Asymptotically Fast Factorization of Integers
نویسنده
چکیده
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 0(exp{ /ftln n In In n)1/2}) for some constant ß > 0. Asymptotically, this algorithm is much faster than any previously analyzed algorithm for factoring integers; earlier algorithms have all required 0(n°) operations where a > 1/5.
منابع مشابه
The University of Western Ontario the School of Graduate And
The factor refinement principle turns a partial factorization of integers (or polynomials) into a more complete factorization represented by basis elements and exponents, with basis elements that are pairwise coprime. There are lots of applications of this refinement technique such as simplifying systems of polynomial inequations and, more generally, speeding up certain algebraic algorithms by ...
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