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The Longer Term: Quantum Information Processing and Communication
Published in Simon Deleonibus, Electronic Device Architectures for the Nano-CMOS Era, 2019
Shor’s quantum algorithm factorizes integers in polynomial time. It relies on a known polynomial cost reduction of the problem of factoring to the problem of finding the period of a function. Then, since period finding can be achieved by a Fourier Transform, the key of Shor’s algorithm is a Quantum Fourier Transform (QFT), which is indeed exponentially more efficient than the classical Fourier Transform, thanks to quantum parallelism, entanglement and tensor product. Shor’s result implies that once a quantum computer with a sufficiently large number of qubits is available, most currently used cryptographic protocols will be broken in few minutes. However, as shown in section 4 of this chapter, quantum information provides also means for building the security of communications upon definitely trustable physical principles, rather than on the not proved exponentiality of integer factoring.
Threat to the Current Blockchain Cryptosystems Due to the Advancement of Quantum Computers
Published in Latesh Malik, Sandhya Arora, Urmila Shrawankar, Vivek Deshpande, Blockchain for Smart Systems, 2022
Shor’s algorithm solves the logarithmic problem of ECDSA by a method called period finding. We can call this a real threat because it can solve this complexity in polynomial time [8, 9]. This is a great increase in speed when compared to classic computers, which have complexity in exponential time (see Figure 8.4). Quantum computers use fundamentals like quantum interference, quantum superposition, and Quantum Fourier Transform (QFT) to maximize the required probabilistic output. In the coming section, we’ll see which are some different cryptosystems that may not be prone to quantum attacks.
6G Security
Published in Paulo Sergio Rufino Henrique, Ramjee Prasad, 6G The Road to the Future Wireless Technologies 2030, 2022
Paulo Sergio Rufino Henrique, Ramjee Prasad
Quantum Computing (QC) is not a new technological proposal. What is new is turning quantum computing into reality due to its physical complexities and challenges to engineer a quantum computer that truly can abide by the quantum mechanics principles. The founding fathers of quantum computing are the Nobel prize in physics laureates of 1965, the North American scientists Richard P. Feynman (1918-1988), Julian Schwinger (1918-1994), and the Japanese scientist Sin-Itiro Tomonaga (1906-1979) for their works in quantum electrodynamics (QED) [90]. The QED is a quantum theory field that describes the behaviors of charged particles with electromagnetic fields. The importance of this theory is a mathematical description of all interactions occurring between light and matter and the particles [91]. The first to propose a quantum computational methodology based on quantum mechanics was the north-American scientist Paul A. Benioff [92]. Paul demonstrated the possibility of quantum computers becoming feasible to implement, in theory, in June of 1979. However, it was in 1995 that the mathematician Peter Shor created the first quantum algorithm to process Qubits [93]. This algorithm was baptized of Shor's algorithms, and its contributions enabled to factored much faster than any classical computing any integer N by its prime numbers. Shor's algorithms embedded quantum Fourier transform within its algorithm, plus the ability to overcome the quantum noise weakness that could lead to loss of information during the quantum computing process. With ShorâĂŹs algorithms, if in theory existed, a perfect quantum computer running 4099 qubits could break a Rivest-Shamir-Adleman's (RSA) cryptographic algorithm of 2048 bits in 10 seconds, while a classic computer would take approximately 300 trillion years to perform the same task [94]. RSA is one of the widely used and safe public-private encryption keys in telecommunications systems. The RSA is used in web browsers, Virtual Private Networks, in which one key is public, and the other is private [95]. However, such a quantum computer does not exist yet, but quantum computers are starting to become a reality, and IBM and Google both have the ultimate state of the art in quantum computing.
Leveraging the power of quantum computing for breaking RSA encryption
Published in Cyber-Physical Systems, 2021
Moolchand Sharma, Vikas Choudhary, R. S. Bhatia, Sahil Malik, Anshuman Raina, Harshit Khandelwal
Modular arithmetic is a part of mathematics that revolves around the remainders of integers. Shor’s algorithm for factorisation uses this as a basis for finding prime factors more efficiently. Shor introduced an algorithm for integer factorisation that is used for finding the prime factors of a number. When running on a quantum computer, the algorithm takes very little time to find the prime factors of the number – running in polynomial time. The efficiency of Shor’s algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squaring. The RSA and the algorithm are based on the same finite group theory. Shor’s algorithm gives us the best efficiency, but it relies on Size of Quantum Computers, which are not possible right now [20,21].