However, a big-Oh of log n cubed quantum algorithm fordoing this named for Shor is fast enough for very large products of primes, which would break RSA encryption.
One algorithm for doing this uses exponent vectors and bitwise adds the values of those vectors mod2; that algorithm, for some input n, multiplies squares and their remainders mod n together to find acongruence of squares mod n in a manner that improves upon Dixon's method for doing this. The periodfindingsub-problem for this task is possible using a superposition of states. The most efficient classicalalgorithm for this is the (*) general number field sieve. However, a big-Oh of log n cubed quantum algorithm fordoing this named for Shor is fast enough for very large products of primes, which would break RSA encryption. For10 points, name this procedure which, for a number of the form a squared minus b squared results in a plus b and aminus b.
One algorithm for doing this uses exponent vectors and bitwise adds the values of those vectors mod2; that algorithm, for some input n, multiplies squares and their remainders mod n together to find acongruence of squares mod n in a manner that improves upon Dixon's method for doing this.
integer factorization [accept prime factorization]