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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]
Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic ...
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10 100. Heuristically , its complexity for factoring an integer n (consisting of ⌊log 2 n ⌋ + 1 bits) is of the form
Euclidean algorithm; Coprime; Euclid's lemma; Bézout's identity, Bézout's lemma; Extended Euclidean algorithm; Table of divisors; Prime number, prime power. Bonse's inequality; Prime factor. Table of prime factors; Formula for primes; Factorization. RSA number; Fundamental theorem of arithmetic; Square-free. Square-free integer; Square-free ...
Integer factorization algorithms include the Elliptic Curve Method, the Quadratic sieve and the Number field sieve. Algebraic number theory; Magma includes the KANT computer algebra system for comprehensive computations in algebraic number fields. A special type also allows one to compute in the algebraic closure of a field. Module theory and ...
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
The NTF funds the Selfridge prize awarded at each Algorithmic Number Theory Symposium (ANTS) [2] [3] and is a regular supporter of several conferences and organizations in number theory, including the Canadian Number Theory Association (CNTA), [4] [5] Women in Numbers (WIN), and the West Coast Number Theory (WCNT) conference. [1]
This category deals with algorithms in number theory, especially primality testing and similar. See also: Category:Computer arithmetic algorithms Subcategories