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Subject: BoS: keylength.txt
From: Julian Assange <proff () suburbia ! net>
Date: 1996-06-05 22:40:04
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Minimal Key Lengths for Symmetric Ciphers
to Provide Adequate Commercial Security
A Report by an Ad Hoc Group of
Cryptographers and Computer Scientists
Matt Blaze (1)
Whitfield Diffie (2)
Ronald L. Rivest (3)
Bruce Schneier (4)
Tsutomu Shimomura (5)
Eric Thompson (6)
Michael Wiener (7)
January 1996
ABSTRACT
Encryption plays an essential role in protecting the privacy of
electronic information against threats from a variety of potential
attackers. In so doing, modern cryptography employs a combination of
_conventional_ or _symmetric_ cryptographic systems for
encrypting data and _public key_ or _asymmetric_ systems for
managing the _keys_ used by the symmetric systems. Assessing the
strength required of the symmetric cryptographic systems is therefore
an essential step in employing cryptography for computer and
communication security.
Technology readily available today (late 1995) makes
_brute-force_ attacks against cryptographic systems considered adequate
for the past several years both fast and cheap. General purpose
computers can be used, but a much more efficient approach is to employ
commercially available _Field Programmable Gate Array (FPGA)_
technology. For attackers prepared to make a higher initial
investment, custom-made, special-purpose chips make such calculations
much faster and significantly lower the amortized cost per solution.
As a result, cryptosystems with 40-bit keys offer virtually no
protection at this point against brute-force attacks. Even the U.S.
Data Encryption Standard with 56-bit keys is increasingly inadequate.
As cryptosystems often succumb to `smarter' attacks than brute-force
key search, it is also important to remember that the keylengths
discussed here are the minimum needed for security against the
computational threats considered.
Fortunately, the cost of very strong encryption is not
significantly greater than that of weak encryption. Therefore, to
provide adequate protection against the most serious threats ---
well-funded commercial enterprises or government intelligence agencies
--- keys used to protect data today should be at least 75 bits long.
To protect information adequately for the next 20 years in the face of
expected advances in computing power, keys in newly-deployed systems
should be at least 90 bits long.
-----------------------------------------
1. AT&T Research, mab@research.att.com
2. Sun Microsystems, diffie@eng.sun.com
3. MIT Laboratory for Computer Science, rivest@lcs.mit.edu
4. Counterpane Systems, schneier@counterpane.com
5. San Diego Supercomputer Center, tsutomu@sdsc.edu
6. Access Data, Inc., eric@accessdata.com
7. Bell Northern Research, wiener@bnr.ca
1. Encryption Plays an Essential Role in Protecting
the Privacy of Electronic Information
1.1 There is a need for information security.
As we write this paper in late 1995, the development of electronic
commerce and the Global Information Infrastructure is at a critical
juncture. The dirt paths of the middle ages only became highways of
business and culture after the security of travelers and the
merchandise they carried could be assured. So too the information
superhighway will be an ill-traveled road unless information, the
goods of the Information Age, can be moved, stored, bought, and sold
securely. Neither corporations nor individuals will entrust their
private business or personal data to computer networks unless they can
assure their information's security.
Today, most forms of information can be stored and processed
electronically. This means a wide variety of information, with
varying economic values and privacy aspects and with a wide variation
in the time over which the information needs to be protected, will be
found on computer networks. Consider the spectrum:
o Electronic Funds Transfers of millions or even billions of
dollars, whose short term security is essential but whose
exposure is brief;
o A company's strategic corporate plans, whose confidentiality
must be preserved for a small number of years;
o A proprietary product (Coke formula, new drug design) that
needs to be protected over its useful life, often decades;
and
o Information private to an individual (medical condition,
employment evaluation) that may need protection for the
lifetime of the individual.
1.2 Encryption can provide strong confidentiality protection.
Encryption is accomplished by scrambling data using mathematical
procedures that make it extremely difficult and time consuming for
anyone other than authorized recipients --- those with the correct
decryption _keys_ --- to recover the _plain text_. Proper encryption
guarantees that the information will be safe even if it falls into
hostile hands.
Encryption --- and decryption --- can be performed by either
computer software or hardware. Common approaches include writing the
algorithm on a disk for execution by a computer central processor;
placing it in ROM or PROM for execution by a microprocessor; and
isolating storage and execution in a computer accessory device (smart
card or PCMCIA card).
The degree of protection obtained depends on several factors.
These include: the quality of the cryptosystem; the way it is
implemented in software or hardware (especially its reliability and
the manner in which the keys are chosen); and the total number of
possible keys that can be used to encrypt the information. A
cryptographic algorithm is considered strong if:
1. There is no shortcut that allows the opponent to recover
the plain text without using brute force to test keys until
the correct one is found; and
2. The number of possible keys is sufficiently large to make
such an attack infeasible.
The principle here is similar to that of a combination lock on a
safe. If the lock is well designed so that a burglar cannot hear or
feel its inner workings, a person who does not know the combination
can open it only by dialing one set of numbers after another until it
yields.
The sizes of encryption keys are measured in bits and the
difficulty of trying all possible keys grows exponentially with the
number of bits used. Adding one bit to the key doubles the number of
possible keys; adding ten increases it by a factor of more than a
thousand.
There is no definitive way to look at a cipher and determine
whether a shortcut exists. Nonetheless, several encryption algorithms
--- most notably the U.S Data Encryption Standard (DES) --- have been
extensively studied in the public literature and are widely believed
to be of very high quality. An essential element in cryptographic
algorithm design is thus the length of the key, whose size places an
upper bound on the system's strength.
Throughout this paper, we will assume that there are no shortcuts
and treat the length of the key as representative of the
cryptosystem's _workfactor_ --- the minimum amount of effort
required to break the system. It is important to bear in mind,
however, that cryptographers regard this as a rash assumption and many
would recommend keys two or more times as long as needed to resist
brute-force attacks. Prudent cryptographic designs not only employ
longer keys than might appear to be needed, but devote more
computation to encrypting and decrypting. A good example of this is
the popular approach of using _triple-DES_: encrypting the output
of DES twice more, using a total of three distinct keys.
Encryption systems fall into two broad classes. Conventional or
symmetric cryptosystems --- those in which an entity with the ability
to encrypt also has the ability to decrypt and vice versa --- are the
systems under consideration in this paper. The more recent public key
or asymmetric cryptosystems have the property that the ability to
encrypt does not imply the ability to decrypt. In contemporary
cryptography, public-key systems are indispensable for managing the
keys of conventional cryptosystems. All known public key
cryptosystems, however, are subject to shortcut attacks and must
therefore use keys ten or more times the lengths of those discussed
here to achieve the an equivalent level of security.
Although computers permit electronic information to be encrypted
using very large keys, advances in computing power keep pushing up the
size of keys that can be considered large and thus keep making it
easier for individuals and organizations to attack encrypted
information without the expenditure of unreasonable resources.
1.3 There are threats from a variety of potential attackers.
Threats to confidentiality of information come from a number
of directions and their forms depend on the resources of the
attackers. `Hackers,' who might be anything from high school
students to commercial programmers, may have access to mainframe
computers or networks of workstations. The same people can readily
buy inexpensive, off-the-shelf, boards, containing _Field
Programmable Gate Array (FPGA)_ chips that function as `programmable
hardware' and vastly increase the effectiveness of a cryptanalytic
effort. A startup company or even a well-heeled individual could
afford large numbers of these chips. A major corporation or organized
crime operation with `serious money' to spend could acquire custom
computer chips specially designed for decryption. An intelligence
agency, engaged in espionage for national economic advantage, could
build a machine employing millions of such chips.
1.4 Current technology permits very strong encryption
for effectively the same cost as weaker encryption.
It is a property of computer encryption that modest increases in
computational cost can produce vast increases in security. Encrypting
information very securely (e.g., with 128-bit keys) typically requires
little more computing than encrypting it weakly (e.g., with 40-bit
keys). In many applications, the cryptography itself accounts for
only a small fraction of the computing costs, compared to such
processes as voice or image compression required to prepare material
for encryption.
One consequence of this uniformity of costs is that there is
rarely any need to tailor the strength of cryptography to the
sensitivity of the information being protected. Even if most of the
information in a system has neither privacy implications nor monetary
value, there is no practical or economic reason to design computer
hardware or software to provide differing levels of encryption for
different messages. It is simplest, most prudent, and thus
fundamentally most economical, to employ a uniformly high level of
encryption: the strongest encryption required for any information that
might be stored or transmitted by a secure system.
2. Readily Available Technology Makes Brute-Force
Decryption Attacks Faster and Cheaper
The kind of hardware used to mount a brute-force attack against an
encryption algorithm depends on the scale of the cryptanalytic
operation and the total funds available to the attacking enterprise.
In the analysis that follows, we consider three general classes of
technology that are likely to be employed by attackers with differing
resources available to them. Not surprisingly, the cryptanalytic
technologies that require larger up-front investments yield the lowest
cost per recovered key, amortized over the life of the hardware.
It is the nature of brute-force attacks that they can be
parallelized indefinitely. It is possible to use as many machines as
are available, assigning each to work on a separate part of the
problem. Thus regardless of the technology employed, the search time
can be reduced by adding more equipment; twice as much hardware can be
expected to find the right key in half the time. The total investment
will have doubled, but if the hardware is kept constantly busy finding
keys, the cost per key recovered is unchanged.
At the low end of the technology spectrum is the use of
conventional personal computers or workstations programmed to test
keys. Many people, by virtue of already owning or having access to
the machines, are in a position use such resources at little or no
cost. However, general purpose computers --- laden with such
ancillary equipment as video controllers, keyboards, interfaces,
memory, and disk storage --- make expensive search engines. They are
therefore likely to be employed only by casual attackers who are
unable or unwilling to invest in more specialized equipment.
A more efficient technological approach is to take advantage of
commercially available Field Programmable Gate Arrays. FPGAs function
as programmable hardware and allow faster implementations of such
tasks as encryption and decryption than conventional processors.
FPGAs are a commonly used tool for simple computations that need to be
done very quickly, particularly simulating integrated circuits during
development.
FPGA technology is fast and cheap. The cost of an AT&T ORCA chip
that can test 30 million DES keys per second is $200. This is 1,000
times faster than a PC at about one-tenth the cost! FPGAs are widely
available and, mounted on cards, can be installed in standard PCs just
like sound cards, modems, or extra memory.
FPGA technology may be optimal when the same tool must be used for
attacking a variety of different cryptosystems. Often, as with DES, a
cryptosystem is sufficiently widely used to justify the construction
of more specialized facilities. In these circumstances, the most
cost-effective technology, but the one requiring the largest initial
investment, is the use of _Application-Specific Integrated
Circuits (ASICs)_. A $10 chip can test 200 million keys per second.
This is seven times faster than an FPGA chip at one-twentieth the
cost.
Because ASICs require a far greater engineering investment than
FPGAs and must be fabricated in quantity before they are economical,
this approach is only available to serious, well-funded operations
such as dedicated commercial (or criminal) enterprises and government
intelligence agencies.
3. 40-Bit Key Lengths Offer Virtually No Protection
Current U.S. Government policy generally limits exportable mass
market software that incorporates encryption for confidentiality to
using the RC2 or RC4 algorithms with 40-bit keys. A 40-bit key length
means that there are 2^40 possible keys. On average, half of
these (2^39) must be tried to find the correct one. Export of
other algorithms and key lengths must be approved on a case by case
basis. For example, DES with a 56-bit key has been approved for
certain applications such as financial transactions.
The recent successful brute-force attack by two French graduate
students on Netscape's 40-bit RC4 algorithm demonstrates the dangers
of such short keys. These students at the Ecole Polytechnique in
Paris used `idle time' on the school's computers, incurring no cost to
themselves or their school. Even with these limited resources, they
were able to recover the 40-bit key in a few days.
There is no need to have the resources of an institution of higher
education at hand, however. Anyone with a modicum of computer
expertise and a few hundred dollars would be able to attack 40-bit
encryption much faster. An FPGA chip --- costing approximately $400
mounted on a card --- would on average recover a 40-bit key in five
hours. Assuming the FPGA lasts three years and is used continuously
to find keys, the average cost per key is eight cents.
A more determined commercial predator, prepared to spend $10,000
for a set-up with 25 ORCA chips, can find 40-bit keys in an average of
12 minutes, at the same average eight cent cost. Spending more money
to buy more chips reduces the time accordingly: $300,000 results in
a solution in an average of 24 seconds; $10,000,000 results in an
average solution in 0.7 seconds.
As already noted, a corporation with substantial resources can
design and commission custom chips that are much faster. By doing
this, a company spending $300,000 could find the right 40-bit key in
an average of 0.18 seconds at 1/10th of a cent per solution; a larger
company or government agency willing to spend $10,000,000 could find
the right key on average in 0.005 seconds (again at 1/10th of a cent
per solution). (Note that the cost per solution remains constant
because we have conservatively assumed constant costs for chip
acquisition --- in fact increasing the quantities purchased of a
custom chip reduces the average chip cost as the initial design and
set-up costs are spread over a greater number of chips.)
These results are summarized in Table I.
4. Even DES with 56-Bit Keys Is Increasingly Inadequate
4.1 DES is no panacea today.
The Data Encryption Standard (DES) was developed in the 1970s by
IBM and NSA and adopted by the U.S. Government as a Federal
Information Processing Standard for data encryption. It was intended
to provide strong encryption for the government's sensitive but
unclassified information. It was recognized by many, even at the time
DES was adopted, that technological developments would make DES's
56-bit key exceedingly vulnerable to attack before the end of the
century.
Today, DES may be the most widely employed encryption algorithm
and continues to be a commonly cited benchmark. Yet DES-like
encryption strength is no panacea. Calculations show that DES is
inadequate against a corporate or government attacker committing
serious resources. The bottom line is that DES is cheaper and easier
to break than many believe.
As explained above, 40-bit encryption provides inadequate
protection against even the most casual of intruders, content to
scavenge time on idle machines or to spend a few hundred dollars.
Against such opponents, using DES with a 56-bit key will provide a
substantial measure of security. At present, it would take a year and
a half for someone using $10,000 worth of FPGA technology to search
out a DES key. In ten years time an investment of this size would
allow one to find a DES key in less than a week.
The real threat to commercial transactions and to privacy on the
Internet is from individuals and organizations willing to invest
substantial time and money. As more and more business and personal
information becomes electronic, the potential rewards to a dedicated
commercial predator also increase significantly and may justify the
commitment of adequate resources.
A serious effort --- on the order of $300,000 --- by a legitimate
or illegitimate business could find a DES key in an average of 19 days
using off-the-shelf technology and in only 3 hours using a custom
developed chip. In the latter case, it would cost $38 to find each
key (again assuming a 3 year life to the chip and continual use). A
business or government willing to spend $10,000,000 on custom chips,
could recover DES keys in an average of 6 minutes, for the same $38
per key.
At the very high end, an organization --- presumably a government
intelligence agency --- willing to spend $300,000,000 could recover
DES keys in 12 seconds each! The investment required is large but not
unheard of in the intelligence community. It is less than the cost of
the Glomar Explorer, built to salvage a single Russian submarine, and
far less than the cost of many spy satellites. Such an expense might
be hard to justify in attacking a single target, but seems entirely
appropriate against a cryptographic algorithm, like DES, enjoying
extensive popularity around the world.
There is ample evidence of the danger presented by government
intelligence agencies seeking to obtain information not only for
military purposes but for commercial advantage. Congressional
hearings in 1993 highlighted instances in which the French and
Japanese governments spied on behalf of their countries' own
businesses. Thus, having to protect commercial information against
such threats is not a hypothetical proposition.
4.2 There are smarter avenues of attack than brute force.
It is easier to walk around a tree than climb up and down it.
There is no need to break the window of a house to get in if the front
door is unlocked.
Calculations regarding the strength of encryption against
brute-force attack are _worst case_ scenarios. They assume that
the ciphers are in a sense perfect and that attempts to find shortcuts
have failed. One important point is that the crudest approach ---
searching through the keys --- is entirely feasible against many
widely used systems. Another is that the keylengths we discuss are
always minimal. As discussed earlier, prudent designs might use keys
twice or three times as long to provide a margin of safety.
4.3 The analysis for other algorithms is roughly comparable.
The above analysis has focused on the time and money required to
find a key to decrypt information using the RC4 algorithm with a
40-bit key or the DES algorithm with its 56-bit key, but the results
are not peculiar to these ciphers. Although each algorithm has its
own particular characteristics, the effort required to find the keys
of other ciphers is comparable. There may be some differences as the
result of implementation procedures, but these do not materially
affect the brute-force breakability of algorithms with roughly
comparable key lengths.
Specifically, it has been suggested at times that differences in
set-up procedures, such as the long key-setup process in RC4, result
in some algorithms having effectively longer keys than others. For
the purpose of our analysis, such factors appear to vary the effective
key length by no more than about eight bits.
5. Appropriate Key Lengths for the Future --- A Proposal
Table I summarizes the costs of carrying out brute-force attacks
against symmetric cryptosystems with 40-bit and 56-bit keys using
networks of general purpose computers, Field Programmable Gate Arrays,
and special-purpose chips.
It shows that 56 bits provides a level of protection --- about a
year and a half --- that would be adequate for many commercial
purposes against an opponent prepared to invest $10,000. Against an
opponent prepared to invest $300,000, the period of protection has
dropped to the barest minimum of 19 days. Above this, the protection
quickly declines to negligible. A very large, but easily imaginable,
investment by an intelligence agency would clearly allow it to recover
keys in real time.
What workfactor would be required for security today? For an
opponent whose budget lay in the $10 to 300 million range, the time
required to search out keys in a 75-bit keyspace would be between 6
years and 70 days. Although the latter figure may seem comparable to
the `barest minimum' 19 days mentioned earlier, it represents ---
under our amortization assumptions --- a cost of $19 million and a
recovery rate of only five keys a year. The victims of such an attack
would have to be fat targets indeed.
Because many kinds of information must be kept confidential for
long periods of time, assessment cannot be limited to the protection
required today. Equally important, cryptosystems --- especially if
they are standards --- often remain in use for years or even decades.
DES, for example, has been in use for more than 20 years and will
probably continue to be employed for several more. In particular, the
lifetime of a cryptosystem is likely to exceed the lifetime of any
individual product embodying it.
A rough estimate of the minimum strength required as a function of
time can be obtained by applying an empirical rule, popularly called
`Moore's Law,' which holds that the computing power available for a
given cost doubles every 18 months. Taking into account both the
lifetime of cryptographic equipment and the lifetime of the secrets it
protects, we believe it is prudent to require that encrypted data
should still be secure in 20 years. Moore's Law thus predicts that
the keys should be approximately 14 bits longer than required to
protect against an attack today.
*Bearing in mind that the additional computational costs of
stronger encryption are modest, we strongly recommend a minimum
key-length of 90 bits for symmetric cryptosystems.*
It is instructive to compare this recommendation with both Federal
Information Processing Standard 46, The Data Encryption Standard
(DES), and Federal Information Processing Standard 185, The Escrowed
Encryption Standard (EES). DES was proposed 21 years ago and used a
56-bit key. Applying Moore's Law and adding 14 bits, we see that the
strength of DES when it was proposed in 1975 was comparable to that of
a 70-bit system today. Furthermore, it was estimated at the time that
DES was not strong enough and that keys could be recovered at a rate
of one per day for an investment of about twenty-million dollars. Our
75-bit estimate today corresponds to 61 bits in 1975, enough to have
moved the cost of key recovery just out of reach. The Escrowed
Encryption Standard, while unacceptable to many potential users for
other reasons, embodies a notion of appropriate key length that is
similar to our own. It uses 80-bit keys, a number that lies between
our figures of 75 and 90 bits.
Table I
Time and cost Length Needed
Type of Budget Tool per key recovered for protection
Attacker 40bits 56bits in Late 1995
Pedestrian Hacker
tiny scavenged 1 week infeasible 45
computer
time
$400 FPGA 5 hours 38 years 50
($0.08) ($5,000)
Small Business
$10,000 FPGA 12 minutes 556 days 55
($0.08) ($5,000)
Corporate Department
$300K FPGA 24 seconds 19 days 60
or ($0.08) ($5,000)
ASIC .18 seconds 3 hours
($0.001) ($38)
Big Company
$10M FPGA .7 seconds 13 hours 70
or ($0.08) ($5,000)
ASIC .005 seconds 6 minutes
($0.001) ($38)
Intellegence Agency
$300M ASIC .0002 seconds 12 seconds 75
($0.001) ($38)
About the Authors
*Matt Blaze* is a senior research scientist at AT&T Research in
the area of computer security and cryptography. Recently Blaze
demonstrated weaknesses in the U.S. government's `Clipper Chip' key
escrow encryption system. His current interests include large-scale
trust management and the applications of smartcards.
*Whitfield Diffie* is a distinguished Engineer at Sun Microsystems
specializing in security. In 1976 Diffie and Martin Hellman created
public key cryptography, which solved the problem of sending coded
information between individuals with no prior relationship and is the
basis for widespread encryption in the digital information age.
*Ronald L. Rivest* is a professor of computer science at the
Massachusetts Institute of Technology, and is Associate Director of
MIT's Laboratory for Computer Science. Rivest, together with Leonard
Adleman and Adi Shamir, invented the RSA public-key cryptosystem that
is used widely throughout industry. Ron Rivest is one of the founders
of RSA Data Security Inc. and is the creator of variable key length
symmetric key ciphers (e.g., RC4).
*Bruce Schneier* is president of Counterpane Systems, a consulting
firm specializing in cryptography and computer security. Schneier
writes and speaks frequently on computer security and privacy and is
the author of a leading cryptography textbook, Applied Cryptography,
and is the creator of the symmetric key cipher Blowfish.
*Tsutomu Shimomura* is a computational physicist employed by the
San Diego Supercomputer Center who is an expert in designing software
security tools. Last year, Shimomura was responsible for tracking
down the computer outlaw Kevin Mitnick, who electronically stole and
altered valuable electronic information around the country.
*Eric Thompson* heads AccessData Corporation's cryptanalytic team
and is a frequent lecturer on applied crytography. AccessData
specializes in data recovery and decrypting information utilizing
brute force as well as `smarter' attacks. Regular clients include the
FBI and other law enforcement agencies as well as corporations.
*Michael Wiener* is a cryptographic advisor at Bell-Northern
Research where he focuses on cryptanalysis, security architectures,
and public-key infrastructures. His influential 1993 paper, Efficient
DES Key Search, describes in detail how to construct a machine to
brute force crack DES coded information (and provides cost estimates
as well).
ACKNOWLEDGEMENT
The authors would like to thank the Business Software Alliance,
which provided support for a one-day meeting, held in Chicago on
20 November 1995.
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