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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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RFC 4772 DES Security Implications December 2006
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
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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 small. Likewise, a single attacker is not likely
to require more than a few of these. The bottom line: per-chip costs
would be very high; when compared to the costs of FPGAs capable of
similar performance, the FPGAs are clear winners. This doesn't mean
such ASICs have never been built, but the return is probably not
worth the investment for the average attacker today, given the other
available options.
7.3. Distributed PCs
Parallel processing is a powerful tool for conducting brute-force
attacks against a block cipher. Since each key can be tested
independently, the keyspace can easily be carved up and distributed
across an arbitrary number of processors, all of which are running
identical code. A central "control" processor is required for
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distributing tasks and evaluating results, but this is
straightforward to implement, and this paradigm has been applied to
many computing problems.
While the EFF demonstrated that a purpose-built system is far
superior to general purpose PCs when applied to cracking DES, the
DESCHALL effort [CURT05][RSA1] aptly demonstrated that the idle
cycles of everyday users' PCs could be efficiently applied to this
problem. As noted above, distributed.net teamed with the EFF group
to solve the third RSA DES Challenge using a combination of PCs and
the EFF's "Deep Crack" machine to find a DES key in 22 hours. And
that was using 1999 technologies.
Clearly, PCs have improved dramatically since 1999. At that time,
state-of-the-art desktops ran at around 800MHz. Today, desktop PCs
commonly run at 3-4 times that speed, and supporting technologies
(memory, cache, storage) offer far higher performance as well. Since
the distributed.net effort used a broad spectrum of computers (from
early 1990s desktops to state-of-the-art (in 1999) multiprocessors,
according to [DIST99]), it is difficult to do a direct comparison
with today's technologies. Still, we know that performance has, in
general, followed the prediction of Moore's Law, so we should expect
an improvement on the order of a factor of 8-16 by now, even with no
algorithmic improvements
7.3.1. Willing Participants
It is important to note that the distributed.net efforts have relied
upon willing participants. That is, participants must explicitly and
voluntarily join the effort. It is equally important to note that
only the idle cycles of the enrolled systems are used. Depending on
the way in which "idle" is defined, along with the user's habits and
computing requirements, this could have a significant effect on the
contribution level of a given system.
These factors impose significant limitations in terms of scale.
While distributed.net was able to enlist over 100,000 computers from
around the world for the third RSA DES Challenge, this is actually a
rather small number when compared to 2^56 (over 72 quadrillion)
possible DES keys. And when you consider the goal (i.e., to prove
DES can be cracked), it seems reasonable to assume these same
participants would not willingly offer up their compute cycles for a
more nefarious use (like attacking the keys used to encrypt your
online banking session). Hence, this particular model does not
appear to pose a significant threat to most uses of encryption today.
However, below, we discuss a variation on this approach that does
pose an immediate threat.
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7.3.2. Spyware and Viruses and Botnets (oh my!)
"Spyware" is a popular topic in security newsfeeds these days. Most
of these applications are intended to display context-sensitive
advertisements to users, and some actually modify a user's web
browsing experience, directing them to sites of the distributor's
choice in an effort to generate revenue. There are many names for
this type of software, but for our purposes, we will refer to it
simply as "spyware". And while there are some instances in which
rogue software actually does spy on hapless users and report things
back to the issuer, we do not focus here on such distinctions.
Indeed, what we are more interested in is the broader modality in
which this software functions: it is typically installed without the
explicit knowledge and/or understanding of the user, and typically
runs without the user's knowledge, sometimes slowing the user's PC to
a crawl. One might note that such behavior seems quite surprising in
view of the fact that displaying ads to users is actually a light-
weight task, and wonder what this software is actually doing with all
those compute cycles.
Worms and viruses are also very interesting: like spyware, these are
installed without the user's knowledge or consent, and they use the
computer in ways the user would not voluntarily allow. And unlike
the spyware that is most common today, this malware usually contains
explicit propagation technology by which it automatically spreads.
It is not difficult to imagine where we are going with this: if you
combine these techniques, forcible induction of user machines into an
"army" of systems becomes possible. This approach was alluded to in
[CURT98] and, in fact, is being done today.
Botnets [BOT05] represent a relatively recent phenomena. Using
various propagation techniques, malware is distributed across a range
of systems, where it lies in wait for a trigger of some sort. These
"triggers" may be implemented through periodic polling of a
centralized authority, the arrival of a particular date, or any of a
large number of other events. Upon triggering, the malware executes
its task, which may involve participating in a Distributed Denial of
Service (DDoS) attack, or some other type of activity.
Criminal groups are currently renting out botnets for various uses
[CERT01]. While reported occurrences have typically involved using
these rogue networks for DDoS attacks, we would be naive to think
other uses (e.g., breaking encryption keys) have not been considered.
Botnets greatly mitigate the scaling problem faced by
distributed.net: it is no longer a volunteer-only effort, and user
activity no longer significantly impedes the application's progress.
This should give us pause.
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It is very important to clearly recognize the implications of this:
botnets are cheap, and there are lots of PCs out there. You don't
need the $15,625 that we speculated would be enough to build a copy
of the EFF system today -- you only need a commodity PC on which to
develop the malware, and the requisite skills. Or, you need access
to someone with those things, and a relatively modest sum of cash.
The game has changed dramatically.
8. Why is DES Still Used?
Obviously, DES is not secure by most measures -- why is it still used
today? There are probably many reasons, but here are perhaps the
most common:
o Backward compatibility - Numerous deployed systems support DES,
and rather than replace those systems, new systems are implemented
with compatibility in mind.
o Performance - Many early VPN clients provided DES as the default
cryptographic algorithm, because PCs of the day suffered a
noticeable performance hit when applying stronger cryptography
(e.g., 3DES).
o Ignorance - People simply do not understand that DES is no longer
secure for most uses.
While there are probably other reasons, these are the most frequently
cited.
Performance arguments are easily dispensed with today. PCs have more
than ample power to implement stronger cryptography with no
noticeable performance impact, and for systems that are resource
constrained, there are strong algorithms that are far better
performers than DES (e.g., AES-128). And while backward
compatibility is sometimes a valid argument, this must be weighed
carefully. At the point where the risk is higher than the cost of
replacement, legacy systems should be abandoned.
With respect to the third reason (ignorance), this note attempts to
address this, and we should continue to make every effort to get the
word out. DES is no longer secure for most uses, and it requires
significant security expertise to evaluate those small number of
cases in which it might be acceptable. Technologies exist that put
DES-cracking capability within reach of a modestly financed or
modestly skilled motivated attacker. There are stronger, cheaper,
faster encryption algorithms available. It is time to move on.
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9. Security Considerations
This entire document deals with security considerations. Still, it
makes sense to summarize a few key points here. It should be clear
by now that the DES algorithm offers little deterrence for a
determined adversary. While it might have cost $250,000 to build a
dedicated DES cracker in 1998, nowadays it can be done for
considerably less. Indeed, botnets are arguably free, if you don't
count the malware author's time in your cost computation.
Does this mean DES should never be used? Well, no - but it does mean
that if it is used at all, it should be used with extreme care. It
is important to carefully evaluate the value of the information being
protected, both to its owner and to an attacker, and to fully grasp
the potential risks. In some cases, DES may still provide an
acceptable level of security, e.g., when you want to encrypt a file
on the family PC, and there are no real threats in your household.
However, it is important to recognize that, in such cases, DES is
much like a cheap suitcase lock: it usually helps honest people
remain honest, but it won't stop a determined thief. Given that
strong, more efficient cryptographic algorithms (e.g., AES) are
available, it seems the only rational reason to continue using DES
today is for compulsory backward compatibility. In such cases, if
there is no plan for gradually phasing out such products, then, as a
security implementer, you can do the following:
o Recommend a phased upgrade approach.
o If possible, use 3DES rather than DES (and in any case, DO NOT
make DES the default algorithm!).
o Replace keys before exceeding 2^32 blocks per key (to avoid
various cryptanalytic attacks).
o If there is a user interface, make users aware of the fact that
the cryptography in use is not strong, and for your particular
application, make appropriate recommendations in this regard.
The bottom line: it is simpler to not use this algorithm than it is
to come up with narrow scenarios in which it might be okay. If you
have legacy systems relying on DES, it makes sense to begin phasing
them out as soon as possible.
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10. Acknowledgements
The author gratefully acknowledges the contributions of Doug Whiting,
Matt Curtin, Eric Rescorla, Bob Baldwin, and Yoav Nir. Their
reviews, comments, and advice immeasurably improved this note. And
of course, we all have the EFF and all those involved with the "Deep
Crack", DESCHALL, and distributed.net efforts to thank for their
pioneering research and implementations in this area.
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Appendix A. What About 3DES?
It seems reasonable, given that we recommend avoiding DES, to ask:
how about 3DES? Is it still safe? Thankfully, most of the
discussion above does not apply to 3DES, and it is still "safe" in
general. Below, we briefly explain why this is true, and what
caveats currently exist.
A.1. Brute-Force Attacks on 3DES
Recall that for DES there are 2^56 possible keys, and that a brute-
force attack consists of trying each key until the right one is
found. Since we are equally likely to find the key on the first,
second, or even last try, on average we expect to find the key after
trying half (2^55) of the keys, or after 36,028,797,018,963,968
decryptions. This doesn't seem completely impossible given current
processor speeds, and as we saw above, we can expect with today's
technology that such an attack could almost certainly be carried out
in around half a day.
For a brute-force attack on 3DES, however, the outlook is far less
optimistic. Consider the problem: we know C (and possibly p), and we
are trying to guess k1, k2, and k3 in the following relation:
C = E_k3(D_k2(E_k1(p)))
In order to guess the keys, we must execute something like the
following (assuming k1, k2, and k3 are 64-bit values, as are Ci and
p):
for ( k3 = 0 to 2^56 step 1 )
compute C2 = D_k3(C1)
for ( k2 = 0 to 2^56 step 1 )
compute C3 = E_k2(C2)
for ( k1 = 0 to 2^56 step 1 )
begin
compute p = D_k1(C3) xor IV
if ( p equals p-expected )
exit loop; we found the keys
end
Note that in the worst case the correct key combination will be the
last one we try, meaning we will have tried 2^168 crypto operations.
If we assume that each 3DES decryption (2 decryptions plus one
encryption) takes a single microsecond, this would amount to 1.19 x
10^37 years. That's FAR longer than scientists currently estimate
our universe to have been in existence.
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While it is important to note that we could slightly prune the key
space by assuming that two equal keys would never be used (i.e., k1
!= k2, k2 != k3, k1 != k3), this does not result in a significant
work reduction when you consider the magnitude of the numbers we're
dealing with. And what if we instead assumed that technological
advances allow us to apply DES far more quickly?
Today, commercial 3DES chips capable of 10-Gbps encryption are widely
available, and this translates to 15,625,000 DES blocks per second.
The estimate given above assumed 1,000,000 DES blocks/second, so
10-Gbps hardware is 15 times as fast. This means in the worst case
it would take 7.6 x 10^35 years -- not much faster in the larger
scheme of things.
Even if we consider hardware that is 1,000,000 times faster, this
would still require 7.6 x 10^29 years - still FAR longer than the
universe has been around. Obviously, we're getting nowhere fast
here. 3DES, for all practical purposes, is probably safe from brute-
force attacks for the foreseeable future.
A.2. Cryptanalytic Attacks Against 3DES
Unlike DES, there are only a few known cryptanalytic attacks against
3DES. Below, we describe those attacks that are currently discussed
in the literature.
A.2.1. Meet-In-The-Middle (MITM) Attacks
The most commonly described 3DES attack is MITM, described in [HAC]
and elsewhere. It works like this: take a ciphertext value 'C' (with
corresponding known plaintext value 'p'), and compute the values of
Cx = D_kx(C) for all possible (2^56) keys. Store each Cx,kx pair in
a table indexed by Cx.
Now, compute the values of Cy = D_ki(E_kj(p)) in a nested loop, as
illustrated above in our brute-force exercise. For each Cy, do a
lookup on the table of Cx's. For each match found, test the triple
of keys. It is important to note that a match does not imply you
have the right keys - you must test this against additional
ciphertext/plaintext pairs to be certain (~3 pairs for a strong
measure of certainty with 3DES). Ultimately, there will be exactly
one correct key triplet.
Note that computing the initial table of Cx,kx pairs requires 2^56
encryptions and 2^56 blocks of storage (about 576 gigabytes).
Computing the lookup elements requires at most 2^112 cryptographic
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operations (table lookups are negligible by comparison), and 2^111
operations on average. Lucks [LUCKS] has come up with optimizations
that reduce this to about 2^108.
3DES, even at a strength of 2^108, is still very strong. If we use
our brute-force limits from above (15,625,000 blocks per second),
this attack will take on the order of 6.586 x 10^17 years to carry
out. Make the machine 1 million times faster, and you still need
more than 658 BILLION years. We are probably safe from MITM attacks
on 3DES for the foreseeable future.
A.2.2. Related Key Attacks
For a detailed description of related key attacks against 3DES (and
other algorithms), see [KELSEY]. In a nutshell, for this approach
the attacker knows the encryption of given plaintext under the
original key K, and some related keys K'_i. There are attacks where
the attacker chooses how the key is to be changed, and attacks in
which the difference is known, but not controlled, by the attacker.
Here's how it works. Assume the following cryptographic relation:
C = E_k3(D_k2(E_k1(p)))
Then, the following defines the key relation:
K = (k1,k2,k3) and K' = (k1 + d,k2,k3)
with d being a fixed constant. Knowing p and C, we need to decrypt C
under K' as follows:
Let kx = k1 + d (note: '+' represents xor)
and
p' = D_kx(E_k1(p))
Once we have p', we can find kx by exhaustively trying each key until
we find a match (2^56 encryptions, worst case). Once we find kx, we
can conduct a double-DES MITM attack to find k2 and k3, which
requires between 2^56 and 2^72 trial offline encryptions.
From a practical standpoint, it's very important to recognize the
"what-if" nature of this attack: the adversary must know the
plaintext/ciphertext pair, he must be able to influence a subsequent
encryption key in a highly controlled fashion (or at least, know
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exactly how the key changes), and then have the cryptographic
cooperation required to compute p'. This is clearly a very difficult
attack in the real world.
A.3. 3DES Block Size
While the effective key length for 3DES is clearly much larger than
for DES, the block size is, unfortunately, still only 64 bits. For
CBC mode (the most commonly deployed mode in Internet security
protocols), this means that, due to the birthday paradox, information
about the plaintext begins to leak after around 2^32 blocks have been
encrypted. For this reason, 3DES may not be the best choice for
high-throughput links, or other high-density encryption applications.
At minimum, care should be taken to refresh keys frequently enough to
minimize ciphertext collisions in such scenarios.
Informative References
[AES] "The Advanced Encryption Standard", November 2001,
<http://csrc.nist.gov/publications/fips/fips197/
fips-197.pdf>.
[AES-NSA] "CNSS Policy No. 15, Fact Sheet No. 1", June 2003,
<http://csrc.nist.gov/cryptval/CNSS15FS.pdf>.
[BIH93] Biham, E. and A. Shamir, "Differential Cryptanalysis of
the Data Encryption Standard", 1993.
[BIH96] Biham, E., "How to Forge DES-Encrypted Messages in 2^28
Steps", 1996.
[BIH96-2] Biham, E. and A. Shamir, "A New Cryptanalytic Attack on
DES", 1996.
[BLAZ96] Blaze, M., Diffie, W., Rivest, R., Schneier, B.,
Shimomura, T., Thompson, E., and M. Wiener, "Minimal Key
Lengths for Symmetric Ciphers to Provide Adequate
Commercial Security", January 1996.
[BOT05] "Know Your Enemy: Tracking Botnets", March 2005,
<http://www.honeynet.org/papers/bots/>.
[CERT01] Ianelli, N. and A. Hackworth, "Botnets as a Vehicle for
Online Crime", December 2005,
<http://www.cert.org/archive/pdb/Botnets.pdf>.
[CURT05] Curtin, M., "Brute Force: Cracking the Data Encryption
Standard", 2005.
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[CURT98] Curtin, M. and J. Dolske, "A Brute Force Search of DES
Keyspace", 1998,
<http://www.interhack.net/pubs/des-key-crack/>.
[DES] "Data Encryption Standard", January 1977,
<http://www.nist.gov>.
[DH77] Hellman, M. and W. Diffie, "Exhaustive Cryptanalysis of
the NBS Data Encryption Standard", June 1977.
[DIST99] Press Release, distributed., "US GOVERNMENT'S ENCRYPTION
STANDARD BROKEN IN LESS THAN A DAY", 1999,
<http://www1.distributed.net/des/release-desiii.txt>.
[EFF98] EFF, "Cracking DES", July 1998.
[FBI01] "NIPC Advisory 01-003", March 2001,
<http://www.fbi.gov/pressrel/pressrel01/nipc030801.htm>.
[FBI06] "FBI Webpage: Focus on Economic Espionage", January 2006,
<http://www.fbi.gov/hq/ci/economic.htm>.
[FERG03] Ferguson, N. and B. Schneier, "Practical Cryptography",
2003.
[FPL02] Koeune, F., Rouvroy, G., Standaert, F., Quisquater, J.,
David, J., and J. Legat, "An FPGA Implementation of the
Linear Cryptanalysis", FPL 2002, Volume 2438 of Lecture
Notes in Computer Science, pages 846-852, Spriger-Verlag,
September 2002.
[HAC] Menezes, A., van Oorschot, P., and S. Vanstone, "Handbook
of Applied Cryptography", 1997.
[JAK97] Jakobsen, T. and L. Knudsen, "The Interpolation Attack on
Block Ciphers", 1997.
[KELSEY] Kelsey, J., Schneier, B., and D. Wagner, "Key-Schedule
Cryptanalysis of 3-WAY, IDEA, G-DES, RC4, SAFER, and
Triple-DES", 1996.
[LUCKS] Lucks, S., "Attacking Triple Encryption", 1998.
[MAT93] Matsui, M., "Linear Cryptanalysis Method for DES Cipher",
1993.
[NIST-TP] "DES Transition Plan", May 2005,
<http://csrc.nist.gov/cryptval/DESTranPlan.pdf>.
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[NYSE1] "Extreme availability: New York Stock Exchange's new IT
infrastructure puts hand-held wireless terminals in
brokers' hands.", June 2005.
[RSA1] Press Release, RSA., "Team of Universities, Companies and
Individual Computer Users Linked Over the Internet Crack
RSA's 56-Bit DES Challenge", 1997, <http://
www.rsasecurity.com/press_release.asp?doc_id=661&id=1034>.
[RSA2] Press Release, RSA., "RSA to Launch "DES Challenge II" at
Data Security Conference", 1998, <http://
www.rsasecurity.com/press_release.asp?doc_id=729&id=1034>.
[RSA3] Press Release, RSA., "Distributed Team Collaborates to
Solve Secret-Key Challenge", 1998, <http://
www.rsasecurity.com/press_release.asp?doc_id=558&id=1034>.
[RSA4] Press Release, RSA., "RSA to Launch DES Challenge III
Contest at 1999 Data Security Conference", 1998, <http://
www.rsasecurity.com/press_release.asp?doc_id=627&id=1034>.
[RSA5] Press Release, RSA., "RSA Code-Breaking Contest Again Won
by Distributed.Net and Electronic Frontier Foundation",
1999, <http://www.rsasecurity.com/
press_release.asp?doc_id=462&id=1034>.
[SCHN96] Schneier, B., "Applied Cryptography, Second Ed.", 1996.
[VA1] "Review of Issues Related to the Loss of VA Information
Involving the Identities of Millions of Veterans (Report
#06-02238-163)", July 2006, <http://www.va.gov/oig/51/
FY2006rpts/VAOIG-06-02238-163.pdf>.
[WIEN94] Wiener, M., "Efficient DES Key Search", August 1993.
Author's Address
Scott G. Kelly
Aruba Networks
1322 Crossman Ave
Sunnyvale, CA 94089
US
EMail: scott@hyperthought.com
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