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Overwriting Hard Drive Data: The Great Wiping Controversy

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Often we hear controversial opinions in digital forensics on the required or desired number of passes to utilize for properly overwriting, sometimes referred to as wiping or erasing, a modern hard drive. The controversy has caused much misconception, with persons commonly quoting that data can be recovered if it has only been overwritten once or twice. Moreover, referencing that it actually takes up to ten, and even as many as 35 (referred to as the Gutmann scheme because of the 1996 Secure Deletion of Data from Magnetic and Solid-State Memory published paper by Peter Gutmann) passes to securely overwrite the previous data. One of the chief controversies is that if a head positioning system is not exact enough, new data written to a drive may not be written back to the precise location of the original data. We demonstrate that the controversy surrounding this topic is unfounded.
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R. Sekar and A.K. Pujari (Eds.): ICISS 2008, LNCS 5352, pp. 243–257, 2008.
© Springer-Verlag Berlin Heidelberg 2008
Overwriting Hard Drive Data: The Great Wiping
Controversy
Craig Wright1, Dave Kleiman2, and Shyaam Sundhar R.S.3
1 BDO Kendalls, Sydney, Australia
Craig.Wright@bdo.com.au
2 ComputerForensicExaminer.com, Florida, US
dave@davekleiman.com
3 Symantec, USA
shyaam@gmail.com
Abstract. Often we hear controversial opinions in digital forensics on the re-
quired or desired number of passes to utilize for properly overwriting, some-
times referred to as wiping or erasing, a modern hard drive. The controversy has
caused much misconception, with persons commonly quoting that data can be
recovered if it has only been overwritten once or twice. Moreover, referencing
that it actually takes up to ten, and even as many as 35 (referred to as the Gut-
mann scheme because of the 1996 Secure Deletion of Data from Magnetic and
Solid-State Memory published paper by Peter Gutmann) passes to securely
overwrite the previous data. One of the chief controversies is that if a head posi-
tioning system is not exact enough, new data written to a drive may not be writ-
ten back to the precise location of the original data. We demonstrate that the
controversy surrounding this topic is unfounded.
Keywords: Digital Forensics, Data Wipe, Secure Wipe, Format.
1 Introduction
Often we hear controversial opinions on the required or desired number of passes to
utilize for properly overwriting, sometimes referred to as wiping or erasing, a modern
hard drive. The controversy has caused much misconception, with persons commonly
quoting that data can be recovered if it has only been overwritten once or twice.
Moreover, referencing that it actually takes up to ten, and even as many as 35 (re-
ferred to as the Gutmann scheme because of the 1996 Secure Deletion of Data from
Magnetic and Solid-State Memory published paper by Peter Gutmann, [12]) passes to
securely overwrite the previous data.
One of the chief controversies is that if a head positioning system is not exact
enough, new data written to a drive may not be written back to the precise location of
the original data. This track misalignment is argued to make possible the process of
identifying traces of data from earlier magnetic patterns alongside the current track.
This was the case with high capacity floppy diskette drives, which have a rudimen-
tary position mechanism. This was at the bit level and testing did not consider the
accumulated error.
244 C. Wright, D. Kleiman, and S. Sundhar R.S.
The basis of this belief is a presupposition is that when a one (1) is written to disk
the actual effect is closer to obtaining a 0.95 when a zero (0) is overwritten with one
(1), and a 1.05 when one (1) is overwritten with one (1). This we can show is false
and that in fact, there is a distribution based on the density plots that supports the
contention that the differential in write patterns is too great to allow for the recovery
of overwritten data.
The argument arises from the statement that “each track contains an image of
everything ever written to it, but that the contribution from each ``layer" gets progres-
sively smaller the further back it was made”. This is a misunderstanding of the phys-
ics of drive functions and magneto-resonance. There is in fact no time component and
the image is not layered. It is rather a density plot.
This is of prime importance to forensic analysts and security personal. The time
needed to run a single wipe of a hard drive is economically expensive. The require-
ments to have up to 35 wipes [12] of a hard drive before disposal become all the more
costly when considering large organisations with tens of thousands of hosts. With a
single wipe process taking up to a day to run per host through software and around an
hour with dedicated equipment, the use of multiple wipes has created a situation
where many organisations ignore the issue all together – resulting in data leaks and
loss.
The inability to recover data forensically following a single wipe makes the use of
data wiping more feasible. As forensic and information security professionals face
these issues on a daily basis, the knowledge that a single wipe is sufficient to remove
trace data and stop forensic recovery will remove a great deal of uncertainty from the
industry and allow practitioners to focus on the real issues.
1.1 What Is Magnetic Force Microscopy1
Magnetic force microscopy (MFM) images the spatial variation of magnetic forces on
a sample surface. The tip of the microscope is coated with a ferromagnetic thin film.
The system operates in non-contact mode, detecting changes in the resonant fre-
quency of the cantilever induced by the magnetic field's dependence on tip-to-sample
separation. A MFM can be used to image naturally occurring and deliberately written
domain structures in magnetic materials. This allows the device to create a field den-
sity map of the device.
1.2 MFM Imagery of Overwritten Hard Disk Tracks
The magnetic field topography (Fig. 2A below) was imaged with an MFM to measure
the magnetic force density. This image was captured using the MFM in Lift Mode
(lift height 35 nm). This results in the mapping of the shift in the cantilever resonant
frequency.
1 The MFM senses the stray magnetic field above the surface of a sample. A magnetic tip is
brought into close proximity with the surface and a small cantilever is used to detect the force
between the tip and the sample. The tip is scanned over the surface to reveal the magnetic
domain structure of the sample at up to 50 nm resolution.
Overwriting Hard Drive Data: The Great Wiping Controversy 245
Fig. 1. The concepts of how Partial Response Maximum Likelihood (PRML) (a method for
converting the weak analog signal from the head of a magnetic disk or tape drive into a digital
signal) (and newer Extended Partial Response Maximum Likelihood (EPRML) drive) encoding
is implemented on a hard drive. The MFM reads the unprocessed analog value. Complex sta-
tistical digital processing algorithms are used to determine the “maximum likelihood” value
associated with the individual reads.
The acquisition time for 1 byte is about 4 minutes (this would improve with newer
machines). The image displays the:
track width and skew,
transition irregularities, and
the difference between written and overwritten areas of the drive.
Because of the misconception, created by much older technologies (such as floppy
drives) with far lower densities, many believe that the use of an electron microscope
will allow for the recovery of forensically usable data. The fact is, with modern drives
(even going as far back as 1990) that this entire process is mostly a guessing game
that fails significantly when tested. Older technologies used a different method of
reading and interpreting bits than modern hard called peak detection. This method is
satisfactory while the peaks in magnetic flux sufficiently exceed the background sig-
nal noise. With the increase in the write density of hard drives (Fig. 3), encoding
schemes based on peak detection (such as Modified Frequency Modulation or MFM)
that are still used with floppy disks have been replaced in hard drive technologies.
The encoding of hard disks is provided using PRML and EPRML encoding technolo-
gies that have allowed the write density on the hard disk to be increased by a full 30-
40% over that granted by standard peak detection encoding.
246 C. Wright, D. Kleiman, and S. Sundhar R.S.
(a)
(b)
Fig. 2. (a). This image was captured and reconstructed at a 25-µm scan from an Atomic Force
Microscope [15]. The image displays the residual from overwrites and alignment. (b). This
image from PCGuide.com displays the configuration of a 20 track hard drive. These tracks are
separated into five zones which are displayed in a separate color as follows: 5 x 16 sector tracks
in the blue zone, 5 x 14 sector tracks in the cyan zone, 4 x 12 sector tracks in the green zone, 3
x 11 sectors tracks in the yellow zone, and 3 x 9 sector tracks in the red.
Additionally, hard disk drives use zoned bit recording (Fig 2b) which differs from
floppy drives and similar technologies. Older technologies (including floppy disks)
used a single zone with a write density that is several orders of magnitude larger than
that used with hard disks. We have not tested recovery from a floppy disk using these
methods, but it would be expected that the recovery rate would be significantly
greater than with respect of that of a hard disk platter - although still stochastically
distributed.
The fact is many people believe that this is a physical impression in the drive that
can belie the age of the impression. This misconception is commonly held as to the
process used to measure the magnetic field strength. Using the MFM in Tapping
Mode2, we get a topography image that represents the physical surface of the drive
platter.
The magnetic flux density follows a function known as the hysteresis loop. The
magnetic flux levels written to the hard drive platter vary in a stochastic manner with
variations in the magnetic flux related to head positioning, temperature and random
error. The surfaces of the drive platters can have differing temperatures at different
points and may vary from the read/write head. This results in differences in the ex-
pansion and contraction rates across the drive platters. This differential can result in
misalignments. Thermal recalibration is used on modern drives to minimize this vari-
ance, but this is still results in an analogue pattern of magnetic flux density.
One of ways used to minimize the resultant error has come through the introduc-
tion of more advanced encoding schemes (such as PRML mentioned previously).
Rather than relying on differentiating the individual peaks at digital maxima,
2 Tapping mode can also be called Dynamic Force mode, intermittent contact mode, non-
contact mode, wave mode, and acoustic AC mode by various microscope vendors. When op-
erating in tapping mode the cantilever is driven to oscillate up and down at near its resonance
frequency by a small piezoelectric element.
Overwriting Hard Drive Data: The Great Wiping Controversy 247
magnetic flux reversals are measured by hard drive heads and processed using an
encoding process (PRML or EPRML) that is based on determining maximum likeli-
hood for the flux value using a digital signal sampling process. Complex statistically
based detection algorithms are employed to process the analog data stream as it is
read the disk. This is the "partial response" component. This stochastic distribution of
data not only varies on each read, but also over time and with temperature differen-
tials. This issue has only grown as drive densities increase.
Fig. 3. This graph from IBM demonstrates how the bit size used with modern hard drives is
shrinking. This has resulted in a dramatic increase in the density of hard disks which has re-
sulted in the error rate from movement and temperature remaining an issue even with the im-
provements in compensating technologies.
A Track is a concentric set of magnetic bits on the disk. Each track is commonly
divided into 512 bytes sectors. The drive sector is the part of each track defined with
magnetic marking and an ID number. Sectors have a sector header and an error cor-
rection code (ECC).
A Cylinder is a group of tracks with the same radius.
Data addressing occurs within the two methods for data addressing:
CHS (cylinder-head-sector) and
LBA (logical block address).
The issue from Guttmann’s paper [12] is that we can recover data with foreknowledge
of the previous values, but not with any level of accuracy. The issues with this are
twofold. First, to have any chance of recovery it is necessary to have perfect
248 C. Wright, D. Kleiman, and S. Sundhar R.S.
Fig. 4. The hysteresis loop3 demonstrates the relationship between the induced magnetic flux
density (B) and the magnetizing force (H). It is often referred to as the B-H loop. This function
varies with a number of prevalent conditions including temperature.
knowledge of what was previously written to the drive. This situation most often
never occurs in a digital forensic investigation. In fact, if a perfect copy of the data
existed, there would be no reason to recover data from the wiped drive. Next, the
level of recovery when presented with a perfect image is too low to be of use even on
a low density pristine drive (which does not exist in any actual environment). Carroll
and Pecora (1993a, 1993b) demonstrated this effect and how stochastic noise results
in a level of controlled chaos. The Guttmann preposition [12] is true based on a
Bayesian a-prior model assuming that we have the original data and the pattern from
the overwrite, but of course this defeats the purpose of the recovery process and as
noted is still not sufficiently accurate to be of any use. Stating that we can recover
data with a high level of accuracy, given that we have the original data, is a tautology,
and there would be no reason to do the recovery.
The previously mentioned paper uses the determination that the magnetic field
strength is larger or smaller than that which would be expected from a write suggests
the prior overwritten value. This is that a factored magnetic field strength of 0.90 or
1.10 (where 1.0 is a “clean” write with no prior information) would represent the
previous information written to the drive that has been overwritten. This is postulated
to be a means through which the use of an electron microscope could be deployed to
recover data from a drive that has been wiped. The problem with this theory is that
there are both small write errors on an unwritten sector and remnant magnetic field
densities from prior use of the drive sector.
3 Image sourced from Iowa’s State University Center for Nondestructive Evaluation NDT (Non
Destructive Testing).
Overwriting Hard Drive Data: The Great Wiping Controversy 249
Fig. 5. This example displays the experimentally derived magnetic field density functions for
hard drive rewrites where “A” displays the measured distribution of binary “1” values on initial
copy. “B” displays the distribution of values associated with a binary “1” value following an
overwrite with another binary “1”.
Magnetic signatures are not time-stamped, accordingly there is no “unerase” capa-
bility [15]. Figure 4 displays the B-H loop for magnetic flux. Starting at a zero flux
density for a drive platter that has not been previously magnetized, the induced flux
density created when the drive head writes to the platter follows the dashed line (dis-
played in Fig. 4) as the magnetizing force is increased. Due to a combination of power
constraints, timing issues and write density, modern hard drives do not saturate the
magnetic flux on the drive to point "a". Rather, they use sophisticated statistical
measures (PRML and EPRML) to determine the maximum likelihood of the value
stored on the drive. In demagnetizing a drive (reducing H to zero) the curve moves
from point "a" to point "b" on Figure 4. Some residue from the prior magnetic flux
remains in the material even though the magnetizing force is zero. This phenomenon
is known as remanence. The retentivity of disk platter will not reach the maxima (de-
fined by points “b” and “d” in figure 4) as the drive heads do not reach saturation.
Further, fluctuations in temperature, movement and prior writes influence the perme-
ability4 of the platter. Jiles [21] notes that in the event that the temperature of a drive
platter is increased from, 20 to 80 centigrade then a typical ferrite can become subject
to a 25% reduction in the in permeability of the platter.
Consequently, the B-H curve does not go back to the originating point when the
magnetic flux is rewritten and the B-H curve will vary with use due to temperature
fluctuations. On subsequent writes, the hysteresis curve follows a separate path from
position "f" in Figure 4. As drive heads do not cause the hard drive platter to reach the
saturation point, the resultant B-H loop will vary on each write.
4 Permeability is a material property that is used to measure how much effort is required to
induce a magnetic flux within a material. Permeability is defined the ratio of the flux density
to the magnetizing force. This may be displayed with the formula: µ = B/H (where µ is the
permeability, B is the flux density and H is the magnetizing force).
250 C. Wright, D. Kleiman, and S. Sundhar R.S.
Fig. 6 (A and B). This example displays the magnetic field density functions that were experi-
mentally obtained following a rewrite (wipe) of the prior binary unit on the hard drive. Plot “A”
displays the density distribution associated with “1” values following an overwrite with a “0”.
Plot “B” displays the density function for an initial “0” value that has been overwritten with a
“1”.
A common misconception concerning the writing of data to a hard drive arises as
many people believe that a digital write is a digital operation. As was demonstrated
above, this is a fallacy, drive writes are analogue with a probabilistic output [6], [8],
[10]. It is unlikely that an individual write will be a digital +1.00000 (1). Rather -
there is a set range, a normative confidence interval that the bit will be in [15].
What this means is that there is generally a 95% likelihood that the +1 will exist in
the range of (0.95, 1.05) there is then a 99% likelihood that it will exist in the range
(0.90, 1.10) for instance. This leaves a negligible probability (1 bit in every 100,000
billion or so) that the actual potential will be less than 60% of the full +1 value. This
error is the non-recoverable error rating for a drive using a single pass wipe [19].
As a result, there is no difference to the drive of a 0.90 or 1.10 factor of the mag-
netic potential. What this means is that due to temperature fluctuations, humidity, etc
the value will most likely vary on each and every pass of a write. The distributions of
these reads are displayed as histograms in Fig. 5. The distribution is marginally dif-
ferent to the original, but we cannot predict values. From Fig. 6 it is simple to see that
even with the prior data from the initial write we gain little benefit. These images
display the differences in the voltage readings of the drives (which are determined
through the magnetic field strength). Clearly, some values that are more distantly
distributed than would be expected in the differenced results (Fig. 6 B) with voltage
values that are significantly greater then are expected. The problem is that the number
of such readings is far lower than the numbers that result through shear probability
alone.
Resultantly, there is no way to even determine if a “1.06” is due to a prior write or
a temperature fluctuation. Over time, the issue of magnetic decay would also come
into play. The magnetic flux on a drive decays slowly over time. This further skews
the results and raises the level of uncertainty of data recovery.
Overwriting Hard Drive Data: The Great Wiping Controversy 251
Consequently, we can categorically state that there is a minimal (less than a
0.01% chance) of recovering any data on a NEW and unused drive that has a sin-
gle raw wipe pass (not even a low-level format). In the cases where a drive has
been used (even being formatted for use) it is not possible to recover the informa-
tion – there is a small chance of bit recovery, but the odds of obtaining a whole
word are small.
The improvement in technology with electron microscopes will do little to change
these results. The error from microscope readings was minimal compared to the drive
error and as such, the issue is based on drive head alignment and not the method used
for testing.
1.3 Read Error Severities and Error Management Logic
A sequence of intricate procedures are performed by the hard drive controller in order
to minimise the errors that occur when either writing data to or reading data for a
drive. These processes vary with each hard drive producer implementing their own
process. Some of the most common error management processes have been listed
below.
ECC Error Detection: A drive sector is read by the head. An error detection algo-
rithm is used to determine the likelihood of a read error. In the event that an error
state is considered to be unlikely, the sector is processed and the read operation is
considered as having been concluded successfully.
ECC Error Correction: The controller uses the ECC codes that it has inter-
preted for the sector in order to try and correct the error. A read error can be
corrected very quickly at this level and is usually deemed to be an "automatic
correction".
Automatic Retry: The next phase involves waiting until the drive platter has com-
pleted a full spin before attempting to read the data again. Stray magnetic field vari-
ances are a common occurrence leading to drive read error. These fluctuations may
result due to sudden movement and temperature variations. If the error is corrected
following a retry, most drives will judge the error condition to be "corrected after
retry".
Advanced Error Correction: Many drives will, on subsequent retries after the first,
invoke more advanced error correction algorithms that are slower and more complex
than the regular correction protocols, but have an increased chance of success. These
errors are "recovered after multiple reads" or "recovered after advanced correction".
Failure: In the event that the drive is incapable of reading the sector, a signal is sent
to the drive controller noting a read error. This type of failure is an unrecoverable read
error.
Modern encoding schemes (PRML and EPRML) have a wide tolerance range al-
lowing the analogue values that the drive head reads from and writes to a hard disk to
vary significantly without loss of data integrity. Consequently, the determination of a
prior write value is also a stochastic process.
252 C. Wright, D. Kleiman, and S. Sundhar R.S.
2 Data and Method
In order to completely validate all possible scenarios, a total of 15 data types were
used in 2 categories. Category A divided the experiment into testing the raw drive
(this is a pristine drive that has never been used), formatted drive (a single format
was completed in Windows using NTFS with the standard sector sizes) and a simu-
lated used drive (a new drive was overwritten 32 times with random data from
/dev/random on a Linux host before being overwritten with all 0’s to clear any
residual data).
The experiment was also divided into a second category in order to test a number
of write patterns. Category B consisted of the write pattern used both for the initial
write and for the subsequent overwrites. This category consisted of 5 dimensions:
all 0’s,
all 1’s,
a “01010101 pattern,
a “00110011” pattern, and
a “00001111” pattern.
The Linux utility “dd” was used to write these patterns with a default block size of
512 (bs=512). A selection of 17 models of hard drive where tested (from an older
Quantum 1 GB drive to current drives dated to 2006). The data patterns where written
to each drive in all possible combinations.
1. The data write was a 1 kb file (1024 bits).
2. Both drive skew and the bit was read.
3. The process was repeated 5 times for an analysis of 76,800 data points.
Table 1. Table of Probability Distributions for the older model drives. Note that a “used” drive
has only a marginally better chance of any recovery than tossing a coin. The Pristine drive is
the optimal case based on an early Seagate 1Gb drive.
Probability of recov-
ery
Pristine drive Used Drive (ideal)
1 bit 0.92 0.56
2 bit 0.8464 0.3136
4 bit 0.71639296 0.098345
8 bits5 0.51321887 0.009672
16 bits 0.26339361 9.35E-05
32 bits 0.06937619 8.75E-09
64 bits 0.00481306 7.66E-17
128 bits 2.3166E-05 5.86E-33
256 bits 5.3664E-10 3.44E-65
512 bits 2.8798E-19 1.2E-129
1024 bits 8.2934E-38 1.4E-258
5 This represents one (1) ASCII character.
Overwriting Hard Drive Data: The Great Wiping Controversy 253
The likelihood calculations were completed for each of the 76,800 points with the
distributions being analyzed for distribution density and distance. This calculation
was based on the Bayesian likelihood where the prior distribution was known. As has
been noted, in real forensic engagements, the prior distribution is unknown. This
presents this method with an advantage to recovering the data that would not be found
when conducting a forensic examination and recovery of a drive.
Even on a single write, the overlap at best gives a probability of just over 50% of
choosing a prior bit (the best read being a little over 56%). This caused the issue to
arise, that there is no way to determine if the bit was correctly chosen or not. There-
fore, there is a chance of correctly choosing any bit in a selected byte (8-bits) – but
this equates a probability around 0.9% (or less) with a small confidence interval either
side for error.
Resultantly, if there is less than a 1% chance of determining each character to be
recovered correctly, the chance of a complete 5-character word being recovered drops
exponentially to 8.463E-11 (or less on a used drive and who uses a new raw drive
format). This results in a probability of less than 1 chance in 10Exp50 of recovering
any useful data. So close to zero for all intents and definitely not within the realm of
use for forensic presentation to a court.
Table 1 below, shows the mapped out results of probable recovery with a pristine
drive of a similar make and model6 to that which would have been used in the paper
by Dr. Gutmann. This drive had never been used and was had raw data written to it
for the first time in this test. The other drive was a newer drive7 that has been used (I
used this for my daily operations for 6 months) prior to the wiping procedure. A total
of 17 variety of drives dated from 1994 to 2006 of both the SCSI and IDE category
where tested for this process. A total of 56 drives where tested. On average only one
(1) drive in four8 (4) was found to function when the platter had been returned after an
initial reading with the MFM.
3 Data Relationships
The only discernable relationship of note is between an initial write of a “1” on a
pristine drive that is overwritten with a “0”. This is a function of the drive write head
and has no correlation to data recovery, so this is a just point of interest and noting to
aid in data extraction from a forensic perspective. All other combinations of wipes
displayed comparative distributions of data that where suggestive of random white
noise.
3.1 Distributions of Data
The tables used in this section display the probabilities of recovery for each of the
drives tested. Although the chances of recovering any single bit from a drive are rela-
tively good, the aim in any forensic engagement is to recover usable data that can be
presented in court.
6 SEAGATE: ST51080N MEDAL.1080 1080MB 3.5"/SL SCSI2 FAST.
7 Western Digital WD1200JS.
8 23.5% of drives where able to be used for an overwrite following an initial MFM scan.
254 C. Wright, D. Kleiman, and S. Sundhar R.S.
These tests where run as a series of 4 tests on each of 17 types of drives. The re-
ported (Table 1) recovery rate of 92% this was the optimal rate (which was itself
stochastically distributed). The results were in distributed over a wide range of values
with the use of the drive impacting on the capacity to recover data.
This clearly shows that any data recovery is minimal and that no forensically sound
recovery is possible. The recovery of a single 32 bit value (such as an IP address) is
highly unlikely. It has been stated9, that the smallest fragment of usable digital foren-
sic evidence is a 32 bit field (the IP address). To be used in a Civil court case, the
evidence needs to be subjected to the balance of probability (usually 51%). In a
criminal matter, the preponderance is set at between 95% and 99% to account for all
reasonable doubt. The rate at which evidence may be recovered using this technique
is too low to be useful. In fact, with the optimal recovery under 7% for a single IP
address on an older drive. This is an event that cannot occur outside the lab.
The bit-by-bit chance of recovery lies between 0.92 (+/- 0.15)10 and 0.54 (+/-
0.16)11. We have used the higher probability in the calculations to add an additional
level of confidence in our conclusions. This demonstrates that the chances of recover-
ing a single 8-bit character on the pristine drive are 51.32%. The recovery rate of a
32-bit word is 0.06937619 (just under 7%). As such, the chances of finding a single 4
letter word correctly from a Microsoft Word document file is 2.3166E-05
(0.00002317%)
Table 2 below is a table that further illustrates the wiping fallacy. We tested this by
completing a single pass wipe, to simulate minimal use we repeated the process.
Once again, we can see the data recovery is minimal.
Table 2. Table of Probability Distributions for the “new” model drives
Probability of re-
covery
Pristine drive
(plus 1 wipe)
Pristine drive
(plus 3 wipe)
1 bit 0.87 0.64
2 bit 0.7569 0.4096
4 bit 0.57289761 0.16777216
8 bits 0.328211672 0.028147498
16 bits 0.107722901 0.000792282
32 bits 0.011604223 6.2771E-07
64 bits 0.000134658 3.9402E-13
128 bits 1.81328E-08 1.55252E-25
256 bits 3.28798E-16 2.41031E-50
512 bits 1.08108E-31 5.8096E-100
1024 bits 1.16873E-62 3.3752E-199
The standard daily use of the drive makes recovery even more difficult, without
even considering a wipe, just prior use. In this case, the 3 former wipes are used to
simulate use (though minimal and real use is far more intensive). The chances of
9 Rob Lee, SANS Forensics 508.
10 For the optimal recovery on an old drive.
11 On a used “new” drive.
Overwriting Hard Drive Data: The Great Wiping Controversy 255
recovering a single 8-bit word (a single character) are 0.0281475 (or 2.8%) – which is
actually lower than randomly selecting the character.
The calculated probability of recovering data from any used drive that uses a newer
encoding scheme (EPRML) and high density was indistinguishable from a random
guess. When recovering data from the 2006 model drive, the best determination of the
prior write value was 49.18% (+/- 0.11)12 from the “all 0’s” pattern when overwritten
with the “all 1’s” pattern. The other overwrite patterns actually produced results as
low as 36.08% (+/- 0.24). Being that the distribution is based on a binomial choice,
the chance of guessing the prior value is 50%. In many instances, using a MFM to
determine the prior value written to the hard drive was less successful than a simple
coin toss.
3.2 Distribution of Recovered Data
The following is a retrieval pattern from the drive. Where the 8-bit word is correctly
read, a “1” is listed. Where the value did not match the correct pattern that was writ-
ten to the drive, a “0” is displayed.
[1] 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1
[48] 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0
[95] 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1
[142] 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0
[189] 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1
[236] 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1
[283] 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0
[330] 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0
[377] 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1
[424] 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1
[471] 1 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0
[518] 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0
[565] 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0
[612] 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0
[659] 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1
[706] 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1
[753] 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0
[800] 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0
[847] 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0
[894] 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1
[941] 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0
[988] 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0
As an example, the following is the start of the paper by Peter Gutmann [12], first
displayed accurately, and next at an optimal retrieval level.
3.2.1 Correct Display
Secure deletion of data - Peter Gutmann - 1996
Abstract
With the use of increasingly sophisticated encryption systems, an attacker
wishing to gain access to sensitive data is forced to look elsewhere for in-
formation. One avenue of attack is the recovery of supposedly erased data
from magnetic media or random-access memory.
3.2.2 Display from Recovery (Optimal)
‘cKræ}d8Œeti²n•of0daÊI0Ptr0G§tWÇíï_¼Á1u960eb8tÈñutW00000Dç•Ã#Ì0
Hf$00¦000%£z0\0ã0000á0áä«it|tþÛ0u³e•Ffºi™%|eàsinqTyøîopÚ”Ë:i†aze0
12 This is reported at a 99% confidence level.
256 C. Wright, D. Kleiman, and S. Sundhar R.S.
®Mcryption0sîÙtems?DKtA""cÐÏ0+¢sinŒ0toK–ai2z÷c(ns~0tü0;e
½iti)e""daÆa>s0foôce¸ÑtÒÍl2o–
ìelI¶˜$eöe›Ÿr""inf¬rm‰ion.0OnRïavem>egoN0-¨tRÁ"1i
läßh±0"eÛoie=y0Cz-
su•¨s/`lÜ{era’Jd0dataF¨ro>•magne³;&£õãÈáã%or*r‰ndoª-Qcc«ÇŸ0mà
@ryl00000000000000000
Although on the perfect drive some words could be recovered, there is little of foren-
sic value.
3.2.3 Display from Recovery (Expected)
¡ÄuÜtÞdM@ª""îFnFã:à•ÅÒ̾‘¨L‘¿ôPÙ!#¯ -×LˆÙÆ!mC
2´³„‡·}NŽýñêZØ^›l©þì®·äÖŒv¿^œº0TÏ[ªHÝBš¸ð
7zô|»òëÖ/""º[ýÀ†,kR¿xt¸÷\Í2$Iå""•ÑU%TóÁ’ØoxÈ$i
Wï^™oËS²Œ,Ê%ñ ÖeS» eüB®Èk‹|YrÍȶ=ÏÌSáöp¥D
ôÈŽ"|ûÚA6¸œ÷U•$µM¢;Òæe•ÏÏMÀùœç]#•Q
Á¹Ù""—OX“h
ÍýïÉûË Ã""W$5Ä=rB+5•ö–GßÜä9ïõNë-ߨYa“–ì%×Ó¿Ô[Mãü
·†Î‚ƒ‚…[Ä‚KDnFJˆ·×ÅŒ¿êäd¬sPÖí8'v0æ#!)YÐúÆ©
k-‹HÈø$°•Ø°Ïm/Wîc@Û»Ì"„zbíþ00000000000000000
On the drive that had been wiped 3 times (prior) to the data being written and then
added, the results are worse. What needs to be noted is that small errors in the calcula-
tions lead to wide discrepancies in the data that is recovered. Further, it needs to be
noted that any drive recovered is not likely to be in a pristine state. The daily use of a
drive reduces the chances of recovery to a level that is truly insignificant.
4 Conclusion
The purpose of this paper was a categorical settlement to the controversy surrounding
the misconceptions involving the belief that data can be recovered following a wipe
procedure. This study has demonstrated that correctly wiped data cannot reasonably
be retrieved even if it is of a small size or found only over small parts of the hard
drive. Not even with the use of a MFM or other known methods. The belief that a tool
can be developed to retrieve gigabytes or terabytes of information from a wiped drive
is in error.
Although there is a good chance of recovery for any individual bit from a drive, the
chances of recovery of any amount of data from a drive using an electron microscope
are negligible. Even speculating on the possible recovery of an old drive, there is no
likelihood that any data would be recoverable from the drive. The forensic recovery
of data using electron microscopy is infeasible. This was true both on old drives and
has become more difficult over time. Further, there is a need for the data to have been
written and then wiped on a raw unused drive for there to be any hope of any level of
recovery even at the bit level, which does not reflect real situations. It is unlikely that
a recovered drive will have not been used for a period of time and the interaction of
defragmentation, file copies and general use that overwrites data areas negates any
chance of data recovery. The fallacy that data can be forensically recovered using an
electron microscope or related means needs to be put to rest.
Overwriting Hard Drive Data: The Great Wiping Controversy 257
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... With the increasing size of storage media, it is also impractical as the time taken to erase a drive would be considerable. Wright et al. (2008) indicated that one overwrite is required for data wiping and that the misconception that recovery tools can retrieve gigabytes of data from erased media drives is unfounded. ...
... Several methods that were previously examined in Wright et al., (2008) for the recovery of data from electromagnetic disks, including the Bitter technique, Lorentz microscopy, and Magnetic Force Microscopy, were discounted as unachievable given the developments in data storage densities of modern disks. For completeness these are detailed below: ...
... First and foremost, the successful and complete wiping of the disk by some of the erasing tools such as Hard Wipe and Puran Wipe Disk confirmed that the write zero method is sufficient for disk erasure. Also, a single overwrite pass is enough to completely wipe a disk as Wright et al. (2008) indicated in their paper, "Overwriting Hard Drive Data: The Great Wiping Controversy". Although one pass overwrite is not necessarily sufficient to make any potential future recovery of the data infeasible, it is adequate for the cleaning of personal disks. ...
... Thus, modulated nanowires are a very attractive topic for the development of logical or spintronic devices, such as spin valves or magnetic tunneling junctions, due to the possibility of coexistence of different phases on a single system [11][12][13][14][15][16][17][18][19][20][21][22][23]. In fact, modulations can come in different forms: alternating magnetic materials [24], intercalations of non-magnetic spacers [25], varying the diameter along the wire axis maintaining the homogeneous material and combinations of the previous ones [26,21]. In the present work we concentrate on geometrical modulations only. ...
... FIGURA 1.8: (a) Esquema de un HDD y (b) escaneo de un HDD con microscopía de fuerza magnética. Figuras adaptadas de[22] y[24]. ...
... On the other hand, the efficiency of the existing data deletion schemes is unsatisfactory, especially for these schemes that achieve deletion by overwriting. 17,18 In the overwriting model, the outsourced data must be overwritten by some random data, whose size is the same with the outsourced data. However, the outsourced data might be large-scale, resulting in heavy computational cost and communication overhead. ...
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... As a result, the outsourced data transfer and deletion have become two new problems because the selfish cloud server might not execute these operations sincerely for economic benefits. In order to permanently remove the outsourced data, a lot of researchers have focused on the problem of data deletion in the past decade and have put forward plenty of methods, such as deletion by overwriting [14][15][16][17][18][19] and deletion by cryptography. [20][21][22][23][24] Although a number of deletion schemes have been proposed, there are still some problems and challenges in deleting the outsourced data. ...
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ELECTROMAGNETISM: MAGNETIC PHENOMENA ON THE MACROSCOPIC SCALE Magnetic Fields Magnetic Field Magnetic Induction Magnetic Field Calculations References Further Reading Exercises Magnetization and Magnetic Moment Magnetic Moment Magnetic Poles and Amperian Bound Currents Magnetization Magnetic Circuits and the Demagnetizing Field Penetration of Alternating Magnetic Fields into Materials References Further Reading Exercises Magnetic Measurements Induction Methods Force Methods Methods Depending on Changes in Material Properties Superconducting Quantum Interference Devices References Further Reading Exercises Magnetic Materials Classification of Magnetic Materials Magnetic Properties of Ferromagnets Different Types of Ferromagnetic Materials for Applications Paramagnetism and Diamagnetism References Further Reading Exercises MAGNETISM IN MATERIALS: MAGNETIC PHENOMENA ON THE MICROSCOPIC SCALE Magnetic Properties Hysteresis and Related Properties Barkhausen Effect and Related Phenomena Magnetostriction Magnetoresistance References Further Reading Exercises Magnetic Domains Development of Domain Theory Energy Considerations and Domain Patterns References Further Reading Exercises Domain Walls Properties of Domain Boundaries Domain-Wall Motion References Further Reading Exercises Domain Processes Reversible and Irreversible Domain Processes Determination of Magnetization Curves from Pinning Models Theory of Ferromagnetic Hysteresis Dynamics of Domain Magnetization Processes References Further Reading Exercises Magnetic Order and Critical Phenomena Theories of Paramagnetism and Diamagnetism Theories of Ordered Magnetism Magnetic Structure References Further Reading Exercises Electronic Magnetic Moments Classical Model of Magnetic Moments of Electrons Quantum Mechanical Model of Magnetic Moments of Electrons Magnetic Properties of Free Atoms References Further Reading Exercises Quantum Theory of Magnetism Electron-Electron Interactions Localized Electron Theory Itinerant Electron Theory References Further Reading Exercises MAGNETICS: TECHNOLOGICAL APPLICATIONS Soft Magnetic Materials Properties and Applications of Soft Magnets Materials for AC Applications Materials for DC Applications Materials for Magnetic Shielding References Further Reading Materials Conferences Hard Magnetic Materials Properties and Applications of Hard Magnets Permanent Magnet Materials References Further Reading Materials Conferences Magnetic Recording History of Magnetic Recording Magnetic Recording Media Recording Heads and the Recording Process Modeling the Magnetic Recording Process References Further Reading Magnetic Evaluation of Materials Methods for Evaluation of Materials Properties Methods for Detection of Flaws and Other Inhomogeneities Magnetic Imaging Methods Sensitivity to Microstructure and Material Treatment References Further Reading Solutions to Exercises
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Thermal noise introduces stochasticity into deterministic equations and makes possible events which are never seen in the zero temperature setting. The driving force behind the thesis work is a desire to bring analysis and probability to bear on a class of relevant and intriguing physical problems, and in so doing, to allow applications to drive the development of new mathematical theory. The unifying theme is the study of rare events under the influence of small, random perturbations, and the manifold mathematical problems which ensue. In the first part, we apply large deviation theory and prefactor estimates to a coherent rotation micromagnetic model in order to analyze thermally activated magnetic switching. We consider recent physical experiments and the mathematical questions "asked" by them. A stochastic resonance type phenomenon is discovered, leading to the definition of finite temperature astroids. Non-Arrhenius behavior is discussed. The analysis is extended to ramped astroids. In addition, we discover that for low damping and ultrashort pulses, deterministic effects can override thermal effects, in accord with very recent ultrashort pulse experiments. Even more interesting, perhaps, is the study of large deviations in the infinite dimensional context, i.e. in spatially extended systems. Inspired by recent numerical investigations, we study the stochastically perturbed Allen Cahn and Cahn Hilliard equations. For the Allen Cahn equation, we study the action minimization problem (a deterministic variational problem) and prove the action scaling in four parameter regimes, via upper and lower bounds. The sharp interface limit is studied. We formally derive a reduced action functional which lends insight into the connection between action minimization and curvature flow. For the Cahn Hilliard equation, we prove upper and lower bounds for the scaling of the energy barrier in the nucleation and growth regime. Finally, we consider rare events in large or infinite domains, in one spatial dimension. We introduce a natural reference measure through which to analyze the invariant measure of stochastically perturbed, nonlinear partial differential equations. Also, for noisy reaction diffusion equations with an asymmetric potential, we discover how to rescale space and time in order to map the dynamics in the zero temperature limit to the Poisson Model, a simple version of the Johnson-Mehl-Avrami-Kolmogorov model for nucleation and growth.