Security Notions for Quantum Public-Key Cryptography (original) (raw)

Quantum Public-Key Cryptosystems

Advances in Cryptology — CRYPTO 2000, 2000

This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f , plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor's discrete logarithm algorithm is efficiently realized on a quantum machine.

Unconditionally secure cryptosystems based on quantum cryptography

Information Sciences, 2008

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.

Sustainability of Public Key Cryptosystem in Quantum Computing Paradigm

Handbook of Research on Natural Computing for Optimization Problems

With the emergence of technological revolution to host services over Internet, secure communication over World Wide Web becomes critical. Cryptographic protocols are being in practice to secure the data transmission over network. Researchers use complex mathematical problem, number theory, prime numbers etc. to develop such cryptographic protocols. RSA and Diffie Hellman public key crypto systems have proven to be secure due to the difficulty of factoring the product of two large primes or computing discrete logarithms respectively. With the advent of quantum computers a new paradigm shift on public key cryptography may be on horizon. Since superposition of the qubits and entanglement behavior exhibited by quantum computers could hold the potential to render most modern encryption useless. The aim of this chapter is to analyze the implications of quantum computing power on current public key cryptosystems and to show how these cryptosystems can be restructured to sustain in the new ...

Achieving unconditional security by quantum cryptography

Classical cryptography algorithms are based on mathematical functions. The robustness of a given cryptosystem is based essentially on the secrecy of its (private) key and the difficulty with which the inverse of its one-way function(s) can be calculated. Unfortunately, there is no mathematical proof that will establish whether it is not possible to find the inverse of a given one-way function. Since few years ago, the progress of quantum physics allowed mastering photons which can be used for informational ends and these technological progresses can also be applied to cryptography (quantum cryptography). Quantum cryptography or Quantum Key Distribution (QKD) is a method for sharing secret keys, whose security can be formally demonstrated. It aims at exploiting the laws of quantum physics in order to carry out a cryptographic task. Its legitimate users can detect eavesdropping, regardless of the technology which the spy may have. In this study, we present quantum cryptosystems as a tool to attain the unconditional security. We also describe the well known protocols used in the field of quantum cryptography.

Progress in Quantum Computational Cryptography

Journal of Universal Computer Science, 2006

Shor's algorithms for the integer factorization and the discrete logarithm problems can be regarded as a negative effect of the quantum mechanism on publickey cryptography. From the computational point of view, his algorithms illustrate that quantum computation could be more powerful. It is natural to consider that the power of quantum computation could be exploited to withstand even quantum adversaries. Over the last decade, quantum cryptography has been discussed and developed even from the computational complexity-theoretic point of view. In this paper, we will survey what has been studied in quantum computational cryptography.

A Quick Glance at Quantum Cryptography

Cryptologia, 1999

The recent application of the principles of quantum mechanics to cryptography has led to a remarkable new dimension in secret communication. As a result of these new developments, it is now possible to construct cryptographic communication systems which detect unauthorized eavesdropping should it occur, and which give a guarantee of no eavesdropping should it not occur.

On Quantum Cryptography

ЖУРНАЛ ЗА БЕЗБЈЕДНОСТ И КРИМИНАЛИСТИКУ

In the late twentieth century, human race entered the era ofinformation technology (IT). The IT industry, which deals with the production,processing, storage and transmission of information, has become an integralpart of the global economic system, a completely independent and significantsector of the economy. The dependence of the modern society on informationtechnologies is so great that omissions in information systems may lead tosignificant incidents. Telecommunications are the key information technologyindustry. However, information is very susceptible to various types of abuseduring transmission. The units for data storage and processing can bephysically protected from anyone wishing harm, but this does not hold truefor the communication lines that span hundreds or thousands of kilometersand are virtually impossible to protect. Therefore, the problem of informationprotection in the field of telecommunications is highly significant. Cryptology,particularly cryptography, deals w...

Quantum Computers and Algorithms: A Threat to Classical Cryptographic Systems 26

International Journal of Engineering and Advanced Technology (IJEAT), 2023

Contemporary cryptographic algorithms are resistant to the strongest threats to cybersecurity and high-profile cyberattacks. In recent times, information security scientists and researchers had developed various cryptographic schemes that defeated attacks using the most sophisticated (in terms of processor speed) classical computer. However, this resistance will soon erode with the arrival of quantum computers. In this paper, we profiled quantum computers and quantum algorithms based on their widely believed threat against currently secure cryptographic primitives. We found that Grover's and Shor's quantum-based algorithms actually pose a threat to the continued security of symmetric cryptosystems (e.g. 128-bit AES) and asymmetric (public key) cryptosystems (e.g. RSA, Elgamal, elliptic curve Diffie Hellman (ECDH), etc.) respectively. We discovered that the source of the algorithms' cryptanalytic power against the current systems, stems from the fact that they (Grover and Shor) both equipped their respective algorithms with a quantum circuit component that can execute the oracle in parallel by applying a single circuit to all possible states of an n-qubit input. With this exponential level of processing characteristic of quantum computers and quantumbased algorithms, it is easy for the current cryptosystems to be broken since the algorithms can existentially solve the underlying mathematical problems such as integer factorization, discrete logarithm problem and elliptic curve problem, which formed the basis of the security of the affected cryptosystems. Based on this realization and as part of our readiness for a post quantum era, we explored other mathematical structures (lattices, hashes, codes, isogenies, high entropy-based symmetric key resistance, and multivariate quadratic problems) whose hardness could surpass the cryptanalytic nightmare posed by quantum computers and quantum-based algorithms. Our contribution is that, based on the findings of this research work, we can confidently assert that all hope is not lost for organizations heavily relying on protocols and applications like HTTPS, TLS, PGP, Bitcoin, etc., which derived their security from the endangered cryptosystems.

Quantum Computational Cryptography

2006

As computational approaches to classical cryptography have succeeded in the establishment of the foundation of the network security, computational approaches even to quantum cryptography are promising, since quantum computational cryptography could offer richer applications than the quantum key distribution. Our project focused especially on the quantum one-wayness and quantum public-key cryptosystems.