The following paper was originally published in the
                      Proceedings of the Sixth USENIX
                             Security Symposium
                      San Jose, California, July 1996.
                                      
                                      
                                      
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     _________________________________________________________________
                                      
        Secure Deletion of Data from Magnetic and Solid-State Memory
                                      
                                      
                               Peter Gutmann
                       Department of Computer Science
                           University of Auckland
                         pgut001@cs.auckland.ac.nz
                                      
Abstract

   With the use of increasingly sophisticated encryption systems, an
   attacker wishing to gain access to sensitive data is forced to look
   elsewhere for information. One avenue of attack is the recovery of
   supposedly erased data from magnetic media or random-access memory.
   This paper covers some of the methods available to recover erased data
   and presents schemes to make this recovery significantly more
   difficult.
   
1. Introduction

   Much research has gone into the design of highly secure encryption
   systems intended to protect sensitive information. However work on
   methods of securing (or at least safely deleting) the original
   plaintext form of the encrypted data against sophisticated new
   analysis techniques seems difficult to find. In the 1980's some work
   was done on the recovery of erased data from magnetic media [1] [2]
   [3], but to date the main source of information is government
   standards covering the destruction of data. There are two main
   problems with these official guidelines for sanitizing media. The
   first is that they are often somewhat old and may predate newer
   techniques for both recording data on the media and for recovering the
   recorded data. For example most of the current guidelines on
   sanitizing magnetic media predate the early-90's jump in recording
   densities, the adoption of sophisticated channel coding techniques
   such as PRML, the use of magnetic force microscopy for the analysis of
   magnetic media, and recent studies of certain properties of magnetic
   media recording such as the behaviour of erase bands. The second
   problem with official data destruction standards is that the
   information in them may be partially inaccurate in an attempt to fool
   opposing intelligence agencies (which is probably why a great many
   guidelines on sanitizing media are classified). By deliberately
   under-stating the requirements for media sanitization in
   publicly-available guides, intelligence agencies can preserve their
   information-gathering capabilities while at the same time protecting
   their own data using classified techniques.
   
   This paper represents an attempt to analyse the problems inherent in
   trying to erase data from magnetic disk media and random-access memory
   without access to specialised equipment, and suggests methods for
   ensuring that the recovery of data from these media can be made as
   difficult as possible for an attacker.
   
2. Methods of Recovery for Data stored on Magnetic Media

   Magnetic force microscopy (MFM) is a recent technique for imaging
   magnetization patterns with high resolution and minimal sample
   preparation. The technique is derived from scanning probe microscopy
   (SPM) and uses a sharp magnetic tip attached to a flexible cantilever
   placed close to the surface to be analysed, where it interacts with
   the stray field emanating from the sample. An image of the field at
   the surface is formed by moving the tip across the surface and
   measuring the force (or force gradient) as a function of position. The
   strength of the interaction is measured by monitoring the position of
   the cantilever using an optical interferometer or tunnelling sensor.
   
   Magnetic force scanning tunneling microscopy (STM) is a more recent
   variant of this technique which uses a probe tip typically made by
   plating pure nickel onto a prepatterned surface, peeling the resulting
   thin film from the substrate it was plated onto and plating it with a
   thin layer of gold to minimise corrosion, and mounting it in a probe
   where it is placed at some small bias potential (typically a few
   tenths of a nanoamp at a few volts DC) so that electrons from the
   surface under test can tunnel across the gap to the probe tip (or vice
   versa). The probe is scanned across the surface to be analysed as a
   feedback system continuously adjusts the vertical position to maintain
   a constant current. The image is then generated in the same way as for
   MFM [4] [5]. Other techniques which have been used in the past to
   analyse magnetic media are the use of ferrofluid in combination with
   optical microscopes (which, with gigabit/square inch recording density
   is no longer feasible as the magnetic features are smaller than the
   wavelength of visible light) and a number of exotic techniques which
   require significant sample preparation and expensive equipment. In
   comparison, MFM can be performed through the protective overcoat
   applied to magnetic media, requires little or no sample preparation,
   and can produce results in a very short time.
   
   Even for a relatively inexperienced user the time to start getting
   images of the data on a drive platter is about 5 minutes. To start
   getting useful images of a particular track requires more than a
   passing knowledge of disk formats, but these are well-documented, and
   once the correct location on the platter is found a single image would
   take approximately 2-10 minutes depending on the skill of the operator
   and the resolution required. With one of the more expensive MFM's it
   is possible to automate a collection sequence and theoretically
   possible to collect an image of the entire disk by changing the MFM
   controller software.
   
   There are, from manufacturers sales figures, several thousand SPM's in
   use in the field today, some of which have special features for
   analysing disk drive platters, such as the vacuum chucks for standard
   disk drive platters along with specialised modes of operation for
   magnetic media analysis. These SPM's can be used with sophisticated
   programmable controllers and analysis software to allow automation of
   the data recovery process. If commercially-available SPM's are
   considered too expensive, it is possible to build a reasonably capable
   SPM for about US$1400, using a PC as a controller [6].
   
   Faced with techniques such as MFM, truly deleting data from magnetic
   media is very difficult. The problem lies in the fact that when data
   is written to the medium, the write head sets the polarity of most,
   but not all, of the magnetic domains. This is partially due to the
   inability of the writing device to write in exactly the same location
   each time, and partially due to the variations in media sensitivity
   and field strength over time and among devices.
   
   In conventional terms, when a one is written to disk the media records
   a one, and when a zero is written the media records a zero. However
   the actual effect is closer to obtaining a 0.95 when a zero is
   overwritten with a one, and a 1.05 when a one is overwritten with a
   one. Normal disk circuitry is set up so that both these values are
   read as ones, but using specialised circuitry it is possible to work
   out what previous "layers" contained. The recovery of at least one or
   two layers of overwritten data isn't too hard to perform by reading
   the signal from the analog head electronics with a high-quality
   digital sampling oscilloscope, downloading the sampled waveform to a
   PC, and analysing it in software to recover the previously recorded
   signal. What the software does is generate an "ideal" read signal and
   subtract it from what was actually read, leaving as the difference the
   remnant of the previous signal. Since the analog circuitry in a
   commercial hard drive is nowhere near the quality of the circuitry in
   the oscilloscope used to sample the signal, the ability exists to
   recover a lot of extra information which isn't exploited by the hard
   drive electronics (although with newer channel coding techniques such
   as PRML (explained further on) which require extensive amounts of
   signal processing, the use of simple tools such as an oscilloscope to
   directly recover the data is no longer possible).
   
   Using MFM, we can go even further than this. During normal readback, a
   conventional head averages the signal over the track, and any remnant
   magnetization at the track edges simply contributes a small percentage
   of noise to the total signal. The sampling region is too broad to
   distinctly detect the remnant magnetization at the track edges, so
   that the overwritten data which is still present beside the new data
   cannot be recovered without the use of specialised techniques such as
   MFM or STM (in fact one of the "official" uses of MFM or STM is to
   evaluate the effectiveness of disk drive servo-positioning mechanisms)
   [7]. Most drives are capable of microstepping the heads for internal
   diagnostic and error recovery purposes (typical error recovery
   strategies consist of rereading tracks with slightly changed data
   threshold and window offsets and varying the head positioning by a few
   percent to either side of the track), but writing to the media while
   the head is off-track in order to erase the remnant signal carries too
   much risk of making neighbouring tracks unreadable to be useful (for
   this reason the microstepping capability is made very difficult to
   access by external means).
   
   These specialised techniques also allow data to be recovered from
   magnetic media long after the read/write head of the drive is
   incapable of reading anything useful. For example one experiment in AC
   erasure involved driving the write head with a 40 MHz square wave with
   an initial current of 12 mA which was dropped in 2 mA steps to a final
   level of 2 mA in successive passes, an order of magnitude more than
   the usual write current which ranges from high microamps to low
   milliamps. Any remnant bit patterns left by this erasing process were
   far too faint to be detected by the read head, but could still be
   observed using MFM [8].
   
   Even with a DC erasure process, traces of the previously recorded
   signal may persist until the applied DC field is several times the
   media coercivity [9].
   
   Deviations in the position of the drive head from the original track
   may leave significant portions of the previous data along the track
   edge relatively untouched. Newly written data, present as wide
   alternating light and dark bands in MFM and STM images, are often
   superimposed over previously recorded data which persists at the track
   edges. Regions where the old and new data coincide create continuous
   magnetization between the two. However, if the new transition is out
   of phase with the previous one, a few microns of erase band with no
   definite magnetization are created at the juncture of the old and new
   tracks. The write field in the erase band is above the coercivity of
   the media and would change the magnetization in these areas, but its
   magnitude is not high enough to create new well- defined transitions.
   One experiment involved writing a fixed pattern of all 1's with a bit
   interval of 2.5 m, moving the write head off-track by approximately
   half a track width, and then writing the pattern again with a
   frequency slightly higher than that of the previously recorded track
   for a bit interval of 2.45 m to create all possible phase differences
   between the transitions in the old and new tracks. Using a 4.2 m wide
   head produced an erase band of approximately 1 m in width when the
   old and new tracks were 180 out of phase, dropping to almost nothing
   when the two tracks were in-phase. Writing data at a higher frequency
   with the original tracks bit interval at 0.5 m and the new tracks bit
   interval at 0.49 m allows a single MFM image to contain all possible
   phase differences, showing a dramatic increase in the width of the
   erase band as the two tracks move from in-phase to 180 out of phase
   [10].
   
   In addition, the new track width can exhibit modulation which depends
   on the phase relationship between the old and new patterns, allowing
   the previous data to be recovered even if the old data patterns
   themselves are no longer distinct. The overwrite performance also
   depends on the position of the write head relative to the originally
   written track. If the head is directly aligned with the track,
   overwrite performance is relatively good; as the head moves offtrack,
   the performance drops markedly as the remnant components of the
   original data are read back along with the newly-written signal. This
   effect is less noticeable as the write frequency increases due to the
   greater attenuation of the field with distance [11].
   
   When all the above factors are combined it turns out that each track
   contains an image of everything ever written to it, but that the
   contribution from each "layer" gets progressively smaller the further
   back it was made. Intelligence organisations have a lot of expertise
   in recovering these palimpsestuous images.
   
3. Erasure of Data stored on Magnetic Media

   The general concept behind an overwriting scheme is to flip each
   magnetic domain on the disk back and forth as much as possible (this
   is the basic idea behind degaussing) without writing the same pattern
   twice in a row. If the data was encoded directly, we could simply
   choose the desired overwrite pattern of ones and zeroes and write it
   repeatedly. However, disks generally use some form of run-length
   limited (RLL) encoding, so that the adjacent ones won't be written.
   This encoding is used to ensure that transitions aren't placed too
   closely together, or too far apart, which would mean the drive would
   lose track of where it was in the data.
   
   To erase magnetic media, we need to overwrite it many times with
   alternating patterns in order to expose it to a magnetic field
   oscillating fast enough that it does the desired flipping of the
   magnetic domains in a reasonable amount of time. Unfortunately, there
   is a complication in that we need to saturate the disk surface to the
   greatest depth possible, and very high frequency signals only "scratch
   the surface" of the magnetic medium. Disk drive manufacturers, in
   trying to achieve ever-higher densities, use the highest possible
   frequencies, whereas we really require the lowest frequency a disk
   drive can produce. Even this is still rather high. The best we can do
   is to use the lowest frequency possible for overwrites, to penetrate
   as deeply as possible into the recording medium.
   
   The write frequency also determines how effectively previous data can
   be overwritten due to the dependence of the field needed to cause
   magnetic switching on the length of time the field is applied. Tests
   on a number of typical disk drive heads have shown a difference of up
   to 20 dB in overwrite performance when data recorded at 40 kFCI (flux
   changes per inch), typical of recent disk drives, is overwritten with
   a signal varying from 0 to 100 kFCI. The best average performance for
   the various heads appears to be with an overwrite signal of around 10
   kFCI, with the worst performance being at 100 kFCI [12]. The track
   write width is also affected by the write frequency - as the frequency
   increases, the write width decreases for both MR and TFI heads. In
   [13] there was a decrease in write width of around 20% as the write
   frequency was increased from 1 to 40 kFCI, with the decrease being
   most marked at the high end of the frequency range. However, the
   decrease in write width is balanced by a corresponding increase in the
   two side- erase bands so that the sum of the two remains nearly
   constant with frequency and equal to the DC erase width for the head.
   The media coercivity also affects the width of the write and erase
   bands, with their width dropping as the coercivity increases (this is
   one of the explanations for the ever-increasing coercivity of newer,
   higher-density drives).
   
   To try to write the lowest possible frequency we must determine what
   decoded data to write to produce a low-frequency encoded signal.
   
   In order to understand the theory behind the choice of data patterns
   to write, it is necessary to take a brief look at the recording
   methods used in disk drives. The main limit on recording density is
   that as the bit density is increased, the peaks in the analog signal
   recorded on the media are read at a rate which may cause them to
   appear to overlap, creating intersymbol interference which leads to
   data errors. Traditional peak detector read channels try to reduce the
   possibility of intersymbol interference by coding data in such a way
   that the analog signal peaks are separated as far as possible. The
   read circuitry can then accurately detect the peaks (actually the head
   itself only detects transitions in magnetisation, so the simplest
   recording code uses a transition to encode a 1 and the absence of a
   transition to encode a 0. The transition causes a positive/negative
   peak in the head output voltage (thus the name "peak detector read
   channel"). To recover the data, we differentiate the output and look
   for the zero crossings). Since a long string of 0's will make clocking
   difficult, we need to set a limit on the maximum consecutive number of
   0's. The separation of peaks is implemented as some form of
   run-length-limited, or RLL, coding.
   
   The RLL encoding used in most current drives is described by pairs of
   run-length limits (d, k), where d is the minimum number of 0 symbols
   which must occur between each 1 symbol in the encoded data, and k is
   the maximum. The parameters (d, k) are chosen to place adjacent 1's
   far enough apart to avoid problems with intersymbol interference, but
   not so far apart that we lose synchronisation.
   
   The grandfather of all RLL codes was FM, which wrote one user data bit
   followed by one clock bit, so that a 1 bit was encoded as two
   transitions (1 wavelength) while a 0 bit was encoded as one transition
   ( wavelength). A different approach was taken in modified FM (MFM),
   which suppresses the clock bit except between adjacent 0's (the
   ambiguity in the use of the term MFM is unfortunate. From here on it
   will be used to refer to modified FM rather than magnetic force
   microscopy). Taking three example sequences 0000, 1111, and 1010,
   these will be encoded as 0(1)0(1)0(1)0, 1(0)1(0)1(0)1, and
   1(0)0(0)1(0)0 (where the ()s are the clock bits inserted by the
   encoding process). The maximum time between 1 bits is now three 0 bits
   (so that the peaks are no more than four encoded time periods apart),
   and there is always at least one 0 bit (so that the peaks in the
   analog signal are at least two encoded time periods apart), resulting
   in a (1,3) RLL code. (1,3) RLL/MFM is the oldest code still in general
   use today, but is only really used in floppy drives which need to
   remain backwards-compatible.
   
   These constraints help avoid intersymbol interference, but the need to
   separate the peaks reduces the recording density and therefore the
   amount of data which can be stored on a disk. To increase the
   recording density, MFM was gradually replaced by (2,7) RLL (the
   original "RLL" format), and that in turn by (1,7) RLL, each of which
   placed less constraints on the recorded signal.
   
   Using our knowledge of how the data is encoded, we can now choose
   which decoded data patterns to write in order to obtain the desired
   encoded signal. The three encoding methods described above cover the
   vast majority of magnetic disk drives. However, each of these has
   several possible variants. With MFM, only one is used with any
   frequency, but the newest (1,7) RLL code has at least half a dozen
   variants in use. For MFM with at most four bit times between
   transitions, the lowest write frequency possible is attained by
   writing the repeating decoded data patterns 1010 and 0101. These have
   a 1 bit every other "data" bit, and the intervening "clock" bits are
   all 0. We would also like patterns with every other clock bit set to 1
   and all others set to 0, but these are not possible in the MFM
   encoding (such "violations" are used to generate special marks on the
   disk to identify sector boundaries). The best we can do here is three
   bit times between transitions, which is generated by repeating the
   decoded patterns 100100, 010010 and 001001. We should use several
   passes with these patterns, as MFM drives are the oldest,
   lowest-density drives around (this is especially true for the
   very-low-density floppy drives). As such, they are the easiest to
   recover data from with modern equipment and we need to take the most
   care with them.
   
   From MFM we jump to the next simplest case, which is (1,7) RLL.
   Although there can be as many as 8 bit times between transitions, the
   lowest sustained frequency we can have in practice is 6 bit times
   between transitions. This is a desirable property from the point of
   view of the clock-recovery circuitry, and all (1,7) RLL codes seem to
   have this property. We now need to find a way to write the desired
   pattern without knowing the particular (1,7) RLL code used. We can do
   this by looking at the way the drives error-correction system works.
   The error- correction is applied to the decoded data, even though
   errors generally occur in the encoded data. In order to make this work
   well, the data encoding should have limited error amplification, so
   that an erroneous encoded bit should affect only a small, finite
   number of decoded bits.
   
   Decoded bits therefore depend only on nearby encoded bits, so that a
   repeating pattern of encoded bits will correspond to a repeating
   pattern of decoded bits. The repeating pattern of encoded bits is 6
   bits long. Since the rate of the code is 2/3, this corresponds to a
   repeating pattern of 4 decoded bits. There are only 16 possibilities
   for this pattern, making it feasible to write all of them during the
   erase process. So to achieve good overwriting of (1,7) RLL disks, we
   write the patterns 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111,
   1000, 1001, 1010, 1011, 1100, 1101, 1110, and 1111. These patterns
   also conveniently cover two of the ones needed for MFM overwrites,
   although we should add a few more iterations of the MFM-specific
   patterns for the reasons given above.
   
   Finally, we have (2,7) RLL drives. These are similar to MFM in that an
   eight-bit-time signal can be written in some phases, but not all. A
   six-bit-time signal will fill in the remaining cracks. Using a 
   encoding rate, an eight-bit-time signal corresponds to a repeating
   pattern of 4 data bits. The most common (2,7) RLL code is shown below:
   
                       The most common (2,7) RLL Code
                    Decoded Data (2,7) RLL Encoded Data
                                  00 1000
                                  01 0100
                                 100 001000
                                 101 100100
                                 111 000100
                               1100 00001000
                               1101 00100100
                                      
   The second most common (2,7) RLL code is the same but with the
   "decoded data" complemented, which doesn't alter these patterns.
   Writing the required encoded data can be achieved for every other
   phase using patterns of 0x33, 0x66, 0xCC and 0x99, which are already
   written for (1,7) RLL drives.
   
   Six-bit-time patterns can be written using 3-bit repeating patterns.
   The all-zero and all-one patterns overlap with the (1,7) RLL patterns,
   leaving six others:
   
      001001001001001001001001
         2   4   9   2   4   9

   in binary or 0x24 0x92 0x49, 0x92 0x49 0x24 and 0x49 0x24 0x92 in hex,
   and
   
      011011011011011011011011
         6   D   B   6   D   B

   in binary or 0x6D 0xB6 0xDB, 0xB6 0xDB 0x6D and 0xDB 0x6D 0xB6 in hex.
   The first three are the same as the MFM patterns, so we need only
   three extra patterns to cover (2,7) RLL drives.
   
   Although (1,7) is more popular in recent (post-1990) drives, some
   older hard drives do still use (2,7) RLL, and with the ever-increasing
   reliability of newer drives it is likely that they will remain in use
   for some time to come, often being passed down from one machine to
   another. The above three patterns also cover any problems with
   endianness issues, which weren't a concern in the previous two cases,
   but would be in this case (actually, thanks to the strong influence of
   IBM mainframe drives, everything seems to be uniformly big-endian
   within bytes, with the most significant bit being written to the disk
   first).
   
   The latest high-density drives use methods like Partial-Response
   Maximum-Likelihood (PRML) encoding, which may be roughly equated to
   the trellis encoding done by V.32 modems in that it is effective but
   computationally expensive. PRML codes are still RLL codes, but with
   somewhat different constraints. A typical code might have (0,4,4)
   constraints in which the 0 means that 1's in a data stream can occur
   right next to 0's (so that peaks in the analog readback signal are not
   separated), the first 4 means that there can be no more than four 0's
   between 1's in a data stream, and the second 4 specifies the maximum
   number of 0's between 1's in certain symbol subsequences. PRML codes
   avoid intersymbol influence errors by using digital filtering
   techniques to shape the read signal to exhibit desired frequency and
   timing characteristics (this is the "partial response" part of PRML)
   followed by maximum- likelihood digital data detection to determine
   the most likely sequence of data bits that was written to the disk
   (this is the "maximum likelihood" part of PRML). PRML channels achieve
   the same low bit error rate as standard peak-detection methods, but
   with much higher recording densities, while using the same heads and
   media. Several manufacturers are currently engaged in moving their
   peak-detection-based product lines across to PRML, giving a 30-40%
   density increase over standard RLL channels [14].
   
   Since PRML codes don't try to separate peaks in the same way that
   non-PRML RLL codes do, all we can do is to write a variety of random
   patterns because the processing inside the drive is too complex to
   second- guess. Fortunately, these drives push the limits of the
   magnetic media much more than older drives ever did by encoding data
   with much smaller magnetic domains, closer to the physical capacity of
   the magnetic media (the current state of the art in PRML drives has a
   track density of around 6700 TPI (tracks per inch) and a data
   recording density of 170 kFCI, nearly double that of the nearest (1,7)
   RLL equivalent. A convenient side-effect of these very high recording
   densities is that a written transition may experience the write field
   cycles for successive transitions, especially at the track edges where
   the field distribution is much broader [15]. Since this is also where
   remnant data is most likely to be found, this can only help in
   reducing the recoverability of the data). If these drives require
   sophisticated signal processing just to read the most recently written
   data, reading overwritten layers is also correspondingly more
   difficult. A good scrubbing with random data will do about as well as
   can be expected.
   
   We now have a set of 22 overwrite patterns which should erase
   everything, regardless of the raw encoding. The basic disk eraser can
   be improved slightly by adding random passes before and after the
   erase process, and by performing the deterministic passes in random
   order to make it more difficult to guess which of the known data
   passes were made at which point. To deal with all this in the
   overwrite process, we use the sequence of 35 consecutive writes shown
   below:
   
                               Overwrite Data

   Pass No.    Data Written                            Encoding Scheme Targeted
      1        Random
      2        Random
      3        Random
      4        Random
      5        01010101 01010101 01010101 0x55              (1,7) RLL MFM
      6        10101010 10101010 10101010 0xAA              (1,7) RLL MFM
      7        10010010 01001001 00100100 0x92 0x49 0x24    (2,7) RLL MFM
      8        01001001 00100100 10010010 0x49 0x24 0x92    (2,7) RLL MFM
      9        00100100 10010010 01001001 0x24 0x92 0x49    (2,7) RLL MFM
     10        00000000 00000000 00000000 0x00              (1,7) RLL (2,7) RLL
     11        00010001 00010001 00010001 0x11              (1,7) RLL
     12        00100010 00100010 00100010 0x22              (1,7) RLL
     13        00110011 00110011 00110011 0x33              (1,7) RLL (2,7) RLL
     14        01000100 01000100 01000100 0x44              (1,7) RLL
     15        01010101 01010101 01010101 0x55              (1,7) RLL MFM
     16        01100110 01100110 01100110 0x66              (1,7) RLL (2,7) RLL
     17        01110111 01110111 01110111 0x77              (1,7) RLL
     18        10001000 10001000 10001000 0x88              (1,7) RLL
     19        10011001 10011001 10011001 0x99              (1,7) RLL (2,7) RLL
     20        10101010 10101010 10101010 0xAA              (1,7) RLL MFM
     21        10111011 10111011 10111011 0xBB              (1,7) RLL
     22        11001100 11001100 11001100 0xCC              (1,7) RLL (2,7) RLL
     23        11011101 11011101 11011101 0xDD              (1,7) RLL
     24        11101110 11101110 11101110 0xEE              (1,7) RLL
     25        11111111 11111111 11111111 0xFF              (1,7) RLL (2,7) RLL
     26        10010010 01001001 00100100 0x92 0x49 0x24    (2,7) RLL MFM
     27        01001001 00100100 10010010 0x49 0x24 0x92    (2,7) RLL MFM
     28        00100100 10010010 01001001 0x24 0x92 0x49    (2,7) RLL MFM
     29        01101101 10110110 11011011 0x6D 0xB6 0xDB    (2,7) RLL
     30        10110110 11011011 01101101 0xB6 0xDB 0x6D    (2,7) RLL
     31        11011011 01101101 10110110 0xDB 0x6D 0xB6    (2,7) RLL
     32        Random
     33        Random
     34        Random
     35        Random

                                      
   The MFM-specific patterns are repeated twice because MFM drives have
   the lowest density and are thus particularly easy to examine. The
   deterministic patterns between the random writes are permuted before
   the write is performed, to make it more difficult for an opponent to
   use knowledge of the erasure data written to attempt to recover
   overwritten data (in fact we need to use a cryptographically strong
   random number generator to perform the permutations to avoid the
   problem of an opponent who can read the last overwrite pass being able
   to predict the previous passes and "echo cancel" passes by subtracting
   the known overwrite data).
   
   If the device being written to supports caching or buffering of data,
   this should be disabled to ensure that physical disk writes are
   performed for each pass instead of everything but the last pass being
   lost in the buffering. For example physical disk access can be forced
   during SCSI-2 Group 1 write commands by setting the Force Unit Access
   bit in the SCSI command block (although at least one popular drive has
   a bug which causes all writes to be ignored when this bit is set -
   remember to test your overwrite scheme before you deploy it). Another
   consideration which needs to be taken into account when trying to
   erase data through software is that drives conforming to some of the
   higher-level protocols such as the various SCSI standards are
   relatively free to interpret commands sent to them in whichever way
   they choose (as long as they still conform to the SCSI specification).
   Thus some drives, if sent a FORMAT UNIT command may return immediately
   without performing any action, may simply perform a read test on the
   entire disk (the most common option), or may actually write data to
   the disk (the SCSI- 2 standard includes an initialization pattern (IP)
   option for the FORMAT UNIT command, however this is not necessarily
   supported by existing drives).
   
   If the data is very sensitive and is stored on floppy disk, it can
   best be destroyed by removing the media from the disk liner and
   burning it, or by burning the entire disk, liner and all (most floppy
   disks burn remarkably well - albeit with quantities of oily smoke -
   and leave very little residue).
   
4. Other Methods of Erasing Magnetic Media

   The previous section has concentrated on erasure methods which require
   no specialised equipment to perform the erasure. Alternative means of
   erasing media which do require specialised equipment are degaussing (a
   process in which the recording media is returned to its initial state)
   and physical destruction. Degaussing is a reasonably effective means
   of purging data from magnetic disk media, and will even work through
   most drive cases (research has shown that the aluminium housings of
   most disk drives attenuate the degaussing field by only about 2 dB
   [16]).
   
   The switching of a single-domain magnetic particle from one
   magnetization direction to another requires the overcoming of an
   energy barrier, with an external magnetic field helping to lower this
   barrier. The switching depends not only on the magnitude of the
   external field, but also on the length of time for which it is
   applied. For typical disk drive media, the short-term field needed to
   flip enough of the magnetic domains to be useful in recording a signal
   is about 1/3 higher than the coercivity of the media (the exact figure
   varies with different media types) [17].
   
   However, to effectively erase a medium to the extent that recovery of
   data from it becomes uneconomical requires a magnetic force of about
   five times the coercivity of the medium [18], although even small
   external magnetic fields are sufficient to upset the normal operation
   of a hard disk (typically a few gauss at DC, dropping to a few
   milligauss at 1 MHz). Coercivity (measured in Oersteds, Oe) is a
   property of magnetic material and is defined as the amount of magnetic
   field necessary to reduce the magnetic induction in the material to
   zero - the higher the coercivity, the harder it is to erase data from
   a medium. Typical figures for various types of magnetic media are
   given below:
   
                      Typical Media Coercivity Figures
                             Medium Coercivity
                       5.25" 360K floppy disk 300 Oe
                       5.25" 1.2M floppy disk 675 Oe
                        3.5" 720K floppy disk 300 Oe
                       3.5" 1.44M floppy disk 700 Oe
                       3.5" 2.88M floppy disk 750 Oe
                       3.5" 21M floptical disk 750 Oe
                   Older (1980's) hard disks 900-1400 Oe
                   Newer (1990's) hard disks 1400-2200 Oe
                         1/2" magnetic tape 300 Oe
                            1/4" QIC tape 550 Oe
                    8 mm metallic particle tape 1500 Oe
                     DAT metallic particle tape 1500 Oe
                                      
   US Government guidelines class tapes of 350 Oe coercivity or less as
   low-energy or Class I tapes and tapes of 350-750 Oe coercivity as
   high-energy or Class II tapes. Degaussers are available for both types
   of tapes. Tapes of over 750 Oe coercivity are referred to as Class
   III, with no known degaussers capable of fully erasing them being
   known [19], since even the most powerful commercial AC degausser
   cannot generate the recommended 7,500 Oe needed for full erasure of a
   typical DAT tape currently used for data backups.
   
   Degaussing of disk media is somewhat more difficult - even older hard
   disks generally have a coercivity equivalent to Class III tapes,
   making them fairly difficult to erase at the outset. Since
   manufacturers rate their degaussers in peak gauss and measure the
   field at a certain orientation which may not be correct for the type
   of medium being erased, and since degaussers tend to be rated by
   whether they erase sufficiently for clean rerecording rather than
   whether they make the information impossible to recover, it may be
   necessary to resort to physical destruction of the media to completely
   sanitise it (in fact since degaussing destroys the sync bytes, ID
   fields, error correction information, and other paraphernalia needed
   to identify sectors on the media, thus rendering the drive unusable,
   it makes the degaussing process mostly equivalent to physical
   destruction). In addition, like physical destruction, it requires
   highly specialised equipment which is expensive and difficult to
   obtain (one example of an adequate degausser was the 2.5 MW Navy
   research magnet used by a former Pentagon site manager to degauss a
   14" hard drive for 1 minutes. It bent the platters on the drive and
   probably succeeded in erasing it beyond the capabilities of any data
   recovery attempts [20]).
   
5. Further Problems with Magnetic Media

   A major issue which cannot be easily addressed using any standard
   software-based overwrite technique is the problem of defective sector
   handling. When the drive is manufactured, the surface is scanned for
   defects which are added to a defect list or flaw map. If further
   defects, called grown defects, occur during the life of the drive,
   they are added to the defect list by the drive or by drive management
   software. There are several techniques which are used to mask the
   defects in the defect list. The first, alternate tracks, moves data
   from tracks with defects to known good tracks. This scheme is the
   simplest, but carries a high access cost, as each read from a track
   with defects requires seeking to the alternate track and a rotational
   latency delay while waiting for the data location to appear under the
   head, performing the read or write, and, if the transfer is to
   continue onto a neighbouring track, seeking back to the original
   position. Alternate tracks may be interspersed among data tracks to
   minimise the seek time to access them.
   
   A second technique, alternate sectors, allocates alternate sectors at
   the end of the track to minimise seeks caused by defective sectors.
   This eliminates the seek delay, but still carries some overhead due to
   rotational latency. In addition it reduces the usable storage capacity
   by 1-3%.
   
   A third technique, inline sector sparing, again allocates a spare
   sector at the end of each track, but resequences the sector ID's to
   skip the defective sector and include the spare sector at the end of
   the track, in effect pushing the sectors past the defective one
   towards the end of the track. The associated cost is the lowest of the
   three, being one sector time to skip the defective sector [21].
   
   The handling of mapped-out sectors and tracks is an issue which can't
   be easily resolved without the cooperation of hard drive
   manufacturers. Although some SCSI and IDE hard drives may allow access
   to defect lists and even to mapped-out areas, this must be done in a
   highly manufacturer- and drive-specific manner. For example the SCSI-2
   READ DEFECT DATA command can be used to obtain a list of all defective
   areas on the drive. Since SCSI logical block numbers may be mapped to
   arbitrary locations on the disk, the defect list is recorded in terms
   of heads, tracks, and sectors. As all SCSI device addressing is
   performed in terms of logical block numbers, mapped-out sectors or
   tracks cannot be addressed. The only reasonably portable possibility
   is to clear various automatic correction flags in the read-write error
   recovery mode page to force the SCSI device to report read/write
   errors to the user instead of transparently remapping the defective
   areas. The user can then use the READ LONG and WRITE LONG commands
   (which allow access to sectors and extra data even in the presence of
   read/write errors), to perform any necessary operations on the
   defective areas, and then use the REASSIGN BLOCKS command to reassign
   the defective sections. However this operation requires an in-depth
   knowledge of the operation of the SCSI device and extensive changes to
   disk drivers, and more or less defeats the purpose of having an
   intelligent peripheral.
   
   The ANSI X3T-10 and X3T-13 subcommittees are currently looking at
   creating new standards for a Universal Security Reformat command for
   IDE and SCSI hard disks which will address these issues. This will
   involve a multiple-pass overwrite process which covers mapped-out disk
   areas with deliberate off-track writing. Many drives available today
   can be modified for secure erasure through a firmware upgrade, and
   once the new firmware is in place the erase procedure is handled by
   the drive itself, making unnecessary any interaction with the host
   system beyond the sending of the command which begins the erase
   process.
   
   Long-term ageing can also have a marked effect on the erasability of
   magnetic media. For example, some types of magnetic tape become
   increasingly difficult to erase after being stored at an elevated
   temperature or having contained the same magnetization pattern for a
   considerable period of time [22]. The same applies for magnetic disk
   media, with decreases in erasability of several dB being recorded
   [23]. The erasability of the data depends on the amount of time it has
   been stored on the media, not on the age of the media itself (so that,
   for example, a five-year-old freshly-written disk is no less erasable
   than a new freshly-written disk).
   
   The dependence of media coercivity on temperature can affect overwrite
   capability if the data was initially recorded at a temperature where
   the coercivity was low (so that the recorded pattern penetrated deep
   into the media), but must be overwritten at a temperature where the
   coercivity is relatively high. This is important in hard disk drives,
   where the temperature varies depending on how long the unit has been
   used and, in the case of drives with power-saving features enabled,
   how recently and frequently it has been used. However the overwrite
   performance depends not only on temperature-dependent changes in the
   media, but also on temperature-dependent changes in the read/write
   head. Thankfully the combination of the most common media used in
   current drives with various common types of read/write heads produce a
   change in overwrite performance of only a few hundredths of a decibel
   per degree over the temperature range -40C to + 40C, as changes in
   the head compensate for changes in the media [24].
   
   Another issue which needs to be taken into account is the ability of
   most newer storage devices to recover from having a remarkable amount
   of damage inflicted on them through the use of various
   error-correction schemes. As increasing storage densities began to
   lead to multiple-bit errors, manufacturers started using sophisticated
   error-correction codes (ECC's) capable of correcting multiple error
   bursts. A typical drive might have 512 bytes of data, 4 bytes of CRC,
   and 11 bytes of ECC per sector. This ECC would be capable of
   correcting single burst errors of up to 22 bits or double burst errors
   of up to 11 bits, and can detect a single burst error of up to 51 bits
   or three burst errors of up to 11 bits in length [25]. Another drive
   manufacturer quotes the ability to correct up to 120 bits, or up to 32
   bits on the fly, using 198-bit Reed-Solomon ECC [26]. Therefore even
   if some data is reliably erased, it may be possible to recover it
   using the built-in error-correction capabilities of the drive.
   Conversely, any erasure scheme which manages to destroy the ECC
   information (for example through the use of the SCSI-2 WRITE LONG
   command which can be used to write to areas of a disk sector outside
   the normal data areas) stands a greater chance of making the data
   unrecoverable.
   
6. Sidestepping the Problem

   The easiest way to solve the problem of erasing sensitive information
   from magnetic media is to ensure that it never gets to the media in
   the first place. Although not practical for general data, it is often
   worthwhile to take steps to keep particularly important information
   such as encryption keys from ever being written to disk. This would
   typically happen when the memory containing the keys is paged out to
   disk by the operating system, where they can then be recovered at a
   later date, either manually or using software which is aware of the
   in-memory data format and can locate it automatically in the swap file
   (for example there exists software which will search the Windows swap
   file for keys from certain DOS encryption programs). An even worse
   situation occurs when the data is paged over a network, allowing
   anyone with a packet sniffer or similar tool on the same subnet to
   observe the information (for example there exists software which will
   monitor and even alter NFS traffic on the fly which could be modified
   to look for known in-memory data patterns moving to and from a
   networked swap disk [27]).
   
   To solve these problems the memory pages containing the information
   can be locked to prevent them from being paged to disk or transmitted
   over a network. This approach is taken by at least one encryption
   library, which allocates all keying information inside protected
   memory blocks visible to the user only as opaque handles, and then
   optionally locks the memory (provided the underlying OS allows it) to
   prevent it from being paged [28]. The exact details of locking pages
   in memory depend on the operating system being used. Many Unix systems
   now support the mlock()/munlock() calls or have some alternative
   mechanism hidden among the mmap()-related functions which can be used
   to lock pages in memory. Unfortunately these operations require
   superuser priviledges because of their potential impact on system
   performance if large ranges of memory are locked. Other systems such
   as Microsoft Windows NT allow user processes to lock memory with the
   VirtualLock()/VirtualUnlock() calls, but limit the total number of
   regions which can be locked.
   
   Most paging algorithms are relatively insensitive to having sections
   of memory locked, and can even relocate the locked pages (since the
   logical to physical mapping is invisible to the user), or can move the
   pages to a "safe" location when the memory is first locked. The main
   effect of locking pages in memory is to increase the minimum working
   set size which, taken in moderation, has little noticeable effect on
   performance. The overall effects depend on the operating system and/or
   hardware implementations of virtual memory. Most Unix systems have a
   global page replacement policy in which a page fault may be satisfied
   by any page frame. A smaller number of operating systems use a local
   page replacement policy in which pages are allocated from a fixed (or
   occasionally dynamically variable) number of page frames allocated on
   a per- process basis. This makes them much more sensitive to the
   effects of locking pages, since every locked page decreases the
   (finite) number of pages available to the process. On the other hand
   it makes the system as a whole less sensitive to the effects of one
   process locking a large number of pages. The main effective difference
   between the two is that under a local replacement policy a process can
   only lock a small fixed number of pages without affecting other
   processes, whereas under a global replacement policy the number of
   pages a process can lock is determined on a system-wide basis and may
   be affected by other processes.
   
   In practice neither of these allocation strategies seem to cause any
   real problems. Although any practical measurements are very difficult
   to perform since they vary wildly depending on the amount of physical
   memory present, paging strategy, operating system, and system load, in
   practice locking a dozen 1K regions of memory (which might be typical
   of a system on which a number of users are running programs such as
   mail encryption software) produced no noticeable performance
   degradation observable by system- monitoring tools. On machines such
   as network servers handling large numbers of secure connections (for
   example an HTTP server using SSL), the effects of locking large
   numbers of pages may be more noticeable.
   
7. Methods of Recovery for Data stored in Random-Access Memory

   Contrary to conventional wisdom, "volatile" semiconductor memory does
   not entirely lose its contents when power is removed. Both static
   (SRAM) and dynamic (DRAM) memory retains some information on the data
   stored in it while power was still applied. SRAM is particularly
   susceptible to this problem, as storing the same data in it over a
   long period of time has the effect of altering the preferred power-up
   state to the state which was stored when power was removed. Older SRAM
   chips could often "remember" the previously held state for several
   days. In fact, it is possible to manufacture SRAM's which always have
   a certain state on power-up, but which can be overwritten later on - a
   kind of "writeable ROM".
   
   DRAM can also "remember" the last stored state, but in a slightly
   different way. It isn't so much that the charge (in the sense of a
   voltage appearing across a capacitance) is retained by the RAM cells,
   but that the thin oxide which forms the storage capacitor dielectric
   is highly stressed by the applied field, or is not stressed by the
   field, so that the properties of the oxide change slightly depending
   on the state of the data. One thing that can cause a threshold shift
   in the RAM cells is ionic contamination of the cell(s) of interest,
   although such contamination is rarer now than it used to be because of
   robotic handling of the materials and because the purity of the
   chemicals used is greatly improved. However, even a perfect oxide is
   subject to having its properties changed by an applied field. When it
   comes to contaminants, sodium is the most common offender - it is
   found virtually everywhere, and is a fairly small (and therefore
   mobile) atom with a positive charge. In the presence of an electric
   field, it migrates towards the negative pole with a velocity which
   depends on temperature, the concentration of the sodium, the oxide
   quality, and the other impurities in the oxide such as dopants from
   the processing. If the electric field is zero and given enough time,
   this stress tends to dissipate eventually.
   
   The stress on the cell is a cumulative effect, much like charging an
   RC circuit. If the data is applied for only a few milliseconds then
   there is very little "learning" of the cell, but if it is applied for
   hours then the cell will acquire a strong (relatively speaking) change
   in its threshold. The effects of the stress on the RAM cells can be
   measured using the built-in self test capabilities of the cells, which
   provide the ability to impress a weak voltage on a storage cell in
   order to measure its margin. Cells will show different margins
   depending on how much oxide stress has been present. Many DRAM's have
   undocumented test modes which allow some normal I/O pin to become the
   power supply for the RAM core when the special mode is active. These
   test modes are typically activated by running the RAM in a nonstandard
   configuration, so that a certain set of states which would not occur
   in a normally-functioning system has to be traversed to activate the
   mode. Manufacturers won't admit to such capabilities in their products
   because they don't want their customers using them and potentially
   rejecting devices which comply with their spec sheets, but have little
   margin beyond that.
   
   A simple but somewhat destructive method to speed up the annihilation
   of stored bits in semiconductor memory is to heat it. Both DRAM's and
   SRAM's will lose their contents a lot more quickly at Tjunction =
   140C than they will at room temperature. Several hours at this
   temperature with no power applied will clear their contents
   sufficiently to make recovery difficult. Conversely, to extend the
   life of stored bits with the power removed, the temperature should be
   dropped below -60C. Such cooling should lead to weeks, instead of
   hours or days, of data retention.
   
8. Erasure of Data stored in Random-Access Memory

   Simply repeatedly overwriting the data held in DRAM with new data
   isn't nearly as effective as it is for magnetic media. The new data
   will begin stressing or relaxing the oxide as soon as it is written,
   and the oxide will immediately begin to take a "set" which will either
   reinforce the previous "set" or will weaken it. The greater the amount
   of time that new data has existed in the cell, the more the old stress
   is "diluted", and the less reliable the information extraction will
   be. Generally, the rates of change due to stress and relaxation are in
   the same order of magnitude. Thus, a few microseconds of storing the
   opposite data to the currently stored value will have little effect on
   the oxide. Ideally, the oxide should be exposed to as much stress at
   the highest feasible temperature and for as long as possible to get
   the greatest "erasure" of the data. Unfortunately if carried too far
   this has a rather detrimental effect on the life expectancy of the
   RAM.
   
   Therefore the goal to aim for when sanitising memory is to store the
   data for as long as possible rather than trying to change it as often
   as possible. Conversely, storing the data for as short a time as
   possible will reduce the chances of it being "remembered" by the cell.
   Based on tests on DRAM cells, a storage time of one second causes such
   a small change in threshold that it probably isn't detectable. On the
   other hand, one minute is probably detectable, and 10 minutes is
   certainly detectable.
   
   The most practical solution to the problem of DRAM data retention is
   therefore to constantly flip the bits in memory to ensure that a
   memory cell never holds a charge long enough for it to be
   "remembered". While not practical for general use, it is possible to
   do this for small amounts of very sensitive data such as encryption
   keys. This is particularly advisable where keys are stored in the same
   memory location for long periods of time and control access to large
   amounts of information, such as keys used for transparent encryption
   of files on disk drives. The bit-flipping also has the convenient
   side-effect of keeping the page containing the encryption keys at the
   top of the queue maintained by the system's paging mechanism, greatly
   reducing the chances of it being paged to disk at some point.
   
9. Conclusion

   Data overwritten once or twice may be recovered by subtracting what is
   expected to be read from a storage location from what is actually
   read. Data which is overwritten an arbitrarily large number of times
   can still be recovered provided that the new data isn't written to the
   same location as the original data (for magnetic media), or that the
   recovery attempt is carried out fairly soon after the new data was
   written (for RAM). For this reason it is effectively impossible to
   sanitise storage locations by simple overwriting them, no matter how
   many overwrite passes are made or what data patterns are written.
   However by using the relatively simple methods presented in this paper
   the task of an attacker can be made significantly more difficult, if
   not prohibitively expensive.
   
Acknowledgments

   The author would like to thank Nigel Bree, Peter Fenwick, Andy
   Hospodor, Kevin Martinez, Colin Plumb, and Charles Preston for their
   advice and input during the preparation of this paper.
   
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     _________________________________________________________________
                                      
   
    Secure Deletion of Data from Magnetic and Solid-State Memory / Peter
    Gutmann / pgut001@cs.auckland.ac.nz