I think it's shorthand English for saying: Rather than doing n^2 comparisons (ie. every key individually GCD compared against every other key individually = (n

I think it's shorthand English for saying: Rather than doing n^2 comparisons (ie. every key individually GCD compared against every other key individually = (n keys)x(n-1 other keys) combinations), you can instead do n total GCD comparisons - every key GCD factored a single time against <large product of every other key> (which works out to (n keys)x(1 big product) GCD comparisons)