English

DTIC ADA047709: Factoring Numbers in 0 (log n) Arithmetic Steps,

A non-trivial factor of a composite number n can be found by performing arithmetic steps in a number proportional to the number of bits in n, and thus there are extremely short straight-line factoring programs. However, this theoretical result does not imply that natural numbers can be factored in polynomial time in the Turing-Machine model of complexity, since the numbers operated on can be as big as 2 to the power c n-squared, thus requiring exponentially many bit operations.

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