Abstract
At the time when RSA was invented in 1977, factoring integers with as few as 80 decimal digits was intractable. The first major breakthrough was quadratic sieve, a relatively simple factoring algorithm invented by Carl Pomerance in 1981, which can factor numbers up to 100 digits and more. It's still the best-known method for numbers under 110 digits or so; for larger numbers, the general number field sieve (GNFS) is now used. However, the general number field sieve is extremely complicated, for even the most basic implementation. However, GNFS is based on the same fundamental ideas as quadratic sieve. The fundamentals of the Quadratic Sieve algorithm are discussed in this chapter.
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