How to center a kernel when using FFT for circular convolution.

I've got Conway's Game of Life running, using conv2. In order to make the convolution circular, I apply conv2 to [m m m; m m m; m m m] where 'm' is the grid of 1 and 0s.

I would like to get this to work with FFT, since I understand that ifft2(fft2(m).*fft2(k)) should give the circular convolution.

However it seems that padding kernel, k, with zeros is not enough, and that I need to do some kind of centering to get the same results as with conv2.

I found some code that does what I want on the file exchange, but I don't understand why the kernel is recentered 'so that y(1,1) corresponds to mask centred on A(1,1)'. The code seems to pad k with zeros, then apply a circular shift. Maybe someone could explain this?

Code (edited) from http://www.mathworks.com/matlabcentral/fileexchange/31012-2-d-convolution-using-the-fft (David Young):

%%Compute circular conv with conv2:
rng(1)

A = randi(5,5);
K = randi(5,5);

A2 = [A,A,A;A,A,A;A,A,A];

convTwo = conv2(A2,K,'same');
convTwo = convTwo(6:10,6:10);

%%Same result with FFT:

Asize = size(A);
Ksize = size(K);

% zero pad K
if any(Ksize < Asize) 
    K = exindex(K, 1:Asize(1), 1:Asize(2), {0});
end

% recentre K so that y(1,1) corresponds to mask centred on A(1,1)
Kc = 1 + floor(Ksize/2);
Ke = Kc + Asize - 1;
K = exindex(K, Kc(1):Ke(1), Kc(2):Ke(2), 'circular');

y = ifft2(fft2(A) .* fft2(K));   % central operation, basic form

% trim to correct output size
if ~isequal(Asize, size(y))
    y = y(1:Asize(1), 1:Asize(2));
end

% y = convTWO