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Pages in category "Number theoretic algorithms" The following 25 pages are in this category, out of 25 total. This list may not reflect recent changes. A.
In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry. [1]
Pollard's rho algorithm for logarithms is an algorithm introduced ... b i−1) x 2i−1 ← f(x 2i−2 ... The algorithm is implemented by the following C++ ...
The Schönhage–Strassen algorithm is based on the fast Fourier transform (FFT) method of integer multiplication. This figure demonstrates multiplying 1234 × 5678 = 7006652 using the simple FFT method. Base 10 is used in place of base 2 w for illustrative purposes. Schönhage (on the right) and Strassen (on the left) playing chess in ...
This category has the following 2 subcategories, out of 2 total. A. Computer arithmetic algorithms (3 C, 20 P) N. Number theoretic algorithms (2 C, 25 P)
The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. [ 1 ] [ 2 ] Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p , it is in fact a ...
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv n{\pmod {p}},} where x , n ∈ F p {\displaystyle x,n\in \mathbf {F} _{p}} , so n is the square of x , and where p {\displaystyle p} is an odd prime .
In number theory, Dixon's factorization method (also Dixon's random squares method [1] or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike for other factor base methods, its run-time bound comes with a rigorous proof that does not rely on conjectures about the smoothness ...