Network Working Group S. Kelly
Request for Comments: 4772 Aruba Networks
Category: Informational December 2006
Security Implications of Using the Data Encryption Standard (DES)
Status of This Memo
This memo provides information for the Internet community. It does
not specify an Internet standard of any kind. Distribution of this
memo is unlimited.
Copyright Notice
Copyright (C) The IETF Trust (2006).
Abstract
The Data Encryption Standard (DES) is susceptible to brute-force
attacks, which are well within the reach of a modestly financed
adversary. As a result, DES has been deprecated, and replaced by the
Advanced Encryption Standard (AES). Nonetheless, many applications
continue to rely on DES for security, and designers and implementers
continue to support it in new applications. While this is not always
inappropriate, it frequently is. This note discusses DES security
implications in detail, so that designers and implementers have all
the information they need to make judicious decisions regarding its
use.
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Table of Contents
1. Introduction ....................................................3
1.1. Executive Summary of Findings and Recommendations ..........4
1.1.1. Recommendation Summary ..............................4
2. Why Use Encryption? .............................................5
3. Real-World Applications and Threats .............................6
4. Attacking DES ...................................................8
4.1. Brute-Force Attacks ........................................9
4.1.1. Parallel and Distributed Attacks ...................10
4.2. Cryptanalytic Attacks .....................................10
4.3. Practical Considerations ..................................12
5. The EFF DES Cracker ............................................12
6. Other DES-Cracking Projects ....................................13
7. Building a DES Cracker Today ...................................14
7.1. FPGAs .....................................................15
7.2. ASICs .....................................................16
7.3. Distributed PCs ...........................................16
7.3.1. Willing Participants ...............................17
7.3.2. Spyware and Viruses and Botnets (oh my!) ...........18
8. Why is DES Still Used? .........................................19
9. Security Considerations ........................................20
10. Acknowledgements ..............................................21
Appendix A. What About 3DES? .....................................22
A.1. Brute-Force Attacks on 3DES ...............................22
A.2. Cryptanalytic Attacks Against 3DES ........................23
A.2.1. Meet-In-The-Middle (MITM) Attacks ..................23
A.2.2. Related Key Attacks ................................24
A.3. 3DES Block Size ...........................................25
Informative References ............................................25
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1. Introduction
The Data Encryption Standard [DES] is the first encryption algorithm
approved by the U.S. government for public disclosure. Brute-force
attacks became a subject of speculation immediately following the
algorithm's release into the public sphere, and a number of
researchers published discussions of attack feasibility and explicit
brute-force attack methodologies, beginning with [DH77].
In the early to mid 1990s, numerous additional papers appeared,
including Wiener's "Efficient DES Key Search" [WIEN94], and "Minimal
Key Lengths for Symmetric Ciphers to Provide Adequate Commercial
Security" [BLAZ96]. While these and various other papers discussed
the theoretical aspects of DES-cracking machinery, none described a
specific implementation of such a machine. In 1998, the Electronic
Frontier Foundation (EFF) went much further, actually building a
device and freely publishing the implementation details for public
review [EFF98].
Despite the fact that the EFF clearly demonstrated that DES could be
brute-forced in an average of about 4.5 days with an investment of
less than $250,000 in 1998, many continue to rely on this algorithm
even now, more than 8 years later. Today, the landscape is
significantly different: DES can be broken by a broad range of
attackers using technologies that were not available in 1998,
including cheap Field Programmable Gate Arrays (FPGAs) and botnets
[BOT05]. These and other attack methodologies are described in
detail below.
Given that the Advanced Encryption Standard [AES] has been approved
by the U.S. government (under certain usage scenarios) for top-secret
applications [AES-NSA], and that triple DES (3DES) is not susceptible
to these same attacks, one might wonder: why even bother with DES
anymore? Under more ideal circumstances, we might simply dispense
with it, but unfortunately, this would not be so simple today. DES
has been widely deployed since its release in the 1970s, and many
systems rely on it today. Wholesale replacement of such systems
would be very costly. A more realistic approach entails gradual
replacement of these systems, and this implies a term of backward
compatibility support of indefinite duration.
In addition to backward compatibility, in isolated instances there
may be other valid arguments for continued DES support. Still,
reliance upon this deprecated algorithm is a serious error from a
security design perspective in many cases. This note aims to clarify
the security implications of this choice given the state of
technology today, so that developers can make an informed decision as
to whether or not to implement this algorithm.
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1.1. Executive Summary of Findings and Recommendations
For many years now, DES usage has been actively discouraged by the
security area of the IETF, but we nevertheless continue to see it in
use. Given that there are widely published accounts of real attacks
and that we have been vocally discouraging its use, a question
arises: why aren't people listening? We can only speculate, but one
possibility is that they simply do not understand the extent to which
DES has been marginalized by advancing cryptographic science and
technology. Another possibility is that we have not yet been
appropriately explicit and aggressive about this. With these
particular possibilities in mind, this note sets out to dispel any
remaining illusions.
The depth of background knowledge required to truly understand and
fully appreciate the security risks of using DES today is somewhat
daunting, and an extensive survey of the literature suggests that
there are very few published materials encompassing more than a
fraction of the considerations all in one place, with [CURT05] being
one notable exception. However, even that work does not gather all
of the pieces in such a way as to inform an implementer of the
current real-world risks, so here we try to fill in any remaining
gaps.
For convenience, the next section contains a brief summary of
recommendations. If you don't know the IETF's current position on
DES, and all you want is a summary, you may be content to simply read
the recommendation summary section, and skip the rest of the
document. If you want a more detailed look at the history and
current state-of-the-art with respect to attacking DES, you will find
that in subsequent sections.
1.1.1. Recommendation Summary
There are several ways to attack a cryptographic algorithm, from
simple brute force (trying each key until you find the right one) to
more subtle cryptanalytic approaches, which take into account the
internal structure of the cipher. As noted in the introduction, a
dedicated system capable of brute-forcing DES keys in less than 5
days was created in 1998. Current "Moore's Law" estimates suggest
that a similar machine could be built today for around $15,000 or
less, and for the cost of the original system (~$250,000) we could
probably build a machine capable of cracking DES keys in a few hours.
Additionally, there have been a number of successful distributed
attacks on DES [CURT05], and with the recent arrival of botnets
[BOT05], these results are all the more onerous. Furthermore, there
are a number of cryptanalytic attacks against DES, and while some of
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these remain purely theoretical in nature at present, at least one
was recently implemented using a FPGA that can deduce a DES key in
12-15 hours [FPL02]. Clearly, DES cannot be considered a "strong"
cryptographic algorithm by today's standards.
To summarize current recommendations on using DES, the simple answer
is "don't use it - it's not safe." While there may be use cases for
which the security of DES would be sufficient, it typically requires
a security expert to determine when this is true. Also, there are
much more secure algorithms available today (e.g., 3DES, AES) that
are much safer choices. The only general case in which DES should
still be supported is when it is strictly required for backward
compatibility, and when the cost of upgrading outweighs the risk of
exposure. However, even in these cases, recommendations should
probably be made to phase out such systems.
If you are simply interested in the current recommendations, there
you have it: don't use DES. If you are interested in understanding
how we arrive at this conclusion, read on.
2. Why Use Encryption?
In order to assess the security implications of using DES, it is
useful and informative to review the basic rationale for using
encryption. In general, we encrypt information because we desire
confidentiality. That is, we want to limit access to information, to
keep something private or secret. In some cases, we want to share
the information within a limited group, and in other cases, we may
want to be the sole owner of the information in question.
Sometimes, the information we want to protect has value only to the
individual (e.g., a diary), and a loss of confidentiality, while
potentially damaging in some limited ways, would typically not be
catastrophic. In other cases, the information might have significant
financial implications (e.g., a company's strategic marketing plan).
And in yet others, lives could be at stake.
In order to gauge our confidentiality requirements in terms of
encryption strength, we must assess the value of the information we
are trying to protect, both to us and to a potential attacker. There
are various metrics we can employ for this purpose:
o Cost of confidentiality loss: What could we lose if an adversary
were to discover our secret? This gives some measure of how much
effort we should be willing to expend to protect the secret.
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o Value to adversary: What does the attacker have to gain by
discovering our secret? This gives some measure of how much an
adversary might reasonably be willing to spend to learn the
secret.
o Window of opportunity: How long does the information have value to
an adversary? This gives some measure of how acceptable a
weakness might be. For example, if the information is valuable to
an attacker for months and it takes only days to break the
encryption, we probably need much stronger encryption. On the
other hand, if the window of opportunity is measured in seconds,
then an encryption algorithm that takes days to break may be
acceptable.
There are certainly other factors we would consider in conducting a
comprehensive security analysis, but these are enough to give a
general sense of important questions to answer when evaluating DES as
a candidate encryption algorithm.
3. Real-World Applications and Threats
Numerous commonly used applications rely on encryption for
confidentiality in today's Internet. To evaluate the sufficiency of
a given cryptographic algorithm in this context, we should begin by
asking some basic questions: what are the real-world risks to these
applications, i.e., how likely is it that an application might
actually be attacked, and by whom, and for what reasons?
While it is difficult to come up with one-size-fits-all answers based
on general application descriptions, we can easily get some sense of
the relative threat to many of these applications. It is important
to note that what follows is not an exhaustive enumeration of all
likely threats and attacks, but rather, a sampling that illustrates
that real threats are more prevalent than intuition might suggest.
Here are some examples of common applications and related threats:
o Site-to-site VPNs: Often, these are used to connect geographically
separate corporate offices. Data traversing such links is often
business critical, and sometimes highly confidential. The FBI
estimates that every year, billions of U.S. dollars are lost to
foreign competitors who deliberately target economic intelligence
in U.S. industry and technologies [FBI06]. Searching for
'corporate espionage' in Google yields many interesting links,
some of which indicate that foreign competitors are not the only
threat to U.S. businesses. Obviously, this threat can be
generalized to include businesses of any nationality.
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o Remote network access for business: See previous item.
o Webmail/email encryption: See Site-to-site VPNs.
o Online banking: Currently, the most common threat to online
banking is in the form of "phishing", which does not rely on
breaking session encryption, but instead relies on tricking users
into providing their account information. In general, direct
attacks on session encryption for this application do not scale
well. However, if a particular bank were known to use a weak
encryption algorithm for session security, it might become
worthwhile to develop a broader attack against that bank. Given
that organized criminal elements have been found behind many
phishing attacks, it is not difficult to imagine such scenarios.
o Electronic funds transfers (EFTs): The ability to replay or
otherwise modify legitimate EFTs has obvious financial incentives
(and implications). Also, an industrial spy might see a great
deal of intelligence value in the financial transactions of a
target company.
o Online purchases (E-commerce): The FBI has investigated a number
of organized attacks on e-commerce applications [FBI01]. If an
attacker has the ability to monitor e-commerce traffic directed to
a large merchant that relies on weak encryption, the attacker
could harvest a great deal of consumer credit information. This
is the sort of data "phishers" currently harvest on a much smaller
scale, so one can easily imagine the value of such a target.
o Internet-based VoIP applications (e.g., Skype): While many uses of
this technology are innocuous (e.g., long distance calls to family
members), VoIP technology is also used for business purposes (see
discussion of FBI estimates regarding corporate espionage above).
o Cellular telephony: Cell phones are very common, and are
frequently used for confidential conversations in business,
medicine, law enforcement, and other applications.
o Wireless LAN: Wireless technology is used by many businesses,
including the New York Stock Exchange [NYSE1]. The financial
incentives for an attacker are significant in some cases.
o Personal communications (e.g., secure instant messaging): Such
communication may be used for corporate communications (see
industrial espionage discussion above), and may also be used for
financial applications such as stock/securities trading. This has
both corporate/industrial espionage and financial implications.
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o Laptop hard-drive encryption: See discussion on corporate/
industrial espionage above. Also, consider that stolen and lost
laptops have been cited for some of the more significant losses of
control over sensitive personal information in recent years,
notably the Veterans Affairs data loss [VA1].
There are real-world threats to everyday encryption applications,
some of which could be very lucrative to an attacker (and by
extension, very costly to the victim). It is important to note that
if some of these attacks are infrequent today, it is precisely
because the threats are recognized, and appropriately strong
cryptographic algorithms are used. If "weak" cryptographic
algorithms were to be used instead, the implications are indeed
thought-provoking.
In keeping with the objectives of this document, it is important to
note that the U.S. government has never approved the use of DES for
anything but unclassified applications. While DES is still approved
for unclassified uses until May 19, 2007, the U.S. government clearly
sees the need to move to higher ground. For details on the National
Institute of Standards and Technology (NIST) DES Transition plan, see
[NIST-TP]. Despite this fact, DES is still sometimes chosen to
protect some of the applications described above. Below, we discuss
why this should, in many cases, be remedied.
4. Attacking DES
DES is a 64-bit block cipher having a key size of 56 bits. The key
actually has 64 bits (matching the block size), but 1 bit in each
byte has been designated a 'parity' bit, and is not used for
cryptographic purposes. For a full discussion of the history of DES
along with an accessible description of the algorithm, see [SCHN96].
A detailed description of the various types of attacks on
cryptographic algorithms is beyond the scope of this document, but
for clarity, we provide the following brief descriptions. There are
two general aspects of attacks we must consider: the form of the
inputs/outputs along with how we might influence them, and the
internal function of the cryptographic operations themselves.
In terms of input/output form, some of the more commonly discussed
attack characteristics include the following:
o known plaintext - the attacker knows some of the plaintext
corresponding to some of the ciphertext
o ciphertext-only - only ciphertext is available to the attacker,
who has little or no information about the plaintext
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o chosen plaintext - the attacker can choose which plaintext is
encrypted, and obtain the corresponding ciphertext
o birthday attacks - relies on the fact that for N elements,
collisions can be expected in ~sqrt(N) randomly chosen samples;
for systems using CBC mode with random Initialization Vectors
(IVs), ciphertext collisions can be expected in about 2^28
samples. Such collisions leak information about the corresponding
plaintexts: if the same cryptographic key is used, then the xor of
the IVs is equal to the xor of the plaintexts.
o meet-in-the-middle attacks - leverages birthday characteristic to
precompute potential key collision values
Due to the limited scope of this document, these are very brief
descriptions of very complex subject matter. For more detailed
discussions on these and many related topics, see [SCHN96], [HAC], or
[FERG03].
As for attack characteristics relating to the operational aspects of
cipher algorithms, there are essentially two broad classes we
consider: cryptanalytic attacks, which exploit some internal
structure or function of the cipher algorithm, and brute-force
attacks, in which the attacker systematically tries keys until the
right one is found. These could alternatively be referred to as
white box and black box attacks, respectively. These are discussed
further below.
4.1. Brute-Force Attacks
In general, a brute-force attack consists of trying each possible key
until the correct key is found. In the worst case, this will require
2^n steps for a key size of n bits, and on average, it will require
2^n-1 steps. For DES, this implies 2^56 encryption operations in the
worst case, and 2^55 encryption operations on average, if we assume
no shortcuts exist. As it turns out, the complementation property of
DES provides an attack that yields a reduction by a factor of 2 for a
chosen plaintext attack, so this attack requires an average of 2^54
encryption operations.
Above, we refer to 2^n 'steps'; note that what a 'step' entails
depends to some extent on the first attack aspect described above,
i.e., what influence and knowledge we have with respect to input/
output forms. Remember, in the worst case, we will be performing
72,057,594,037,927,936 -- over 72 quadrillion -- of these 'steps'.
In the most difficult case, we have ciphertext only, and no knowledge
of the input, and this is very important.
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If the input is effectively random, we cannot tell by simply looking
at a decrypted block whether we've succeeded or not. We may have to
resort to other potentially expensive computation to make this
determination. While the effect of any additional computation will
be linear across all keys, repeating a large amount of added
computation up to 72 quadrillion times could have a significant
impact on the cost of a brute-force attack against the algorithm.
For example, if it takes 1 additional microsecond per computation,
this will add almost 101 days to our worst-case search time, assuming
a serial key search.
On the other hand, if we can control the input to the encryption
function (known plaintext), we know precisely what to expect from the
decryption function, so detecting that we've found the key is
straightforward. Alternatively, even if we don't know the exact
input, if we know something about it (e.g., that it's ASCII), with
limited additional computation we can infer that we've most likely
found a key. Obviously, which of these conditions holds may
significantly influence attack time.
4.1.1. Parallel and Distributed Attacks
Given that a brute-force attack involves systematically trying keys
until we find the right one, it is obviously a good candidate for
parallelization. If we have N processors, we can find the key
roughly N times faster than if we have only 1 processor. This
requires some sort of centralized control entity that distributes the
work and monitors the search process, but is quite straightforward to
implement.
There are at least two approaches to parallelization of a brute-force
attack on a block cipher: the first is to build specialized high-
speed hardware that can rapidly cycle through keys while performing
the cryptographic and comparison operations, and then replicate that
hardware many times, while providing for centralized control. The
second involves using many copies of general purpose hardware (e.g.,
a PC), and distributing the load across these while placing them
under the control of one or more central systems. Both of these
approaches are discussed further in sections 5 and 6.
4.2. Cryptanalytic Attacks
Brute-force attacks are so named because they don't require much
intelligence in the attack process -- they simply try one key after
the other, with little or no intelligent keyspace pruning.
Cryptanalytic attacks, on the other hand, rely on application of some
intelligence ahead of time, and by doing so, provide for a
significant reduction of the search space.
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While an in-depth discussion of cryptanalytic techniques and the
resulting attacks is well beyond the scope of this document, it is
important to briefly touch on this area in order to set the stage for
subsequent discussion. It is also important to note that, in
general, cryptanalysis can be applied to any cryptographic algorithm
with varying degrees of success. However, we confine ourselves here
to discussing specific results with respect to DES.
Here is a very brief summary of the currently known cryptanalytic
attacks on DES:
o Differential Cryptanalysis - First discussed by Biham and Shamir,
this technique (putting it very simply) analyzes how differences
in plaintext correspond to differences in ciphertext. For more
detail, see [BIH93].
o Linear Cryptanalysis - First described by Matsui, this technique
uses linear approximations to describe the internal functions of
DES. For more detail, see [MAT93].
o Interpolation Attack - This technique represents the S-boxes of
DES with algebraic functions, and then estimates the coefficients
of the functions. For more information, see [JAK97].
o Key Collision Attack - This technique exploits the birthday
paradox to produce key collisions [BIH96].
o Differential Fault Analysis - This attack exploits the electrical
characteristics of the encryption device, selectively inducing
faults and comparing the results with uninfluenced outputs. For
more information, see [BIH96-2].
Currently, the best publicly known cryptanalytic attacks on DES are
linear and differential cryptanalysis. These attacks are not
generally considered practical, as they require 2^43 and 2^47 known
plaintext/ciphertext pairs, respectively. To get a feel for what
this means in practical terms, consider the following:
o For linear cryptanalysis (the more efficient of the two attacks),
the attacker must pre-compute and store 2^43 ciphertexts; this
requires 8,796,093,022,208 (almost 9 trillion) encryption
operations.
o Each ciphertext block is 8 bytes, so the total required storage is
70,368,744,177,664 bytes, or about 70,369 gigabytes of storage.
If the plaintext blocks cannot be automatically derived, they too
must be stored, potentially doubling the storage requirements.
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o The 2^43 known plaintext blocks must be somehow fed to the device
under attack, and that device must not change the encryption key
during this time.
Clearly, there are practical issues with this attack. Still, it is
sobering to look at how much more realistic 70,000 gigabytes of
storage is today than it must have seemed in 1993, when Matsui first
proposed this attack. Today, 400-GB hard drives can be had for
around $0.35/gigabyte. If we only needed to store the known
ciphertext, this amounts to ~176 hard drives at a cost of less than
$25,000. This is probably practical with today's technology for an
adversary with significant financial resources, though it was
difficult to imagine in 1993. Still, numerous other practical issues
remain.
4.3. Practical Considerations
Above, we described several types of attacks on DES, some of which
are more practical than others, but it's very important to recognize
that brute force represents the very worst case, and cryptanalytic
attacks can only improve on this. If a brute-force attack against a
given DES application really is feasible, then worrying about the
practicality of the other theoretical attack modes is just a
distraction. The bottom line is this: if DES can be brute-forced at
a cost the attacker can stomach today, this cost will invariably come
down as technology advances.
5. The EFF DES Cracker
On the question as to whether DES is susceptible to brute-force
attack from a practical perspective, the answer is a resounding and
unequivocal "yes". In 1998, the Electronic Frontier Foundation
financed the construction of a "DES Cracker", and subsequently
published "Cracking DES" [EFF98]. For a cost of less than $250,000,
this system can find a 56-bit DES key in the worst-case time of
around 9 days, and in 4.5 days on average.
Quoting from [EFF98],
"The design of the EFF DES Cracker is simple in concept. It consists
of an ordinary personal computer connected with a large array of
custom chips. Software in the personal computer instructs the custom
chips to begin searching, and interacts with the user. The chips run
without further help from the software until they find a potentially
interesting key, or need to be directed to search a new part of the
key space. The software periodically polls the chips to find any
potentially interesting keys that they have turned up.
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The hardware's job isn't to find the answer. but rather to eliminate
most of the answers that are incorrect. Software is then fast enough
to search the remaining potentially-correct keys, winnowing the false
positives from the real answer. The strength of the machine is that
it replicates a simple but useful search circuit thousands of times,
allowing the software to find the answer by searching only a tiny
fraction of the key space.
As long as there is a small bit of software to coordinate the effort,
the problem of searching for a DES key is 'highly parallelizable'.
This means the problem can be usefully solved by many machines
working in parallel, simultaneously. For example, a single DES-
Cracker chip could find a key by searching for many years. A
thousand DES-Cracker chips can solve the same problem in one
thousandth of the time. A million DES-Cracker chips could
theoretically solve the same problem in about a millionth of the
time, though the overhead of starting each chip would become visible
in the time required. The actual machine we built contains 1536
chips."
This project clearly demonstrated that a practical system for brute
force DES attacks was well within reach of many more than previously
assumed. Practically any government in the world could easily
produce such a machine, and in fact, so could many businesses. And
that was in 1998; the technological advances since then have greatly
reduced the cost of such a device. This is discussed further below.
6. Other DES-Cracking Projects
In the mid-1990s, many were interested in whether or not DES was
breakable in a practical sense. RSA sponsored a series of DES
Challenges over a 3-year period beginning January of 1997. These
challenges were created in order to help underscore the point that
cryptographic strength limitations imposed by the U.S. government's
export policies were far too modest to meet the security requirements
of many users.
The first DES challenge was solved by the DESCHALL group, led by
Rocke Verser, Matt Curtin, and Justin Dolske [CURT05][RSA1]. They
created a loosely-knit distributed effort staffed by volunteers and
backed by Universities and corporations all over the world who
donated their unused CPU cycles to the effort. They found the key in
90 days.
The second DES challenge was announced on December 19, 1997
[RSA2][CURT05], and on February 26, 1998, RSA announced a winner.
This time, the challenge was solved by group called distributed.net
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working together with the EFF, in a total of 39 days [RSA3] [CURT05].
This group coordinated 22,000 participants and over 50,000 CPUs.
The third DES challenge was announced on December 22, 1998
[RSA4][CURT05], and on January 19, 1999, RSA announced the winner.
This time, the challenge was again solved by distributed.net working
together with the EFF, in a total of 22 hours [RSA5]. This was a
dramatic improvement over the second challenge, and should give some
idea of where we're headed with respect to DES.
7. Building a DES Cracker Today
We've seen what was done in the late 1990s -- what about today? A
survey of the literature might lead one to conclude that this topic
is no longer interesting to cryptographers. Hence, we are left to
infer the possibilities based on currently available technologies.
One way to derive an approximation is to apply a variation on
"Moore's Law": assume that the cost of a device comparable to the one
built by the EFF would be halved roughly every N months. If we take
N=18, then for a device costing $250,000 at the end of 1998, this
would predict the following cost curve:
o mid-2000............: $125,000
o beginning of 2002...: $62,500
o mid-2003............: $31,250
o beginning of 2006...: $15,625
It's important to note that strictly speaking, "Moore's Law" is more
an informal approximation than a law, although it has proven to be
uncannily accurate over the last 40 years or so. Also, some would
disagree with the use of an 18-month interval, preferring a more
conservative 24 months instead. So, these figures should be taken
with the proverbial grain of salt. Still, it's important to
recognize that this is the cost needed not to crack one key, but to
get into the key-cracking business. Offering key-cracking services
and keeping the machine relatively busy would dramatically decrease
the cost to a few hundred dollars per unit or less.
Given that such calculations roughly hold for other computing
technologies over the same time interval, the estimate above does not
seem too unreasonable, and is probably within a factor of two of
today's costs. Clearly, this would seem to indicate that DES-
cracking hardware is within reach of a much broader group than in
1998, and it is important to note that this assumes no design or
algorithm improvements since then.
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To put this in a slightly different light, let's consider the typical
rendition of Moore's Law for such discussions. Rather than
considering shrinking cost for the same capability, consider instead
increasing capability for the same cost (i.e., doubling circuit
densities every N months). Again choosing N=18, our DES-cracking
capability (in worst-case time per key) could be expected to have
approximately followed this performance curve over the last 7 or so
years:
o 1998................: 9 days
o mid-2000............: 4.5 days
o beginning of 2002...: 2.25 days
o mid-2003............: 1.125 days
o beginning of 2006...: 0.5625 days
That's just over a half-day in the worst case for 2006, and under 7
hours on average. And this, for an investment of less than $250,000.
It's also very important to note that we are talking about worst-case
and average times here - sometimes, keys will be found much more
quickly. For example, using such a machine, 1/4 of all possible DES
keys will be found within 3.375 hours. 1/8 of the keys will be found
in less than 1 hour and 42 minutes. And this assumes no algorithmic
improvements have occurred. And again, this is an estimate; your
actual mileage may vary, but the estimate is probably not far from
reality.
7.1. FPGAs
Since the EFF device first appeared, Field Programmable Gate Arrays
(FPGAs) have become quite common, and far less costly than they were
in 1998. These devices allow low-level logic programming, and are
frequently used to prototype new logic designs prior to the creation
of more expensive custom chips (also known as Application Specific
Integrated Circuits, or ASICs). They are also frequently used in
place of ASICs due to their lower cost and/or flexibility. In fact,
a number of embedded systems implementing cryptography have employed
FPGAs for this purpose.
Due to their generalized nature, FPGAs are naturally slower than
ASICs. While the speed difference varies based on many factors, it
is reasonable for purposes of this discussion to say that well-
designed FPGA implementations typically perform cryptographic
Kelly Informational [Page 15]
RFC 4772 DES Security Implications December 2006
operations at perhaps 1/4 the speed of well-designed ASICs performing
the same operations, and sometimes much slower than that. The
significance of this comparison will become obvious shortly.
In our Moore's Law estimate above, we noted that the cost
extrapolation assumes no design or algorithm improvements since 1998.
It also implies that we are still talking about a brute-force attack.
In section 4 ("Attacking DES"), we discussed several cryptanalytic
attacks, including an attack that employs linear cryptanalysis
[MAT93]. In general, this attack has been considered impractical,
but in 2002, a group at Universite Catholique de Louvain in Belgium
built a DES cracker based on linear cryptanalysis, which, employing a
single FPGA, returns a DES key in 12-15 hours [FPL02].
While there are still some issues of practicality in terms of
applying this attack in the real world (i.e., the required number of
known plaintext-ciphertext pairs), this gives a glimpse of where
technology is taking us with respect to DES attack capabilities.
7.2. ASICs
Application Specific Integrated Circuits are specialized chips,
typically optimized for a particular set of operations (e.g.,
encryption). There are a number of companies that are in the
business of designing and selling cryptographic ASICs, and such chips
can be had for as little as $15 each at the low end. But while these
chips are potentially much faster than FPGAs, they usually do not
represent a proportionally higher threat when it comes to
DES-cracking system construction.
The primary reason for this is cost: it currently costs more than
$1,000,000 to produce an ASIC. There is no broad commercial market
for crypto-cracking ASICs, so the number a manufacturer could expect
to sell is probably