how to scramble pixels of specific part of image

Can anyone suggest a way to scramble all the pixels within a circle of an image?

I am using this code to scramble all the pixels within an image:

img=imread(SpecificStimuli);
rmig=reshape(img,[],size(img,3));
n=size(rmig,1);
simg=rmig(randperm(n),:);
simg=reshape(simg,size(img));
imwrite(simg, OutputName);

But, rather than scrambling all the pixels I would like to only scramble the pixels within this oval of the original image:

Radius=608; Centered at: Center Row=676 Center Column=642