Tossup

Hendrik Lenstra developed an algorithm for performing this task using elliptic curves, (-5[1])whose two-stage (-5[1])variant is analogous to one named after Pollard. Dixon’s method for performing this task (-5[1])forms the basis of an algorithm for performing this task using continued fractions. In 1994, a quantum algorithm for performing (-5[1])this (10[1])task in polynomial time was developed by Peter Shor. (10[1]-5[1])RSA encryption relies on the difficulty of performing this task for large integers. (10[2])For an integer n, a brute force method for performing this task checks all the integers from 1 to the square root of n. For 10 points, name this task that decomposes an integer into a product (10[1])of smaller integers. ■END■ (10[2])

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