Abstract

. bu are given two integers, a and b, and ' asked to compute their product, ab = c. An algorithm for this task is taught in the early primary grades. For those of us who were day dreaming in class that day, a computer implemen tation of the algorithm yields an answer in micro seconds, even if a and b are rather large numbers, say 60 or 70 decimal digits. Now suppose you are given the number c and asked to discover the two factors a and b, which you may assume are prime numbers (that is, they have no factors of their own, apart from 1 and themselves). This is a much harder assignment. If a and b are in the 60-digit range, so that c has more than 120 digits, finding the factors is definitely not elementary-school homework. The dramatic asymmetry between multiplica tion and factorization is the basis of an important cryptographic system: the RSA public-key cryptosystem, named for the initials of its inventors,

Citations