Accelerating the Wheel Factoring Techniques
10 Feb 2023
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TL;DR: In this paper , the wheel factorization algorithm was adapted to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time of the wheel factoring algorithm.
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Abstract: The efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems′ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a traditional computer, there is no polynomial time algorithm. We investigate how to enhance the wheel factoring technique in this paper. Current wheel factorization algorithms rely on a very restricted set of prime integers as a base. In this study, we intend to adapt this notion to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time. The experiments on composite numbers n reveal that the proposed algorithm improves on the existing wheel factoring algorithm by about 75%
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Citations
Accelerating the Wheel Factoring Techniques
10 Feb 2023
TL;DR: In this paper , the wheel factorization algorithm was adapted to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time of the wheel factoring algorithm.
1
References
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TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for both problems, which takes a number of steps polynomial in the input size, e.g., the number of digits to be factored.
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Factoring larger integers with fewer qubits via quantum annealing with optimized parameters
TL;DR: This study optimize the problem Hamiltonian to reduce the number of qubits involved in the final Hamiltonian while maintaining the QUBO coefficients in a reasonable range, enabling the improved algorithm to factorize larger integers with fewer qubits.
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Explaining the wheel sieve
TL;DR: A simple mathematical framework is developed, which leads to a smoother and more insightful derivation of the new algorithm, and which may be of independent interest to the number theorist.
48
Primality Testing and Integer Factorization in Public-Key Cryptography
Song Y. Yan
TL;DR: The paper covers topics in computer and network security, including primality testing and integer factorization, and aims to establish the state of the art and set the course for future research.
A new RSA vulnerability using continued fractions
Dieaa I. Nassr,Hatem M. Bahig,Ashraf Bhery,Sameh S. Daoud +3 more
- 31 Mar 2008
TL;DR: This work shows that the RSA public key system is insecure if delta < 1-alpha/2, and its result is deterministic polynomial time and an extension of Coppersmith's result on a factorization.
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