Postprocessing of “general-case” methods for this task often requires finding the kernel of a sparse matrix using the block Lanczos (“LAHN-chohsh”) algorithm. Richard Brent added a “birthday paradox” phase to an algorithm for this task. L-notation was developed to describe the sub-exponential runtime of methods for this task like GNFS and Lenstra’s method of (*) elliptic curves. This task, which is easily performed (10[1])on B-smooth inputs, (-5[1])can be accomplished using Pollard’s rho algorithm or the quadratic sieve. Theoretically, many public-key cryptosystems (10[2])can be broken (10[1])with a polynomial time quantum algorithm (-5[1])for this task (10[1])discovered by Peter Shor. For 10 points, trial division can be used to accomplish what task in which an integer is decomposed into primes? ■END■ (10[2])