aqora

Faster Search plus Threatening the Foundation of Asymmetric Cryptography with Grover and Shor

Vladimir Silva

This chapter brings proceedings to a close with two algorithms that have generated excitement about the possibilities of practical quantum computation:

Apress eBooksJan 1, 20180 citations

Quantum Integral Transforms

Mikio Nakahara

We demonstrated in the previous chapter that there are some quantum algorithms superior to their classical counterparts. It is, however, rather diﬃcult to ﬁnd any practical use of these algorithms. There are two quantum algorithms, known to date, which are potentially useful: Grover’s search algorithm and Shor’s prime number factorization algorithm. Both of them depend on quantum integral transforms, which will be introduced in the present chapter. We mainly follow [1] in our presentation.We demonstrated in the previous chapter that there are some quantum algorithms superior to their classical counterparts. It is, however, rather diﬃcult to ﬁnd any practical use of these algorithms. There are two quantum algorithms, known to date, which are potentially useful: Grover’s search algorithm and Shor’s prime number factorization algorithm. Both of them depend on quantum integral transforms, which will be introduced in the present chapter. We mainly follow [1] in our presentation.

CRC Press eBooksMar 11, 20080 citations

Quantum Computing Algorithms – Survey of Shor's, Grover's, and Future Directions

Rajeev, Shreya

For decades, classical computers have been governed by predictable rules. But as we approach the physical limits of computation, a new paradigm is emerging. Quantum computing operates on the strange and powerful laws of quantum mechanics—superposition, entanglement, and interference—to tackle problems far beyond the reach of any classical machine. The true potential of this field was unlocked by two landmark discoveries: Shor’s algorithm, a revolutionary method for integer factorization that threatens to upend modern cryptography, and Grover’s algorithm, a versatile tool that offers a quadratic speedup for unstructured search problems. This paper serves as a guide to these foundational algorithms, detailing their inner workings and their profound impact. We also explore post-quantum cryptography, hybrid frameworks, and quantum machine learning—illustrating the evolving role of quantum algorithms in shaping the future of science and technology.For decades, classical computers have been governed by predictable rules. But as we approach the physical limits of computation, a new paradigm is emerging. Quantum computing operates on the strange and powerful laws of quantum mechanics—superposition, entanglement, and interference—to tackle problems far beyond the reach of any classical machine. The true potential of this field was unlocked by two landmark discoveries: Shor’s algorithm, a revolutionary method for integer factorization that threatens to upend modern cryptography, and Grover’s algorithm, a versatile tool that offers a quadratic speedup for unstructured search problems. This paper serves as a guide to these foundational algorithms, detailing their inner workings and their profound impact. We also explore post-quantum cryptography, hybrid frameworks, and quantum machine learning—illustrating the evolving role of quantum algorithms in shaping the future of science and technology.

Nov 13, 20250 citations

Quantum Techniques for Image Processing

Arti Ranjan, Ashish K. S. Arya, M. Ravinder

Quantum computing is revolutionizing every field of knowledge. With advent of affordable quantum computing almost possible the importance and relevance of quantum computing for all the recent research trends cannot be overemphasized. We have already witnessed quantum analogues of most celebrated classical algorithms starting from Shor’s algorithm for integer factorization, Grover’s search algorithms for unstructured database. Quantum Image Processing is an emerging field borne by applying quantum computing techniques to the Image Processing problems. This paper attempts to summarize and review the state of development in the field of Quantum Image Processing. All major quantum computing platforms have been presented, At the end a discussion on the current trends and future possibilities is presented.Quantum computing is revolutionizing every field of knowledge. With advent of affordable quantum computing almost possible the importance and relevance of quantum computing for all the recent research trends cannot be overemphasized. We have already witnessed quantum analogues of most celebrated classical algorithms starting from Shor’s algorithm for integer factorization, Grover’s search algorithms for unstructured database. Quantum Image Processing is an emerging field borne by applying quantum computing techniques to the Image Processing problems. This paper attempts to summarize and review the state of development in the field of Quantum Image Processing. All major quantum computing platforms have been presented, At the end a discussion on the current trends and future possibilities is presented.

International Conference on Advances in Computing, Communication Control and Networking (ICAC3N)Dec 18, 202011 citations

3 Factorization with Quantum Computers: Shor’s Algorithm

Daniel Neuenschwander

Lecture notes in computer scienceJan 1, 20040 citations

Enhanced Security Algorithm for Integer Factorization in Quantum Computing: Optimizing Shor’s Algorithm

Rashmi Kuksal, Sumit Chaudhary, Ashish Bhatt

International Conference on Innovative Mechanisms for Industry ApplicationsOct 1, 20260 citations

Advanced Algorithms: Unstructured Search and Integer Factorization with Grover and Shor

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Advanced Algorithms: Unstructured Search and Integer Factorization with Grover and Shor

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