The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerably simpler than the number field sieve. It is a general-purpose factorization algorithm, meaning that its running time depends solely on the size of the integer to be factored, and not on special structure or properties. It was invented by Carl Pomerance in 1981 as an improvement to Schroeppel's linear sieve.
Read more about Quadratic Sieve: Basic Aim, The Approach, The Algorithm, How QS Optimizes Finding Congruences, Example of Basic Sieve, Multiple Polynomials, Parameters From Realistic Example, Factoring Records, Implementations
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