Exponential Factoring Algorithms

For almost all of the multicentury history of factoring, the only algorithms available were exponential, namely, the running time was, in the worst case, a fixed positive power of the number being factored. But in the early 1970s, subexponential factoring algorithms began to come “on line.” These methods, discussed in the next chapter, have their running time to factor n bounded by an expression of the form n°(1) One might wonder, then, why the current chapter exists in this book. We have several reasons for including it.