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 (-5[1])of methods (15[1])for this task like GNFS (15[1])and Lenstra’s method of (*) elliptic (-5[1])curves. (10[2])This (-5[1])task, (10[2]-5[1])which is easily (10[2])performed (10[2])on (-5[2])B-smooth inputs, (-5[1])can be accomplished using Pollard’s rho (10[1])algorithm (10[1])or the quadratic (10[1])sieve. (10[1])Theoretically, (10[1])many public-key (-5[1])cryptosystems (10[6]-5[1])can (10[1])be broken (10[2])with a polynomial (10[1]-5[1])time (10[1])quantum algorithm (10[1]-5[1])for this task (10[3])discovered by Peter (10[1])Shor. (10[1])For (10[1])10 points, trial division (10[1])can be used to accomplish what task (10[1])in which an integer is decomposed into primes? (10[3])■END■ (10[8])