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INTEGER FACTORIZATION IMPLEMENTATIONS [PDF]
ICTACT Journal on Communication Technology, 2016 One difficult problem of mathematics that forms the basics of some public key cryptography systems like RSA, is finding factors of big numbers. To solve this problem, many factorization algorithms have been offered with different complexities.
Reza Alimoradi, Hamid Reza Arkian
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A deterministic algorithm for integer factorization [PDF]
Mathematics of Computation, 2014 A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.
G. Hiary
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On the factorization of squarefree integers [PDF]
Proceedings of the American Mathematical Society, 1952 In recent years several papers [1; 3; 4; 5; 6; 7; 9; 10; 11] have appeared dealing with the problem of "Factorisatio numerorum," the number f(n) of representations of an integer n as an ordered product of factors greater than 1. As a result, the basic combinatorial properties of f(n) and the asymptotic behavior of its summatory function are well known.
A. Sklar
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Asymptotically fast factorization of integers [PDF]
Mathematics of Computation, 1981 The paper describes a "probabilistic algorithm" for finding a factor of any large composite integer n (the required input is the integer n together with an auxiliary sequence of random numbers). It is proved that the expected number of operations which will be required is O ( exp { β (
John D. Dixon
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Research on Quantum Annealing Integer Factorization Based on Different Columns
Frontiers in Physics, 2022 The majority of scholars believe that Shor’s algorithm is a unique and powerful quantum algorithm for RSA cryptanalysis, so current postquantum cryptography research has largely considered only the potential threats of Shor’s algorithm.
Baonan Wang, Xiaoting Yang, Dan Zhang
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Scalable set of reversible parity gates for integer factorization [PDF]
Communications Physics, 2023 Classical microprocessors operate on irreversible gates, that, when combined with AND, half-adder and full-adder operations, execute complex tasks such as multiplication of integers.
Martin Lanthaler +2 more
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The Integer Factorization Algorithm With Pisano Period
IEEE Access, 2019 Large integer factorization is one of the basic issues in number theory and is the subject of this paper. Our research shows that the Pisano period of the product of two prime numbers (or an integer multiple of it) can be derived from the two prime ...
Liangshun Wu, H. J. Cai, Zexi Gong
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Integer factorization with a neuromorphic sieve [PDF]
2017 IEEE International Symposium on Circuits and Systems (ISCAS), 2017 The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence.
John V. Monaco, Manuel M. Vindiola
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On the Tower Factorization of Integers [PDF]
The American Mathematical MonthlyUnder the fundamental theorem of arithmetic, any integer $n>1$ can be uniquely written as a product of prime powers $p^a$; factoring each exponent $a$ as a product of prime powers $q^b$, and so on, one will obtain what is called the tower factorization of $n$.
Jean–Marie De Koninck +1 more
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Automatic Extraction and Compensation of P-Bit Device Variations in Large Array Utilizing Boltzmann Machine Training [PDF]
MicromachinesA Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the ...
Bolin Zhang +6 more
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