x = 11234;
y = 52342;
X = Reverse[IntegerDigits[x]];
Y = Reverse[IntegerDigits[y]];
n = Length[X] + Length[Y] + 1;
X = PadRight[X, n];
Y = PadRight[Y, n];
U = InverseFourier[X];
V = InverseFourier[Y];
Q = Round[Re[Fourier[U*V]*Sqrt[n]]];
Sum[Q[[k]] 10^(k - 1), {k, n}]
x*y

Update October 20, 2019:
A news story
in Popular mechanics featuring David Harvey who had been a graduate student here at Harvard.
Was also discussed in Slashdot.