Question

How and why do 7- and 35-pass erases work? Shouldn’t a simple rewrite with all zeroes be enough?

Answer 1

I’d never heard of the 35-part erase: http://en.wikipedia.org/wiki/Gutmann_method

The Gutmann method is an algorithm for securely erasing the contents of computer hard drives, such as files. Devised by Peter Gutmann and Colin Plumb, it does so by writing a series of 35 patterns over the region to be erased. The selection of patterns assumes that the user doesn’t know the encoding mechanism used by the drive, and so includes patterns designed specifically for three different types of drives. A user who knows which type of encoding the drive uses can choose only those patterns intended for their drive. A drive with a different encoding mechanism would need different patterns. Most of the patterns in the Gutmann method were designed for older MFM/RLL encoded disks. Relatively modern drives no longer use the older encoding techniques, making many of the patterns specified by Gutmann superfluous.[1]

Also interesting:

One standard way to recover data that has been overwritten on a hard drive is to capture the analog signal which is read by the drive head prior to being decoded. This analog signal will be close to an ideal digital signal, but the differences are what is important. By calculating the ideal digital signal and then subtracting it from the actual analog signal it is possible to ignore that last information written, amplify the remaining signal and see what was written before.