Reaching the speed limit of classical block ciphers via quantum-like operator spreading (original) (raw)
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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.
Cryptography in Quantum Computing
2021
Quantum cryptography is based on using photons and theirfundamental Quantum properties develop an indestructible cryptosystem because it is not possible to measure the quantum state of any system without alarming the system. Classical cryptography is built upon classical information theory and the Turing model of computation. The development of Quantum information theory and computing amounts to a paradigm shift. In many respects, Quantum information processing is radically different from classical information processing. A Quantum computer with hundreds or thousands of qubits is needed to solve problems beyond the capability of conventional computers, and it is not known when such a computer might be built. Identifying new cryptanalytic improvements that make use of Quantum algorithms and expanding the applicability is known cryptanalytic attacks by means of Quantum technology
Quantum information scrambling through a high-complexity operator mapping
Physical Review A
Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalizaiton-irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into non-separable many-body-correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wavefunction and compute all physical observables in dynamics with a polynomial cost in system-size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hammingdistance. At late time, we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator-mapping enabled growth in out-of-time-order-correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling and quantum thermalization.
25 Years of Quantum Cryptography
ACM Sigact News, 1996
I n t r o d u c t i o n The fates of S I G A C T News and Quantum Cryptography are inseparably entangled. The exact date of Stephen Wiesner's invention of "conjugate coding" is unknown but it cannot be far from April 1969, when the premier issue of SIGACT News-or rather S I C A C T News as it was known at the time-came out. Much later, it was in S I G A C T News that Wiesner's paper finally appeared [74] in the wake of the first author's early collaboration with Charles H. Bennett [7]. It was also in SIGACT News that the original experimental demonstration for quantum key distribution was announced for the first time [6] and that a thorough bibliography was published [19]. Finally, it was in S I G A C T News that Doug Wiedemann chose to publish his discovery when he reinvented quantum key distribution in 1987, unaware of all previous work but Wiesner's [73, 5].
An Examination of Quantum Information Processing Through Quantum Cryptography; A study
Journal on Applied and Chemical Physics, 2022
Along with these developments, personal microwave technology has enabled strong non-linear effects at the photon level, leading to readily observable novel parameter regimes in quantum optics. Circuit QED has opened up new opportunities to explore the rich physics of quantum information processing (QIP) and quantum optics (QO), making them scalable on the road to quantum computing. However, we must also discuss some of the challenges involved. Quantum Technologies (QT) is a cross-disciplinary field that has made great progress in recent years. Technologies that can explicitly represent individual quantum states, as well as superposition and entanglement, are now being developed to exploit the 'strange' properties of quantum mechanics. In quantum communication, individual or entangled photons are used to securely send data, while quantum simulation utilizes well-controlled quantum systems that are less accessible. Interest is growing in higher dimensional quantum states and quantum communication, as the extended availability of Hilbert space and greater information capacity, along with increased noise elasticity, offer many advantages and new research possibilities. Let's focus our attention on the benefits of higher dimensional quantum states for quantum communication, as shown by Kuditz and others. Nevertheless, it has been demonstrated that higher dimensional quantum states can also provide improvements in many other areas."
Information scrambling in quantum circuits
Science, 2021
Quantum scrambling Information spreading in interacting quantum systems is of relevance to a wide range of settings, from black holes to strange metals. Mi et al . used the Sycamore quantum processor to study this process. Through judicial design of quantum circuits, the researchers were able to separate the contributions of operator spreading and operator entanglement. Measuring the mean value and fluctuations of a specific correlator enabled quantifying these distinct contributions. —JS
Lecture Notes in Computer Science, 2004
We consider the scenario where Alice wants to send a secret (classical) n-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to obtain perfect secrecy with key length smaller then n. We study the question of whether there might still be fundamental differences between the case where quantum as opposed to classical communication is used. In this direction, we show that there exist ciphers with perfect security producing quantum ciphertext where, even if an adversary knows the plaintext and applies an optimal measurement on the ciphertext, his Shannon uncertainty about the key used is almost maximal. This is in contrast to the classical case where the adversary always learns n bits of information on the key in a known plaintext attack. We also show that there is a limit to how different the classical and quantum cases can be: the most probable key, given matching plain-and ciphertexts, has the same probability in both the quantum and the classical cases. We suggest an application of our results in the case where only a short secret key is available and the message is much longer. Namely, one can use a pseudorandom generator to produce from the short key a stream of keys for a quantum cipher, using each of them to encrypt an n-bit block of the message. Our results suggest that an adversary with bounded resources in a known plaintext attack may potentially be in a much harder situation against quantum stream-ciphers than against any classical stream-cipher with the same parameters. 1 Introduction In this paper, we consider the scenario where Alice wants to send a secret (classical) n-bit message to Bob using an m-bit classical shared key, and where only one-way transmission from Alice to Bob is possible (or at least where interaction is only available with a prohibitively long delay). If interaction had been available, we could have achieved (almost) perfect secrecy using standard quantum ⋆ Part of this research was funded by European project PROSECCO.
Approximate quantum encryption with faster key expansion
2022
Perfect encryption of a qubit state using the Quantum One-Time Pad (QOTP) requires 2 classical key bits. More generally, perfect encryption of a 2n-dimensional state requires 2n classical bits. However, almost-perfect encryption, with information-theoretic security, can be achieved with only little more than 1 key bit per qubit. It has been shown that key length n+2log1/ε suffices to encrypt n qubits in such a way that the cipherstate has trace distance ≤ε from the fully mixed state. In this paper, we present a fast key expansion method to create a 2n-bit pseudorandom string which is then used as a QOTP key. In this expansion we make use of 2n bits of public randomness which are included as a classical part of the cipherstate. Our key expansion is a factor 2 faster than the previous fastest scheme, while achieving the shortest known key length n+2log1/ε.
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.