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You have to be careful doing this. If your blur tool happens to be of the variety that conserves total brightness (i.e. the blurring is accomplished by 2D convolution with a kernel that has a volume of 1, so sum of all pixel values remains constant before and after blurring), it can still be dictionary attacked pretty easily no matter which random ways you blur, since each digit in the cheque font probably has a different amount of total black area, and your blurring preserves that information perfectly.

If you blur tool is of the variety that doesn't conserve total brightness, such as most "smudge" tools, and you use human randomness to blur it, then it would probably be pretty hard to reverse.

I still recommend cutting out the sensitive information rather than blurring it, just to be safe. Also, leave a generous margin, (1) to avoid giving information about length, and (2) because lossy compressors may have left tiny artifacts of the sensitive information in the areas around it.

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