires very long keys which are not practical in most scenarios. Further, the key exchange bit-rate for quantum key distribution is very low. Consequently, often quantum key distribution algorithms only exchange (128, 192 or 256 bit) AES keys and then AES is used for data encryption. While Grover's algorithm will force us to only use AES- 256 and does not pose a catastrophic failure to AES, AES does not provide provable security. In this paper, we discuss methods that provide provable security but at the same time the key lengths may be controlled to practical levels. Difficulty of breaking the cipher is directly proportional to the key length and depends on the specific algorithm employed. The key idea is that key lengths can be tweaked such that an acceptable and provable level of security is achieved and therefore the cipher is not reliant on any assumptions for security. The paper will discuss different ways of achieving the above goal.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
Quantum cryptography represents a revolutionary paradigm shift in secure communication by leveraging the principles of quantum mechanics to guarantee unbreakable encryption. Unlike classical cryptographic methods dependent on computational hardness, quantum cryptography exploits quantum phenomena such as superposition and entanglement to provide provable security against eavesdropping. This paper explores fundamental quantum cryptographic protocols, their operational principles, and recent advances that enable practical deployment. We further discuss challenges, implementation issues, and the future scope of quantum key distribution (QKD) technologies in securing global communication infrastructures
The quantum cryptography approach is a significant change in secure communication in the sense that quantum cryptography bases its security on the law of quantum physics as opposed to computation difficulty. With classical encryption methods rapidly losing their resistance to the power of the underlying computers as well as the expected possibilities of the quantum computers, quantum cryptography comes into the limelight as a possible method of securing information in the long term. The paper is a detailed and systematic review of quantum cryptography along with the fundamentals of this practice, the way it works, and its practical implementation. It describes the ability of quantum phenomena to be unique (including superposition, uncertainty, and disturbance of measurement) and able to secure a key exchange as well as ensure any attempt of eavesdropping would be automatically noticed.In the review, the authors mainly discuss quantum key distribution (QKD) protocols, their functioning principles, security assurances, and the benefits of quantum over classical key exchange schemes. Besides that, the paper critically evaluates the real issues surrounding the implementation of quantum cryptographic systems such as hardware limitations, transmission range, environmental noise, and compatibility, to existing compatibility infrastructures. Recent advances in the field of experiments and pilot implementations are presented to determine the maturity of new technologies, and their suitability to be used on a large scale. Through its analytical review of theoretical assets, as well as practical constraints, this paper offers a definite and equalist view of the state of quantum cryptography today and also explains the research priorities important in its scale, moving away of the test production systems to the dependable and extensive security measures.