The problem of factoring large numbers has been much studied in recent years because of its importance in cryptography. Find out about one of the following factorization methods and write a short description of how it works. (Information on these methods is available in number theory textbooks and on the web.)
(a) Pollard’s ρ method (that is the Greek letter rho)
(b) Pollard’s p − 1 method
(c) The quadratic sieve factorization method
(d) Lenstra’s elliptic curve factorization method
(e) The number field sieve
(The last two methods require advanced ideas, so you will need to learn about elliptic curves or number fields before you can understand them.) The number field sieve is the most powerful factorization method currently known. It is capable of factoring numbers of more than 150 digits.
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