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P System Design for Integer Factorization
Applied Sciences (Switzerland), 2023 Membrane computing is a natural computing branch inspired by the structure of biological cells. The mathematical abstract model of a membrane computing system is called a P System, which is one of the main topics in membrane computing research for the ...
Hai Nan, Mingqiang Zhou, Xiaoyang Liu
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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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Spectral Signatures of Prime Factorization [PDF]
EntropyWe present a protocol for integer factorization for all integers N below a certain cut-off Λ=2d, grounded in the theory of quantum measurement. In this framework, the factorization of an integer N≤Λ is achieved in a number of steps equal to the total ...
Giuseppe Mussardo, Andrea Trombettoni
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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, Hengjin Cai
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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
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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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Remark on Laquer's theorem for circulant determinants [PDF]
International Journal of Group Theory, 2023 Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of
Naoya Yamaguchi, Yuka Yamaguchi
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Acceleration of Wheel Factoring Techniques
Mathematics, 2023 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 ...
Alaa M. Zaki +4 more
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On the Number of Factorizations of an Integer [PDF]
Integers, 2011 AbstractLet ƒ(
R. Balasubramanian, Florian Luca
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On oracle factoring of integers
Journal of Complexity, 2023 We present an oracle factorisation algorithm which finds a nontrivial factor of almost all positive integers $n$ based on the knowledge of the number of points on certain elliptic curves in residue rings modulo $n$.
Andrzej Dabrowski +2 more
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