An Improvement to the Number Field Sieve

Mathematics – Number Theory

Scientific paper

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9 pages

Scientific paper

We improve the "sieve" part of the number field sieve used in factoring
integer and computing discrete logarithm. The runtime of our method is shorter
than that of existing methods. Under some reasonable assumptions, we prove that
it is less than two-thirds of the running time of the algorithm used before
asymptotically with probability gr

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