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Post-Quantum Cryptography
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
Amandeep Singh Bhatia, Ajay Kumar
Over the last three decades, public-key cryptosystems (Diffie–Hellman key exchange, the RSA cryptosystem, the digital signature algorithm [DSA], and elliptic curve cryptosystems [ECC]) have become a crucial component of cyber security. In this regard, security depends on the difficulty of a definite number of theoretic problems (integer factorization or the discrete log problem). (Shor, 1994) designed an algorithm to calculate factors of a large number n with space complexity O(logn) and runs in O((logn)2 * loglog n) on a quantum computer, and then perform O(logn) post-processing time on a classical computer, which could be applied for cracking the RSA algorithm at Bell Laboratories (US). (Grover, 1996) designed a searching algorithm with great quadratic gain for finding an element in an unstructured set of size n in n operations approximately. Furthermore, (Kwiat et al., 2000) implemented Grover’s algorithm at Los Alamos National Laboratory using conventional optical interferometers. Quantum parallelism is one of the main features of quantum computation which allows quantum algorithms to gain speedup as compared to classical algorithms.
The Longer Term: Quantum Information Processing and Communication
Published in Simon Deleonibus, Electronic Device Architectures for the Nano-CMOS Era, 2019
One year later, in 1994, Peter Shor, from AT&T, shows that finding the prime factors of an integer number in a time which is a polynomial function of the number of digits needed for writing that integer, is possible with quantum computing, whereas the best classical algorithm known for solving this problem takes an exponential time. This exponential drop of complexity was immediately noticed as a threat to the most widely used cryptographic systems. This was the real trigger for a very wide and very diverse expansion of research activities in quantum information processing and communication. In 1996, Lov Grover, from Lucent Technologies, designs a quantum algorithm for finding an item in unordered database that takes a time which is the square root of the time needed by classical computers for the same problem: this also came as a big surprise to the algorithmic research community. In 1997, Anton Zeilinger, from the University of Vienna, realizes the first experimental teleportation of the state of a photon, an experiment which has now been repeated in many other places, over distances much beyond the size of a laboratory, like a recent experiment over 144 km between two Canary Islands. Then, from 1999 to 2002, Isaac Chuang, from IBM Research Almaden, designs and builds the first quantum computer, based on NMR technology, which, although of a very modest size with only 7 quantum bits, has permitted to show experimentally that the new quantum algorithmic ingredients imagined and applied in theory by Shor and Grover in their algorithms, could indeed be implemented in practice within a physical quantum system.
Quantum Algorithm for Sequence Clustering
Published in Siddhartha Bhattacharyya, Anirban Mukherjee, Indrajit Pan, Paramartha Dutta, Arup Kumar Bhaumik, Hybrid Intelligent Techniques for Pattern Analysis and Understanding, 2017
Arit Kumar Bishwas, Ashish Mani, Vasile Palade
A quantum algorithm runs on a realistic model of quantum computation; the quantum circuit models of computation are the most commonly used models, as is the recently explored adiabatic quantum computation model. The quantum algorithm is a step-by-step procedure where each step is performed on a quantum computer. The term quantum algorithm is usually associated with those algorithms which use some essential features of quantum computation like quantum superposition or quantum entanglement. Although it is to note that all classical algorithms can also be executed on a quantum computer. Some of the famous quantum algorithms are Shor's algorithm [11] for factorization, and Grover's algorithm [12] used for searching an unstructured database. Shor's algorithm is exponentially faster than the best known classical algorithm for factorization. Grover's algorithm runs with quadratic speed improvement compared to the best possible counter classical algorithm for the similar task.
Systematic Survey: Secure and Privacy-Preserving Big Data Analytics in Cloud
Published in Journal of Computer Information Systems, 2023
Arun Amaithi Rajan, Vetriselvi V
The majority of authentication mechanisms in classical cryptosystems are based on cryptographic primitives. For instance, RSA and ElGamal are cryptosystems built on factorization or discrete logarithm hard problems. It is widely assumed that such primitives are vulnerable to quantum algorithms. Shor’s algorithm32 is a quantum algorithm that solves discrete logarithm and factorization problems in sub-exponential time complexity. So, if we continue to have the same cryptosystem, there is a chance that quantum computers will attack secure applications within polynomial time in the future. So, with a longer vision, more works are being done in quantum cryptography.33 As we have hard problems in traditional systems, such as discrete logarithm, there are some hard problems in the quantum environment also such as lattice problems which prompted scientists to develop quantum cryptography algorithms. A survey on lattice-based cryptography implementations in software and hardware by Nejatollahi et al.34 gives an overview of existing algorithms in post-quantum cryptography based on lattice problems. The authors worked on implementations which tackles different issues such as memory footprint, energy, security and, given some proposals for lattices in information security
The first iteration of Grover's algorithm using classical light with orbital angular momentum
Published in Journal of Modern Optics, 2018
Benjamin Perez-Garcia, Raul I. Hernandez-Aranda, Andrew Forbes, Thomas Konrad
In the mid-1990s, Lov Grover devised a quantum algorithm to efficiently find an element within an unstructured database of N elements in steps (23). Although Grover's search results only in a quadratic speed up compared to classical search algorithms, it might be considered the ‘work horse’ of quantum computation. The reason is that it can be employed to amplify the amplitude of a particular state within a superposition of states that encodes the solution of a computational task and thereby increases the probability to detect this solution (see Part III in (24)). In a certain sense, it allows to make an a priori improbable event to occur frequently. Grover's algorithm has been implemented, in proof of principle experiments, with entangled photons (12), NMR systems (25), with path-qubits (26), among others.
A small-scale distributed polygeneration with local renewable resources for a remote place of India: techno-economic optimisation
Published in International Journal of Ambient Energy, 2021
Quantum inspired algorithms belong to a set of new class of optimisation algorithms implemented using the theory of quantum computing. The key objective of quantum computing is to discover quantum algorithms which are much more efficient and quicker than the classical algorithms. The basic component of quantum computing is ‘qubit’. It is a unit vector defined over two-dimensional Hilbert space, where a particular basic state can be indicated by and.