Round 6: Tossup 14

Hendrik Lenstra developed an algorithm for performing this task using elliptic curves, (-5[1])whose two-stage variant is analogous to one named after Pollard. Dixon’s method for performing this task forms the basis of an algorithm for performing this task using continued fractions. In 1994, a quantum algorithm for performing this task (-5[1])in polynomial time was developed by Peter Shor. (-5[1])RSA encryption relies on the difficulty (-5[1])of performing this task for large integers. For an integer n, a brute force method for performing this task checks all the integers from 1 to the square root (10[1])of n. For 10 points, name this task that decomposes an integer into a product of smaller integers. ■END■ (10[4])

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Summary