Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the al...Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.展开更多
This research paper analyzes the urgent topic of quantum cybersecurity and the current federal quantum-cyber landscape. Quantum-safe implementations within existing and future Internet of Things infrastructure are dis...This research paper analyzes the urgent topic of quantum cybersecurity and the current federal quantum-cyber landscape. Quantum-safe implementations within existing and future Internet of Things infrastructure are discussed, along with quantum vulnerabilities in public key infrastructure and symmetric cryptographic algorithms. Other relevant non-encryption-specific areas within cybersecurity are similarly raised. The evolution and expansion of cyberwarfare as well as new developments in cyber defense beyond post-quantum cryptography and quantum key distribution are subsequently explored, with an emphasis on public and private sector awareness and vigilance in maintaining strong security posture.展开更多
As technological innovations in computers begin to advance past their limit (Moore’s law), a new problem arises: What computational device would emerge after the classical supercomputers reach their physical limitati...As technological innovations in computers begin to advance past their limit (Moore’s law), a new problem arises: What computational device would emerge after the classical supercomputers reach their physical limitations? At this moment in time, quantum computers are at their starting stage and there are already some strengths and advantages when compared with modern, classical computers. In its testing period, there are a variety of ways to create a quantum computer by processes such as the trapped-ion and the spin-dot methods. Nowadays, there are many drawbacks with quantum computers such as issues with decoherence and scalability, but many of these issues are easily emended. Nevertheless, the benefits of quantum computers at the moment outweigh the potential drawbacks. These benefits include its use of many properties of quantum mechanics such as quantum superposition, entanglement, and parallelism. Using these basic properties of quantum mechanics, quantum computers are capable of achieving faster computational times for certain problems such as finding prime factors of an integer by using Shor’s algorithm. From the advantages such as faster computing times in certain situations and higher computing powers than classical computers, quantum computers have a high probability to be the future of computing after classical computers hit their peak.展开更多
In this paper, based on the implementation of semiclassical quantum Fourier transform, we first propose the concept of generation vector of ternary binary representation, construct the generation function's truth ...In this paper, based on the implementation of semiclassical quantum Fourier transform, we first propose the concept of generation vector of ternary binary representation, construct the generation function's truth table, prove that the generation vector of ternary binary representation is one kind of k 's NAF representation and further find that its number of nonzero is not more than [(「logk」+1) /2]. Then we redesign a quantum circuit for Shor's algorithm, whose computation resource is approximately equal to that of Parker (Their requirements of elementary quantum gate are both O (「logN」3), and our circuit requires 2 qubits more than Parker's). However, our circuit is twice as fast as Parker's.展开更多
文摘Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.
文摘This research paper analyzes the urgent topic of quantum cybersecurity and the current federal quantum-cyber landscape. Quantum-safe implementations within existing and future Internet of Things infrastructure are discussed, along with quantum vulnerabilities in public key infrastructure and symmetric cryptographic algorithms. Other relevant non-encryption-specific areas within cybersecurity are similarly raised. The evolution and expansion of cyberwarfare as well as new developments in cyber defense beyond post-quantum cryptography and quantum key distribution are subsequently explored, with an emphasis on public and private sector awareness and vigilance in maintaining strong security posture.
文摘As technological innovations in computers begin to advance past their limit (Moore’s law), a new problem arises: What computational device would emerge after the classical supercomputers reach their physical limitations? At this moment in time, quantum computers are at their starting stage and there are already some strengths and advantages when compared with modern, classical computers. In its testing period, there are a variety of ways to create a quantum computer by processes such as the trapped-ion and the spin-dot methods. Nowadays, there are many drawbacks with quantum computers such as issues with decoherence and scalability, but many of these issues are easily emended. Nevertheless, the benefits of quantum computers at the moment outweigh the potential drawbacks. These benefits include its use of many properties of quantum mechanics such as quantum superposition, entanglement, and parallelism. Using these basic properties of quantum mechanics, quantum computers are capable of achieving faster computational times for certain problems such as finding prime factors of an integer by using Shor’s algorithm. From the advantages such as faster computing times in certain situations and higher computing powers than classical computers, quantum computers have a high probability to be the future of computing after classical computers hit their peak.
基金supported by the National Natural Science Foundation of China (10501053)
文摘In this paper, based on the implementation of semiclassical quantum Fourier transform, we first propose the concept of generation vector of ternary binary representation, construct the generation function's truth table, prove that the generation vector of ternary binary representation is one kind of k 's NAF representation and further find that its number of nonzero is not more than [(「logk」+1) /2]. Then we redesign a quantum circuit for Shor's algorithm, whose computation resource is approximately equal to that of Parker (Their requirements of elementary quantum gate are both O (「logN」3), and our circuit requires 2 qubits more than Parker's). However, our circuit is twice as fast as Parker's.
