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When erasing a drive with Disk Utility, you have a couple options. An insecure wipe, a single pass of zeroes, a "DOE-compliant" 3 pass, and a DOD (Department of Defense) 7 pass.

DOE doesn't stand for Department of Energy, does it? That sounds silly.

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DOE is a method to wipe disks, developed by Department of Energy as part in their manual to ensure the confidentiality of Department of Energy information.

From macs.about.com :

When Disk Utility uses the DOE-compliant 3-pass secure erase, it will write two passes of random data and then a single pass of a known data pattern. This will take anywhere from a day to a week or more, depending on the size of the drive. You can run this stress test in the background while you use your Mac for other activities.

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The answer is correct, but the thing about “3-pass” secure is the whole methodology of going over a disk multiple times is based on old hard drive technology where sectors & tracks were so wide there was a risk of residual data being still in place. Meaning with the right tools to amplify or slow down the drive, one could recreate data. But modern hard drives all have such tight tracking & multiple platters a simple zeroing out of data once is enough. – JakeGould Feb 16 '13 at 7:20
    
Here's an article on HowToGeek backing up JakeGould's claim that only one pass is required. – hunse Dec 18 '15 at 0:45

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