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. (-5[1])L-notation was developed to describe the sub-exponential runtime of methods for this task like GNFS (15[1])and Lenstra’s method of (*) elliptic (-5[1])curves. This task, which is easily (10[1])performed (10[1])on B-smooth inputs, can be accomplished using Pollard’s rho algorithm or the quadratic sieve. Theoretically, (10[1])many public-key cryptosystems can be broken with a polynomial (-5[1])time (10[1])quantum algorithm (10[1])for this task discovered by Peter Shor. For 10 points, trial division (10[1])can be used to accomplish what task in which an integer is decomposed into primes? (10[2])■END■