For instance, the FAST paper found that, in most cases, performing a full overwrite of all of the data on the SSD twice was enough to sanitize the disk drive, but there were a few exceptional cases where some of the data still remained present. There may be other reasons not to want to perform repeated overwrites of the full drive: it is very slow, and it may reduce the subsequent lifetime of the drive....
Moreover, the FAST paper found that standard utilities for sanitizing individual files were highly unreliable on SSDs: often a large fraction of the data remained present somewhere on the drive. Therefore, you should assume there is no reliable way to securely erase individual files on a SSD; you need to sanitize the whole drive, as an entire unit.
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The most reliable way to securely erase an entire SSD is to use the ATA Secure Erase command. However, this is not foolproof. The FAST paper found that most SSDs implement this correctly, but not all. In particular, 8 of the 12 SSDs they studied supported ATA Secure Erase, and 4 did not. Of the 8 that did support it, 3 had a buggy implementation. 1 buggy implementation was really bad: it reported success, but actually left the data laying around.