Two Fast Parallel Gcd Algorithms Of Many Integers

We present two new parallel algorithms which compute the GCD of n integers of O(n) bits in O(n/ logn) time with O(n(2+epsilon)) processors in the worst case, for any epsilon > 0 in CRCW PRAM model. More generally, we prove that computing the GCD of m integers of O(n) bits can be achieved in O(n/ logn)parallel time with O(mn(1+epsilon)) processors, for any 2 <=( )m <= n(3/2)/ log n, i.e. the parallel time does not depend on the number m of integers considered in this range. We suggest an extended GCD version for many integers as well as an algorithm to solve linear Diophantine equations.