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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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Research on Quantum Annealing Integer Factorization Based on Different Columns [PDF]
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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New integer factorizations [PDF]
Mathematics of Computation, 1983 New factorizations of Fibonacci numbers, Lucas numbers, and numbers of the form 2 n ± 1 {2^n} \pm 1 are presented together with the strategy (a combination of known factorization methods) used to obtain them.
Thorkil Naur
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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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On the Tower Factorization of Integers [PDF]
The American Mathematical Monthly, 2023 Under 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 $n$.
De Koninck, Jean-Marie +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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A novel approach to explore common prime divisor graphs and their degree based topological descriptor. [PDF]
PLoS ONEFor the construction of a common prime divisor graph, we consider an integer [Formula: see text] with its prime factorization, where [Formula: see text] are distinct primes and [Formula: see text] are fixed positive integers. Every divisor of the integer
Ali N A Koam +3 more
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Deterministic Integer Factorization Algorithms [PDF]
, 2013 A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced integer $N = pq$, where $p$ and $q$ are primes, the algorithm factors the integer in polynomial time $O(\log(N)^c)$,
N. A. Carella
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Integer factorization algorithms
, 2020 The mathematical area of integer factorization has gone a long way since the early days of Pierre de Fermat, and with simpler algorithms developed in the last century such as the Trial division and Pollards rho algorithm to the more complex method of the Quadratic sieve algorithm (QS), we have now arrived at the General Number Field Sieve (GNFS) which ...
Joakim Nilsson
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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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