Unconditionally secure cryptosystems based on quantum cryptography

Abstract

Most modern cryptographic studies design cryptosystems and algorithms using mathematical concepts. In designing and analyzing cryptosystems and protocols, mathematical concepts are critical in supporting the claim that the intended cryptosystem is secure. Most early cryptographic algorithms are based either on factorization or on discrete logarithm problem. Such systems generally adopt rather simple mathematics, and, therefore, need extensive secondary index computation. This study discusses quantum cryptosystems, protection of system security, and optimization of system efficiency. Quantum cryptography detects intrusion and wiretap. In quantum mechanics, a wiretap is neither external nor passive; rather it modifies its entity based on the internal component of the system. The status of the quantum system changes once a wiretap is detected. Hence, only the designer of the system can discover the quantum status of the system; an eavesdropper can neither determine the quantum state nor duplicate the system. The quantum cryptosystem can achieve unconditional security, and thus guarantees secure communication.

Introduction

As computer science rapidly advances, related technologies are also emerging. Computer technology has rapidly improved from the vacuum tube through transistor technology to super-scaled integrated circuits. Recently, the size of transistors in processors has once again been significantly reduced, a phenomenon that is crucial to improve computer mechanics. However, this continuous size reduction cannot continue for long. Transistors that are too small restrict the overall functionality of a computer. Hence, in 1982, Nobel-Prize-winning physicist Richard Feynman [39] proposed the concept of the quantum computer, which exploits the quantum features such as superposition and entanglement.

The most basic structural element of a traditional computer, the bit, can exist in only one of two mutually exclusive states, 0 or 1. However, this rule does not apply in Feynman’s proposed quantum computer. A quantum bit can exist not only in the traditional 0 or 1 state, but also in continuous or overlapping states. A quantum bit that is in continuous or overlapping states can be recognized to be in two domains, namely 0 and 1. However, the operations based on such a quantum bit affects the two values simultaneously, as revealed in Fig. 1. Therefore, operating on a single quantum bit implies working on two values. Similarly, a bi-quantum bit system can work on four values, and a tri-quantum bit system can operate on eight values. Accordingly, as the number of quantum bits rises, the quantum collateral effect obtained from the system is increased by the exponential method.

Although the concept of quantum computers has remained purely theoretical for a long time, recent developments in quantum computers have aroused interest. Shor et al. [38] designed an algorithm that successfully calculated a large amount of data using quantum computers. A quantum computer can utilize this algorithm as a solution to problems based on exponential operations, such as the NP problem [44], [45] or factorization [16]. The temporal cost is much less than that of any conventional computer. Therefore, quantum computer is now increasingly studied with many researchers attempting to produce a practical quantum computer.

While most current cryptographic technologies, such as RSA, DES, ECC and others are based on factorization, discrete logarithms, and other exponential operations, Shor’s algorithm [38] for a quantum computer can efficiently solve the exponential equation problems. Thus, currently available cryptosystems will in comparison become useless and lacking in security [17], [20], [28] when quantum computers become practical reality. Most public key cryptosystems apply simple mathematics that can be hacked easily by scanning for loopholes and backdoors. This weakness is the limitation of modern cryptography. Accordingly, developing an entirely new cryptosystem has become the research goal in various fields [9], [34]. The quantum cryptosystem is one such system.

Wiesner [42] proposed the one-time pad method for key distributions, exploiting the laws of physics to scan for system intrusion or wiretap in the 1970s. A wiretap was identified from an altered quantum state. Quantum mechanics does not regard measurement as an external and passive process, but instead as one that changes the internal states of the system. Detection, wiretaps, and intrusion are measurement behaviors, any wiretap and intrusion during key distribution can be detected. Hence, a quantum cryptosystem attains unconditional security.

Fig. 2 illustrates the quantum cryptosystem structure which employs two main channels of communication. The first is the quantum channel which aims to transmit and receive quantum bits and to generate the session key. The second is the open channel which is adopted by the sender and receiver to compare their quantum bits, and thus discover whether they are being tapped. Both sender and receiver encrypt the plain text and decrypt the cipher text by their session key, thus securing their communication.

System security in a quantum cryptosystem lies in key distribution. A change in the quantum state of the system occurs once an eavesdropper obtains the quantum bits used to compose the session key; the eavesdropper can thus be detected. Therefore, the development of quantum cryptology is devoted to practical and efficient Quantum Key Distribution Protocol (QKDP), which has recently become a major topic in research into quantum mechanics.