A Compare between Shor's quantum factoring algorithm and General Number Field Sieve

Hamdi, Shah Muhammad; Zuhori, Syed Tauhid; Mahmud, Firoz; Pal, Biprodip

doi:10.1109/iceeict.2014.6919115

Cited by 7 publications

(4 citation statements)

References 11 publications

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“…A building-block state corresponds to only one qubit on the cluster state, i.e., one data qubit of the surface code, which could correspond to just one ion in an ion-trap quantum computer or one superconducting qubit in a superconducting quantum computer. It is anticipated that a fault-tolerant quantum computer will need at least approximately 10 6 data qubits in order to be able to compete with state-of-the-art classical computers [18,39]. We therefore do not consider buildingblock states with a resource requirement of greater than 2 × 10 9 detectors, since at that point one finds the entire computer requires thousands of trillions of components.…”

Section: Thresholdsmentioning

confidence: 99%

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

et al. 2015

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Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors. However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems. Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than 10 −3 or the per-component noise rate is worse than 10 −5 . We identify the performance of switches in the network as the single most influential factor influencing resource scaling.

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Section: Thresholdsmentioning

confidence: 99%

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

et al. 2015

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“…The result of measurement is a multiple of Q/r. Going back to the first step, getting enough distinct results and computing gcd of the retrieve Q/r will be the final step [13].…”

Section: Tpcee 2022mentioning

confidence: 99%

Comparison of Performances for Quantum and Conventional Algorithms: Shor’s algorithm and Boson Sampling

Jia¹

2023

HSET

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Quantum computing has been extensive popularity discussed recently. The foundation of quantum study is the investigation of how quantum computing shows its superiority compared with conventional algorithms. On this basis, this paper focuses on the comparison of the performances of quantum and conventional algorithms about the same relevant area. Two classic problems, factorization of large integer and boson sampling, are chosen to show the specific difference of related quantum and conventional algorithms towards the same problem. This paper specifically compares the performance of Shor's algorithm and other advanced traditional integer factorization algorithms for prime factorization problems and compares the processing capabilities of traditional algorithms and Gaussian Boson sampling for sampling problems. According to the analysis, for the same research problem, quantum algorithms show strong advantages over traditional algorithms in many performances, e.g., time efficiency, algorithm adaptability. It leads to a deeper understanding of quantum superiority and a further explanation of the significance of the development of quantum computing.

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“…For the first group, it is called the general purposed group. All algorithms are based on only size of n. Number Field Sieve (NFS) [17] which is one of efficient algorithms in this group is considered as the best integer factorization algorithm. In fact, it has very high performance when n is large.…”

Section: Integer Factorization Algorithmsmentioning

confidence: 99%

The new Weakness of RSA and The Algorithm to Solve this Problem

2020

KSII TIIS

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RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Φ (n), can be rewritten as Φ (n) = ad + b, where d is the private key and , a b ∈  , if a divides both of Φ (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = h a is higher than modulus.

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A Compare between Shor's quantum factoring algorithm and General Number Field Sieve

Cited by 7 publications

References 11 publications

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

Comparison of Performances for Quantum and Conventional Algorithms: Shor’s algorithm and Boson Sampling

The new Weakness of RSA and The Algorithm to Solve this Problem

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