You've likely seen images with portions blurred out to protect text or numbers--stuff like credit card numbers or names on a document. It's not as secure as this might sound.
Dheera Venkatraman illustrates why this is a bad idea with a blurred check image example and a script, which he says is pretty trivial to create and apply. Algorithms running through the blurred image pixels can compute the nearest-shape numbers or text characters. In essence, all you're doing when using simple mosaics to blur images is obscure the information--but it's better to completely remove the information by, say, putting a black box over it or deleting it in Photoshop.
I've also seen software (though I can't find it for the life of me now) that does a really good job of undoing blurring on an image. That's an even easier way for someone to get to the information you're trying to hide by blurring.
Just a word to the wise.
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