Data Encryption Standard

Data Encryption Standard

The Feistel function (F function) of DES
General
Designers	IBM
First published	1975 (standardized on January 1977)
Derived from	Lucifer
Successors	Triple DES, G-DES, DES-X, LOKI89, ICE
Cipher detail
Key sizes	56 bits
Block sizes	64 bits
Structure	Feistel network
Rounds	16
Best public cryptanalysis
DES is now considered insecure because a brute force attack is possible (see EFF DES cracker). As of 2004, the best analytical attack is linear cryptanalysis, which requires 243 known plaintexts and has a time complexity of 239–43 (Junod, 2001); under a chosen-plaintext assumption, the data complexity can be reduced by a factor of four (Knudsen and Mathiassen, 2000).

The Data Encryption Standard (DES) is a cipher (a method for encrypting information) selected as an official Federal Information Processing Standard (FIPS) for the United States in 1976, and which has subsequently enjoyed widespread use internationally. The algorithm was initially controversial, with classified design elements, a relatively short key length, and suspicions about a National Security Agency (NSA) backdoor. DES consequently came under intense academic scrutiny, and motivated the modern understanding of block ciphers and their cryptanalysis.

DES is now considered to be insecure for many applications. This is chiefly due to the 56-bit key size being too small; DES keys have been broken in less than 24 hours. There are also some analytical results which demonstrate theoretical weaknesses in the cipher, although they are infeasible to mount in practice. The algorithm is believed to be practically secure in the form of Triple DES, although there are theoretical attacks. In recent years, the cipher has been superseded by the Advanced Encryption Standard (AES).

In some documentation, a distinction is made between DES as a standard, and the algorithm, which is referred to as the DEA (the Data Encryption Algorithm). When spoken, "DES" is either spelled out (/diː iː ɛs/) or pronounced as a single syllable (/dɛs/).

History of DES

The origins of DES go back to the early 1970s. In 1972, after concluding a study on the US government's computer security needs, the US standards body NBS (National Bureau of Standards) — now named NIST (National Institute of Standards and Technology) — identified a need for a government-wide standard for encrypting unclassified, sensitive information. Accordingly, on 15 May 1973, after consulting with the NSA, NBS solicited proposals for a cipher that would meet rigorous design criteria. None of the submissions, however, turned out to be suitable. A second request was issued on 27 August 1974. This time, IBM submitted a candidate which was deemed acceptable, a cipher developed during the period 1973–1974 based on an earlier algorithm, Horst Feistel's Lucifer cipher. The team at IBM involved in cipher design and analysis included Feistel, Walter Tuchman, Don Coppersmith, Alan Konheim, Carl Meyer, Mike Matyas, Roy Adler, Edna Grossman, Bill Notz, Lynn Smith, and Bryant Tuckerman.

NSA's involvement in the design

On March 17, 1975, the proposed DES was published in the Federal Register. Public comments were requested, and in the following year two open workshops were held to discuss the proposed standard. There was some criticism from various parties, including from public-key cryptography pioneers Martin Hellman and Whitfield Diffie, citing a shortened key length and the mysterious "S-boxes" as evidence of improper interference from the NSA. The suspicion was that the algorithm had been covertly weakened by the intelligence agency so that they — but no-one else — could easily read encrypted messages. Alan Konheim (one of the designers of DES) commented, "We sent the S-boxes off to Washington. They came back and were all different." The United States Senate Select Committee on Intelligence reviewed the NSA's actions to determine whether there had been any improper involvement. In the unclassified summary of their findings, published in 1978, the Committee wrote:

"In the development of DES, NSA convinced IBM that a reduced key size was sufficient; indirectly assisted in the development of the S-box structures; and certified that the final DES algorithm was, to the best of their knowledge, free from any statistical or mathematical weakness."

However, it also found that

"NSA did not tamper with the design of the algorithm in any way. IBM invented and designed the algorithm, made all pertinent decisions regarding it, and concurred that the agreed upon key size was more than adequate for all commercial applications for which the DES was intended."

Another member of the DES team, Walter Tuchman, is quoted as saying, "We developed the DES algorithm entirely within IBM using IBMers. The NSA did not dictate a single wire!"

Some of the suspicions about hidden weaknesses in the S-boxes were allayed in 1990, with the independent discovery and open publication by Eli Biham and Adi Shamir of differential cryptanalysis, a general method for breaking block ciphers. The S-boxes of DES were much more resistant to the attack than if they had been chosen at random, strongly suggesting that IBM knew about the technique back in the 1970s. This was indeed the case — in 1994, Don Coppersmith published the original design criteria for the S-boxes. According to Steven Levy, IBM Watson researchers discovered differential cryptanalytic attacks in 1974 and were asked by the NSA to keep the technique secret. Coppersmith explains IBM's secrecy decision by saying, "that was because [differential cryptanalysis] can be a very powerful tool, used against many schemes, and there was concern that such information in the public domain could adversely affect national security." Levy quotes Walter Tuchman: "[t]hey asked us to stamp all our documents confidential... We actually put a number on each one and locked them up in safes, because they were considered U.S. government classified. They said do it. So I did it". Shamir himself commented, "I would say that, contrary to what some people believe, there is no evidence of tampering with the DES so that the basic design was weakened."

The other criticism — that the key length was too short — was supported by the fact that the reason given by the NSA for reducing the key length from 64 bits to 56 was that the other 8 bits could serve as parity bits, which seemed somewhat specious. It was widely believed that NSA's decision was motivated by the possibility that they would be able to brute force attack a 56 bit key several years before the rest of the world would.

The algorithm as a standard

Despite the criticisms, DES was approved as a federal standard in November 1976, and published on 15 January 1977 as FIPS PUB 46, authorized for use on all unclassified data. It was subsequently reaffirmed as the standard in 1983, 1988 (revised as FIPS-46-1), 1993 (FIPS-46-2), and again in 1998 (FIPS-46-3), the latter prescribing "Triple DES" (see below). On 26 May 2002, DES was finally superseded by AES, the Advanced Encryption Standard, following a public competition (see AES process). Even as of 2004, however, DES remains in widespread use. On 19 May 2005, FIPS 46-3 was officially withdrawn, but NIST has approved Triple DES through the year 2030 for sensitive government information. [1]

Another theoretical attack, linear cryptanalysis, was published in 1994, but it was a brute force attack in 1998 that demonstrated that DES could be attacked very practically, and highlighted the need for a replacement algorithm. These and other methods of cryptanalysis are discussed in more detail later in the article.

The introduction of DES is considered to have been a catalyst for the academic study of cryptography, particularly of methods to crack block ciphers. According to a NIST retrospective about DES,

The DES can be said to have "jump started" the nonmilitary study and development of encryption algorithms. In the 1970s there were very few cryptographers, except for those in military or intelligence organizations, and little academic study of cryptography. There are now many active academic cryptologists, mathematics departments with strong programs in cryptography, and commercial information security companies and consultants. A generation of cryptanalysts has cut its teeth analyzing (that is trying to "crack") the DES algorithm. In the words of cryptographer Bruce Schneier [9], "DES did more to galvanize the field of cryptanalysis than anything else. Now there was an algorithm to study." An astonishing share of the open literature in cryptography in the 1970s and 1980s dealt with the DES, and the DES is the standard against which every symmetric key algorithm since has been compared.

Chronology

Date	Year	Event
15 May	1973	NBS publishes a first request for a standard encryption algorithm
27 August	1974	NBS publishes a second request for encryption algorithms
17 March	1975	DES is published in the Federal Register for comment
August	1976	First workshop on DES
September	1976	Second workshop, discussing mathematical foundation of DES
November	1976	DES is approved as a standard
15 January	1977	DES is published as a FIPS standard FIPS PUB 46
	1983	DES is reaffirmed for the first time
	1986	Videocipher II, a TV satellite scrambling system based upon DES begins use by HBO
22 January	1988	DES is reaffirmed for the second time as FIPS 46-1, superseding FIPS PUB 46
July	1990	Biham and Shamir rediscover differential cryptanalysis, and apply it to a 15-round DES-like cryptosystem.
	1992	Biham and Shamir report the first theoretical attack with less complexity than brute force: differential cryptanalysis. However, it requires an unrealistic 247 chosen plaintexts.
30 December	1993	DES is reaffirmed for the third time as FIPS 46-2
	1994	The first experimental cryptanalysis of DES is performed using linear cryptanalysis (Matsui, 1994).
June	1997	The DESCHALL Project breaks a message encrypted with DES for the first time in public.
July	1998	The EFF's DES cracker (Deep Crack) breaks a DES key in 56 hours.
January	1999	Together, Deep Crack and distributed.net break a DES key in 22 hours and 15 minutes.
25 October	1999	DES is reaffirmed for the fourth time as FIPS 46-3, which specifies the preferred use of Triple DES, with single DES permitted only in legacy systems.
26 November	2001	The Advanced Encryption Standard is published in FIPS 197
26 May	2002	The AES standard becomes effective
26 July	2004	The withdrawal of FIPS 46-3 (and a couple of related standards) is proposed in the Federal Register [2]
19 May	2005	NIST withdraws FIPS 46-3
15 March	2007	The FPGA based parallel machine COPACOBANA of the University of Bochum and Kiel, Germany, breaks DES in 6.4 days at $10,000 hardware cost

Replacement algorithms

Concerns about security and the relatively slow operation of DES in software motivated researchers to propose a variety of alternative block cipher designs, which started to appear in the late 1980s and early 1990s: examples include RC5, Blowfish, IDEA, NewDES, SAFER, CAST5 and FEAL. Most of these designs kept the 64-bit block size of DES, and could act as a "drop-in" replacement, although they typically used a 64-bit or 128-bit key. In the USSR the GOST 28147-89 algorithm was introduced, with a 64-bit block size and a 256-bit key, which was also used in Russia later.

DES itself can be adapted and reused in a more secure scheme. Many former DES users now use Triple DES (TDES) which was described and analysed by one of DES's patentees (see FIPS Pub 46-3); it involves applying DES three times with two (2TDES) or three (3TDES) different keys. TDES is regarded as adequately secure, although it is quite slow. A less computationally expensive alternative is DES-X, which increases the key size by XORing extra key material before and after DES. GDES was a DES variant proposed as a way to speed up encryption, but it was shown to be susceptible to differential cryptanalysis.

In 2001, after an international competition, NIST selected a new cipher, the Advanced Encryption Standard (AES), as a replacement. The algorithm which was selected as the AES was submitted by its designers under the name Rijndael. Other finalists in the NIST AES competition included RC6, Serpent, MARS, Twofish.

Description

Figure 1 — The overall Feistel structure of DES

For brevity, the following description omits the exact transformations and permutations which specify the algorithm; for reference, the details can be found in DES supplementary material.

DES is the archetypal block cipher — an algorithm that takes a fixed-length string of plaintext bits and transforms it through a series of complicated operations into another ciphertext bitstring of the same length. In the case of DES, the block size is 64 bits. DES also uses a key to customize the transformation, so that decryption can only be performed by those who know the particular key used to encrypt. The key ostensibly consists of 64 bits; however, only 56 of these are actually used by the algorithm. Eight bits are used solely for checking parity, and are thereafter discarded. Hence the effective key length is 56 bits, and it is usually quoted as such.

Like other block ciphers, DES by itself is not a secure means of encryption but must instead be used in a mode of operation. FIPS-81 specifies several modes for use with DES [3]. Further comments on the usage of DES are contained in FIPS-74 [4].

Overall structure

The algorithm's overall structure is shown in Figure 1: there are 16 identical stages of processing, termed rounds. There is also an initial and final permutation, termed IP and FP, which are inverses (IP "undoes" the action of FP, and vice versa). IP and FP have almost no cryptographic significance, but were apparently included in order to facilitate loading blocks in and out of mid-1970s hardware, as well as to make DES run slower in software.

Before the main rounds, the block is divided into two 32-bit halves and processed alternately; this criss-crossing is known as the Feistel scheme. The Feistel structure ensures that decryption and encryption are very similar processes — the only difference is that the subkeys are applied in the reverse order when decrypting. The rest of the algorithm is identical. This greatly simplifies implementation, particularly in hardware, as there is no need for separate encryption and decryption algorithms.

The red ⊕ symbol denotes the exclusive-OR (XOR) operation. The F-function scrambles half a block together with some of the key. The output from the F-function is then combined with the other half of the block, and the halves are swapped before the next round. After the final round, the halves are not swapped; this is a feature of the Feistel structure which makes encryption and decryption similar processes.

The Feistel (F) function

The F-function, depicted in Figure 2, operates on half a block (32 bits) at a time and consists of four stages:

Figure 2 —The Feistel function (F-function) of DES

1. Expansion — the 32-bit half-block is expanded to 48 bits using the expansion permutation, denoted E in the diagram, by duplicating some of the bits.
2. Key mixing — the result is combined with a subkey using an XOR operation. Sixteen 48-bit subkeys — one for each round — are derived from the main key using the key schedule (described below).
3. Substitution — after mixing in the subkey, the block is divided into eight 6-bit pieces before processing by the S-boxes, or substitution boxes. Each of the eight S-boxes replaces its six input bits with four output bits according to a non-linear transformation, provided in the form of a lookup table. The S-boxes provide the core of the security of DES — without them, the cipher would be linear, and trivially breakable.
4. Permutation — finally, the 32 outputs from the S-boxes are rearranged according to a fixed permutation, the P-box.

The alternation of substitution from the S-boxes, and permutation of bits from the P-box and E-expansion provides so-called "confusion and diffusion" respectively, a concept identified by Claude Shannon in the 1940s as a necessary condition for a secure yet practical cipher.

Key schedule

Figure 3 — The key-schedule of DES

Figure 3 illustrates the key schedule for encryption — the algorithm which generates the subkeys. Initially, 56 bits of the key are selected from the initial 64 by Permuted Choice 1 (PC-1) — the remaining eight bits are either discarded or used as parity check bits. The 56 bits are then divided into two 28-bit halves; each half is thereafter treated separately. In successive rounds, both halves are rotated left by one or two bits (specified for each round), and then 48 subkey bits are selected by Permuted Choice 2 (PC-2) — 24 bits from the left half, and 24 from the right. The rotations (denoted by "<<<" in the diagram) mean that a different set of bits is used in each subkey; each bit is used in approximately 14 out of the 16 subkeys.

The key schedule for decryption is similar — it must generate the keys in the reverse order. Hence the rotations are to the right, rather than the left.

Security and cryptanalysis

Although more information has been published on the cryptanalysis of DES than any other block cipher, the most practical attack to date is still a brute force approach. Various minor cryptanalytic properties are known, and three theoretical attacks are possible which, while having a theoretical complexity less than a brute force attack, require an unrealistic amount of known or chosen plaintext to carry out, and are not a concern in practice.

In spite of all the criticism and weaknesses of DES, there is no known example of anyone actually suffering monetary losses because of DES security limitations.

Brute force attack

For any cipher, the most basic method of attack is brute force — trying every possible key in turn. The length of the key determines the number of possible keys, and hence the feasibility of this approach. For DES, questions were raised about the adequacy of its key size early on, even before it was adopted as a standard, and it was the small key size, rather than theoretical cryptanalysis, which dictated a need for a replacement algorithm. It is known that the NSA encouraged, if not persuaded, IBM to reduce the key size from 128 to 64 bits, and from there to 56 bits; this is often taken as an indication that the NSA thought it would be able to break keys of this length even in the mid-1970s.

The EFF's US$250,000 DES cracking machine contained 1,536 custom chips and could brute force a DES key in a matter of days — the photo shows a DES Cracker circuit board fitted with several Deep Crack chips.

In academia, various proposals for a DES-cracking machine were advanced. In 1977, Diffie and Hellman proposed a machine costing an estimated US$20 million which could find a DES key in a single day. By 1993, Wiener had proposed a key-search machine costing US$1 million which would find a key within 7 hours. However, none of these early proposals were ever implemented, at least no implementations were publicly acknowledged. The vulnerability of DES was practically demonstrated in the late 1990s. In 1997, RSA Security sponsored a series of contests, offering a $10,000 prize to the first team that broke a message encrypted with DES for the contest. That contest was won by the DESCHALL Project, led by Rocke Verser, Matt Curtin, and Justin Dolske, using idle cycles of thousands of computers across the Internet. The feasibility of cracking DES quickly was demonstrated in 1998 when a custom DES-cracker was built by the Electronic Frontier Foundation (EFF), a cyberspace civil rights group, at the cost of approximately US$250,000 (see EFF DES cracker). Their motivation was to show that DES was breakable in practice as well as in theory: "There are many people who will not believe a truth until they can see it with their own eyes. Showing them a physical machine that can crack DES in a few days is the only way to convince some people that they really cannot trust their security to DES." The machine brute-forced a key in a little more than 2 days' search; at about the same time at least one attorney from the US Justice Department was announcing that DES was unbreakable.

File:Copacobana.jpg

The COPACOBANA machine, built for US$10,000 by the Universities of Bochum and Kiel, Germany, contains 120 low-cost FPGAs and can perform an exhaustive key search on DES in 6.4 days on average. The photo shows the backplane of the machine with the FPGAs.

The only other confirmed DES cracker was the COPACOBANA machine (abbreviation of cost-optimized parallel code breaker) built more recently by teams of the Universities of Bochum and Kiel, both in Germany. Unlike the EFF machine, COPACOBANA consist of commercially available, reconfigurable integrated circuits. 120 of these FPGAs of type XILINX Spartan3-1000 run in parallel. They are grouped in 20 DIMM modules, each containing 6 FPGAs. The use of reconfigurable hardware makes the machine applicable to other code breaking tasks as well. The figure shows a full-sized COPACOBANA. One of the more interesting aspects of COPACOBANA is its cost factor. One machine can be built for approximately $10,000. The cost decrease by roughly a factor of 25 over the EFF machine is an impressive example for the continuous improvement of digital hardware. Interestingly Moore’s law predicts an improvement of about 32, since about 8 years have passed between the design of the two machines, which allows for about five doublings of computer power (or 5 reductions by 50% of the cost for doing the same computation).

Attacks faster than brute-force

There are three attacks known that can break the full sixteen rounds of DES with less complexity than a brute-force search: differential cryptanalysis (DC), linear cryptanalysis (LC), and Davies' attack. However, the attacks are theoretical and are infeasible to mount in practice; these types of attack are sometimes termed certificational weaknesses.

• Differential cryptanalysis was rediscovered in the late 1980s by Eli Biham and Adi Shamir, it was known earlier to both IBM and the NSA and kept secret. To break the full 16 rounds, differential cryptanalysis requires 2⁴⁷ chosen plaintexts. DES was designed to be resistant to DC.
• Linear cryptanalysis was discovered by Mitsuru Matsui, and needs 2⁴³ known plaintexts (Matsui, 1993); the method was implemented (Matsui, 1994), and was the first experimental cryptanalysis of DES to be reported. There is no evidence that DES was tailored to be resistant to this type of attack. A generalisation of LC — multiple linear cryptanalysis — was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov et al (2004); their analysis suggests that multiple linear approximations could be used to reduce the data requirements of the attack by at least a factor of 4 (i.e. 2⁴¹ instead of 2⁴³). A similar reduction in data complexity can be obtained in a chosen-plaintext variant of linear cryptanalysis (Knudsen and Mathiassen, 2000). Junod (2001) performed several experiments to determine the actual time complexity of linear cryptanalysis, and reported that it was somewhat faster than predicted, requiring time equivalent to 2³⁹–2⁴¹ DES evaluations.
• Improved Davies' attack: while linear and differential cryptanalysis are general techniques and can be applied to a number of schemes, Davies' attack is a specialised technique for DES, first suggested by Donald Davies in the eighties, and improved by Biham and Biryukov (1997). The most powerful form of the attack requires 2⁵⁰ known plaintexts, has a computational complexity of 2⁵⁰, and has a 51% success rate.

There have also been attacks proposed against reduced-round versions of the cipher, i.e. versions of DES with fewer than sixteen rounds. Such analysis gives an insight into how many rounds are needed for safety, and how much of a "security margin" the full version retains. Differential-linear cryptanalysis was proposed by Langford and Hellman in 1994, and combines differential and linear cryptanalysis into a single attack. An enhanced version of the attack can break 9-round DES with 2^15.8 known plaintexts and has a 2^29.2 time complexity (Biham et al, 2002).

Minor cryptanalytic properties

DES exhibits the complementation property, namely that

$E_{K}(P)=C\Leftrightarrow E_{\overline {K}}({\overline {P}})={\overline {C}}$

where ${\overline {x}}$ is the bitwise complement of $x.$ $E_{K}$ denotes encryption with key $K.$ $P$ and $C$ denote plaintext and ciphertext blocks respectively. The complementation property means that the work for a brute force attack could be reduced by a factor of 2 (or a single bit) under a chosen-plaintext assumption.

DES also has four so-called weak keys. Encryption (E) and decryption (D) under a weak key have the same effect (see involution):

$E_{K}(E_{K}(P))=P$ or equivalently, $E_{K}=D_{K}$

There are also six pairs of semi-weak keys. Encryption with one of the pair of semiweak keys, $K_{1}$, operates identically to decryption with the other, $K_{2}$:

$E_{K_{1}}(E_{K_{2}}(P))=P$ or equivalently, $E_{K_{2}}=D_{K_{1}}$

It is easy enough to avoid the weak and semiweak keys in an implementation, either by testing for them explicitly, or simply by choosing keys randomly; the odds of picking a weak or semiweak key by chance are negligible. The keys are not really any weaker than any other keys anyway, as they do not give an attack any advantage.

DES has also been proved not to be a group, or more precisely, the set $\{E_{K}\}$ (for all possible keys $K$) under functional composition is not a group, nor "close" to being a group (Campbell and Wiener, 1992). This was an open question for some time, and if it had been the case, it would have been possible to break DES, and multiple encryption modes such as Triple DES would not increase the security.

It is known that the maximum cryptographic security of DES is limited to about 64 bits, even when independently choosing all round subkeys instead of deriving them from a key, which would otherwise permit a security of 768 bits.

See also

• DES supplementary material
• Symmetric key algorithm
• Advanced Encryption Standard
• Skipjack

References

• Ehrsam et al., Product Block Cipher System for Data Security, U.S. patent 3,962,539, Filed Feb. 24, 1975
• Eli Biham, Adi Shamir, (1990). Differential Cryptanalysis of DES-like Cryptosystems. Advances in Cryptology — CRYPTO '90. Springer-Verlag. 2–21.
• Eli Biham, Adi Shamir, Differential Cryptanalysis of the Data Encryption Standard, Springer Verlag, 1993. ISBN 0-387-97930-1, ISBN 3-540-97930-1.
• Eli Biham, Alex Biryukov: An Improvement of Davies' Attack on DES. J. Cryptology 10(3): 195–206 (1997)
• Eli Biham, Orr Dunkelman, Nathan Keller: Enhancing Differential-Linear Cryptanalysis. ASIACRYPT 2002: pp254–266
• Eli Biham: A Fast New DES Implementation in Software Cracking DES: Secrets of Encryption Research, Wiretap Politics, and Chip Design, Electronic Frontier Foundation
• A.Biryukov, C.De Canniere, M.Quisquater, "On Multiple Linear Approximations", CRYPTO 2004 (to appear); preprint (PDF).
• Keith W. Campbell, Michael J. Wiener: DES is not a Group. CRYPTO 1992: pp512–520
• Don Coppersmith. (1994). The data encryption standard (DES) and its strength against attacks. IBM Journal of Research and Development, 38(3), 243–250. [5]
• Whitfield Diffie, Martin Hellman, "Exhaustive Cryptanalysis of the NBS Data Encryption Standard" IEEE Computer 10(6), June 1977, pp74–84
• John Gilmore, "Cracking DES: Secrets of Encryption Research, Wiretap Politics and Chip Design", 1998, O'Reilly, ISBN 1-56592-520-3.
• Pascal Junod, "On the Complexity of Matsui's Attack." Selected Areas in Cryptography, 2001, pp199–211.
• Burton S. Kaliski Jr., Matthew J. B. Robshaw: Linear Cryptanalysis Using Multiple Approximations. CRYPTO 1994: pp26–39
• Lars R. Knudsen, John Erik Mathiassen: A Chosen-Plaintext Linear Attack on DES. Fast Software Encryption - FSE 2000: pp262–272
• Susan K. Langford, Martin E. Hellman: Differential-Linear Cryptanalysis. CRYPTO 1994: 17–25
• Steven Levy, Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age, 2001, ISBN 0-14-024432-8.
• Mitsuru Matsui: Linear Cryptanalysis Method for DES Cipher. EUROCRYPT 1993: pp386–397
• Mitsuru Matsui: The First Experimental Cryptanalysis of the Data Encryption Standard. CRYPTO 1994: pp1–11
• National Bureau of Standards, Data Encryption Standard, FIPS-Pub.46. National Bureau of Standards, U.S. Department of Commerce, Washington D.C., January 1977.

External links

• FIPS 46-3: The official document describing the DES standard (PDF); An older version in HTML.
• The EFF DES cracker project
• COPACOBANA, a $10,000 DES cracker based on FPGAs by the Universities of Bochum and Kiel
• Helger Lipmaa's links for DES
• A worked example of the DES algorithm
• A Javascript DES calculator showing intermediate values
• John Savard's description of DES
• A Fast New DES Implementation in Software - Biham
• Bit slice implementation of DES
• On Multiple Linear Approximations
• FPGA DES Cracking at hardware-hacking.com
• RFC4772 : Security Implications of Using the Data Encryption Standard (DES)