We consider the use of pseudorandom number generators in quantum cryptography. They can be used in two ways: for basis choice according to pseudorandom sequence shared between Alice and Bob and for setting the pseudorandom phase for each coherent state to make worse the performance of some attacks. We propose this technology for the situations where the use of classical cryptographic methods like AES is satisfactory for the legitimate users.
We consider the use of pseudorandom number generators in quantum cryptography. They can be used in two ways: for basis choice according to pseudorandom sequence shared between Alice and Bob and for setting the pseudorandom phase for each coherent state to make worse the performance of some attacks. We propose this technology for the situations where the use of classical cryptographic methods like AES is satisfactory for the legitimate users.
Abstract Quantum key distribution plays an important role in modern cryptography, since the security of the transmitted keys is guaranteed by fundamental laws of nature. A method using pseudorandom number generators well known from classical cryptography is considered. It is shown that their use in quantum cryptography makes it possible to increase the key generation rate under very weak assumptions about the capabilities of the eavesdropper. A practical scheme of a coherent-state quantum key distribution protocol using pseudorandom sequences is proposed. The cryptographic strength of the proposed protocol against a beam-splitting attack is considered.
The rapid development of modern computing technology threatens the confidentiality of information that is provided, usually, by traditional cryptographic means and forces researchers to look for alternative methods of security. Considering the development tendencies one of these alternatives may be quantum cryptography that unlike traditional (which is mostly based on the impossibility of solving a certain class of mathematical problems by certain period of time) uses specific unique properties of quantum particles, based on the inviolability of the quantum physics laws. It is known that some quantum cryptography protocols allowing to achieve information-theoretic stability – a key distribution protocols mostly. Another class of quantum cryptography protocols - secure direct communication protocols, most of which have asymptotic stability. Therefore, it was suggested a number of methods to increase the stability of such protocols. One of these methods will increase the asymptotic stability of quantum secure direct connection protocols with entangled pairs (correlated) of qutrit, but this method requires the generation of ternary (trit) pseudorandom sequences. In the work proposed generating pseudorandom trit sequences method based on the number of irreversible functions and transformation over the field GF (3). Also at the basis of a method developed appropriate algorithm that reflected as pseudo code. Further research will focus on the development of a quality evaluation of trit generated pseudorandom sequences method, as virtually all existing methods focused on binary sequence.
In the last few years, development of quantum cryptography has attracted the scientist’s attention. Researches passed from the theoretical level to introduction of ready commercial decisions. The main difference between the methods of quantum cryptography and traditional (symmetric and asymmetric) cryptography consists in use of absolutely different principles in the basis. The quantum cryptography does not depend on computing or other intruder opportunities, uses specific unique quantum particles properties and based on inviolability of quantum physics laws. Among the most developed technologies of quantum cryptography is worth noting quantum secure direct communication, which can transmit information by open channel without encryption - removing key distribution problem, but in these protocols each bit of information is confidential and intruder shouldn’t get it, that's why requirements for protocols stability is much higher and require security amplification methods. Such method was previously developed by authors, but its implementation requires the use of reliable trit pseudorandom sequences. In this context, this study presents an experimental research of trit pseudorandom sequence generating method for cryptographic applications. For evaluating the effectiveness of this method was developed experimental methodology, which confirms the possibility of using trit sequences generated by the method for ensuring the stability of quantum cryptography qutrit protocols to non-coherent attacks and for other crypto-graphic applications in modern information and communication technologies.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to implement on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously - by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to realize on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously -- by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z-rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.