Data Encryption Standard

The Data Encryption Standard (DES) is a block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

 that uses shared secret

Shared secret

In cryptography, a shared secret is a piece of data, known only to the parties involved, in a secure communication. The shared secret can be a password, a passphrase, a big number or an array of randomly chosen bytes....

 encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard

Federal Information Processing Standard

A Federal Information Processing Standard is a publicly announced standardization developed by the United States federal government for use in computer systems by all non-military government agencies and by government contractors, when properly invoked and tailored on a contract...

 (FIPS) for the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 in 1976 and which has subsequently enjoyed widespread use internationally. It is based on a symmetric-key algorithm

Symmetric-key algorithm

Symmetric-key algorithms are a class of algorithms for cryptography that use trivially related, often identical, cryptographic keys for both encryption of plaintext and decryption of ciphertext. The encryption key is trivially related to the decryption key, in that they may be identical or there is...

 that uses a 56-bit key

56-bit encryption

In computing, 56-bit encryption refers to a key size of fifty-six bits, or seven bytes, for symmetric encryption. While stronger than 40-bit encryption, this still represents a relatively low level of security in the context of a brute force attack....

. The algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 was initially controversial because of classified

Classified information

Classified information is sensitive information to which access is restricted by law or regulation to particular groups of persons. A formal security clearance is required to handle classified documents or access classified data. The clearance process requires a satisfactory background investigation...

 design elements, a relatively short key length, and suspicions about a National Security Agency

National Security Agency

The National Security Agency/Central Security Service is a cryptologic intelligence agency of the United States Department of Defense responsible for the collection and analysis of foreign communications and foreign signals intelligence, as well as protecting U.S...

 (NSA) backdoor. DES consequently came under intense academic scrutiny which motivated the modern understanding of block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

s and their cryptanalysis

Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

.

DES is now considered to be insecure for many applications. This is chiefly due to the 56-bit key size being too small; in January, 1999, distributed.net

Distributed.net

distributed.net is a worldwide distributed computing effort that is attempting to solve large scale problems using otherwise idle CPU or GPU time. It is officially recognized as a non-profit organization under U.S...

 and the Electronic Frontier Foundation

Electronic Frontier Foundation

The Electronic Frontier Foundation is an international non-profit digital rights advocacy and legal organization based in the United States...

 collaborated to publicly break a DES key in 22 hours and 15 minutes (see chronology). 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

Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....

, although there are theoretical attacks. In recent years, the cipher has been superseded by the Advanced Encryption Standard

Advanced Encryption Standard

Advanced Encryption Standard is a specification for the encryption of electronic data. It has been adopted by the U.S. government and is now used worldwide. It supersedes DES...

 (AES). Furthermore, DES has been withdrawn as a standard by the National Institute of Standards and Technology

National Institute of Standards and Technology

The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

 (formerly the National Bureau of Standards).

In some documentation, a distinction is made between DES as a standard and DES the algorithm which is referred to as the DEA (the Data Encryption Algorithm). When spoken, "DES" is either spelled out as an abbreviation

Abbreviation

An abbreviation is a shortened form of a word or phrase. Usually, but not always, it consists of a letter or group of letters taken from the word or phrase...

 (ˌdiːˌiːˈɛs), or pronounced as a one-syllable acronym (ˈdɛz).

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

Computer security

Computer security is a branch of computer technology known as information security as applied to computers and networks. The objective of computer security includes protection of information and property from theft, corruption, or natural disaster, while allowing the information and property to...

 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

Horst Feistel

Horst Feistel was a German-born cryptographer who worked on the design of ciphers at IBM, initiating research that would culminate in the development of the Data Encryption Standard in the 1970s....

's Lucifer

Lucifer (cipher)

In cryptography, Lucifer was the name given to several of the earliest civilian block ciphers, developed by Horst Feistel and his colleagues at IBM. Lucifer was a direct precursor to the Data Encryption Standard...

 cipher. The team at IBM involved in cipher design and analysis included Feistel, Walter Tuchman

Walter Tuchman

Walter Tuchman led the Data Encryption Standard development team at IBM. He was also responsible for the development of Triple DES.-See also:* Horst Feistel...

, Don Coppersmith

Don Coppersmith

Don Coppersmith is a cryptographer and mathematician. He was involved in the design of the Data Encryption Standard block cipher at IBM, particularly the design of the S-boxes, strengthening them against differential cryptanalysis...

, Alan Konheim, Carl Meyer, Mike Matyas, Roy Adler, Edna Grossman

Edna Grossman

Edna Grossman is an American mathematician. She was born in Germany, grew up in Brooklyn, New York, and graduated with a B.S. in mathematics from Brooklyn College. She earned her M.S. in mathematics from New York University's Courant Institute of Mathematical Sciences, where she also received her...

, Bill Notz, Lynn Smith, and Bryant Tuckerman

Bryant Tuckerman

Louis Bryant Tuckerman, III was an American mathematician, born in Lincoln, Nebraska. He was a member of the team that developed the Data Encryption Standard ....

.

NSA's involvement in the design

On 17 March 1975, the proposed DES was published in the Federal Register

Federal Register

The Federal Register , abbreviated FR, or sometimes Fed. Reg.) is the official journal of the federal government of the United States that contains most routine publications and public notices of government agencies...

. 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

Public-key cryptography

Public-key cryptography refers to a cryptographic system requiring two separate keys, one to lock or encrypt the plaintext, and one to unlock or decrypt the cyphertext. Neither key will do both functions. One of these keys is published or public and the other is kept private...

 pioneers Martin Hellman

Martin Hellman

Martin Edward Hellman is an American cryptologist, and is best known for his invention of public key cryptography in cooperation with Whitfield Diffie and Ralph Merkle...

 and Whitfield Diffie

Whitfield Diffie

Bailey Whitfield 'Whit' Diffie is an American cryptographer and one of the pioneers of public-key cryptography.Diffie and Martin Hellman's paper New Directions in Cryptography was published in 1976...

, citing a shortened key length and the mysterious "S-boxes

Substitution box

In cryptography, an S-Box is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext — Shannon's property of confusion...

" 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

United States Senate Select Committee on Intelligence

The United States Senate Select Committee on Intelligence is dedicated to overseeing the United States Intelligence Community—the agencies and bureaus of the federal government of the United States who provide information and analysis for leaders of the executive and legislative branches. The...

 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:

However, it also found that

Another member of the DES team, Walter Tuchman, stated "We developed the DES algorithm entirely within IBM using IBMers. The NSA did not dictate a single wire!"
In contrast, a declassified NSA book on cryptologic history states:

and

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

Eli Biham

Eli Biham is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion Israeli Institute of Technology Computer Science department. Starting from October 2008, Biham is the dean of the Technion Computer Science department, after serving for two years as chief of CS graduate...

 and Adi Shamir

Adi Shamir

Adi Shamir is an Israeli cryptographer. He is a co-inventor of the RSA algorithm , a co-inventor of the Feige–Fiat–Shamir identification scheme , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer...

 of differential cryptanalysis

Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output...

, 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 in the 1970s. This was indeed the case; in 1994, Don Coppersmith published some of the original design criteria for the S-boxes. According to Steven Levy

Steven Levy

Steven Levy is an American journalist who has written several books on computers, technology, cryptography, the Internet, cybersecurity, and privacy.-Career:...

, 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". Bruce Schneier observed that "It took the academic community two decades to figure out that the NSA 'tweaks' actually improved the security of DES."

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

Federal Information Processing Standard

A Federal Information Processing Standard is a publicly announced standardization developed by the United States federal government for use in computer systems by all non-military government agencies and by government contractors, when properly invoked and tailored on a contract...

 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 1999 (FIPS-46-3), the latter prescribing "Triple DES

Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....

" (see below). On 26 May 2002, DES was finally superseded by the Advanced Encryption Standard (AES), following a public competition

Advanced Encryption Standard process

The Advanced Encryption Standard , the block cipher ratified as a standard by National Institute of Standards and Technology of the United States , was chosen using a process markedly more open and transparent than its predecessor, the aging Data Encryption Standard...

. On 19 May 2005, FIPS 46-3 was officially withdrawn, but NIST has approved Triple DES

Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....

 through the year 2030 for sensitive government information.

The algorithm is also specified in ANSI X3.92, NIST SP 800-67 and ISO/IEC 18033-3 (as a component of TDEA).

Another theoretical attack, linear cryptanalysis, was published in 1994, but it was a brute force attack

Brute force attack

In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data. Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system that would make the task easier...

 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

Cryptanalysis

Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

 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

Bruce Schneier

Bruce Schneier is an American cryptographer, computer security specialist, and writer. He is the author of several books on general security topics, computer security and cryptography, and is the founder and chief technology officer of BT Managed Security Solutions, formerly Counterpane Internet...

, "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 Videocipher VideoCipher is a brand name of analog scrambling and de-scrambling equipment for cable and satellite television invented primarily to keep consumer Television receive-only satellite equipment from receiving TV programing except on a subscription basis. It was invented in 1983 by Linkabit...  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 Differential cryptanalysis Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output... , 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 Differential cryptanalysis Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output... . 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 DESCHALL Project DESCHALL, short for DES Challenge, was the first group to publicly break a message which used the Data Encryption Standard , becoming the $10,000 winner of the first of the set of DES Challenges proposed by RSA Security in 1997...  breaks a message encrypted with DES for the first time in public.
July	1998	The EFF Electronic Frontier Foundation The Electronic Frontier Foundation is an international non-profit digital rights advocacy and legal organization based in the United States... 's DES cracker EFF DES cracker In cryptography, the EFF DES cracker is a machine built by the Electronic Frontier Foundation in 1998 to perform a brute force search of DES cipher's key space — that is, to decrypt an encrypted message by trying every possible key...  (Deep Crack) breaks a DES key in 56 hours.
January	1999	Together, Deep Crack and distributed.net Distributed.net distributed.net is a worldwide distributed computing effort that is attempting to solve large scale problems using otherwise idle CPU or GPU time. It is officially recognized as a non-profit organization under U.S...  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 Triple DES In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block.... , 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
19 May	2005	NIST withdraws FIPS 46-3 (see Federal Register vol 70, number 96)
April	2006	The FPGA Field-programmable gate array A field-programmable gate array is an integrated circuit designed to be configured by the customer or designer after manufacturing—hence "field-programmable"...  based parallel machine COPACOBANA of the Universities of Bochum and Kiel, Germany, breaks DES in 9 days at $10,000 hardware cost. Within a year software improvements reduced the average time to 6.4 days.
Nov.	2008	The successor of COPACOBANA, the RIVYERA machine reduced the average time to less than one single day.

Replacement algorithms

Concerns about security and the relatively slow operation of DES in software motivated researchers to propose a variety of alternative block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

 designs, which started to appear in the late 1980s and early 1990s: examples include RC5

RC5

In cryptography, RC5 is a block cipher notable for its simplicity. Designed by Ronald Rivest in 1994, RC stands for "Rivest Cipher", or alternatively, "Ron's Code"...

, Blowfish

Blowfish (cipher)

Blowfish is a keyed, symmetric block cipher, designed in 1993 by Bruce Schneier and included in a large number of cipher suites and encryption products. Blowfish provides a good encryption rate in software and no effective cryptanalysis of it has been found to date...

, IDEA

International Data Encryption Algorithm

In cryptography, the International Data Encryption Algorithm is a block cipher designed by James Massey of ETH Zurich and Xuejia Lai and was first described in 1991. As a block cipher, it is also symmetric. The algorithm was intended as a replacement for the Data Encryption Standard[DES]...

, NewDES

NewDES

In cryptography, NewDES is a symmetric key block cipher. It was created in 1984–1985 by Robert Scott as a potential DES replacement. Despite its name, it is not derived from DES and has a quite different structure. Its intended niche as a DES replacement has now mostly been filled by AES...

, SAFER

SAFER

In cryptography, SAFER is the name of a family of block ciphers designed primarily by James Massey on behalf of Cylink Corporation. The early SAFER K and SAFER SK designs share the same encryption function, but differ in the number of rounds and the key schedule...

, CAST5 and FEAL

FEAL

In cryptography, FEAL is a block cipher proposed as an alternative to the Data Encryption Standard , and designed to be much faster in software. The Feistel based algorithm was first published in 1987 by Akihiro Shimizu and Shoji Miyaguchi from NTT...

. 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

GOST 28147-89

The GOST block cipher, defined in the standard GOST 28147-89, is a Soviet and Russian government standard symmetric key block cipher. Also based on this block cipher is the GOST hash function....

 algorithm was introduced, with a 64-bit block size and a 256-bit key, which was also used in Russia

Russia

Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

 later.

DES itself can be adapted and reused in a more secure scheme. Many former DES users now use Triple DES

Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....

 (TDES) which was described and analysed by one of DES's patentees (see FIPS

Federal Information Processing Standard

A Federal Information Processing Standard is a publicly announced standardization developed by the United States federal government for use in computer systems by all non-military government agencies and by government contractors, when properly invoked and tailored on a contract...

 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

DES-X

In cryptography, DES-X is a variant on the DES block cipher intended to increase the complexity of a brute force attack using a technique called key whitening....

, which increases the key size by XORing extra key material before and after DES. GDES

GDES

In cryptography, the Generalized DES Scheme is a variant of the DES block cipher designed with the intention of speeding up the encryption process while improving its security...

 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

RC6

In cryptography, RC6 is a symmetric key block cipher derived from RC5. It was designed by Ron Rivest, Matt Robshaw, Ray Sidney, and Yiqun Lisa Yin to meet the requirements of the Advanced Encryption Standard competition. The algorithm was one of the five finalists, and was also submitted to the...

, Serpent

Serpent (cipher)

Serpent is a symmetric key block cipher which was a finalist in the Advanced Encryption Standard contest, where it came second to Rijndael. Serpent was designed by Ross Anderson, Eli Biham, and Lars Knudsen....

, MARS and Twofish

Twofish

In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but was not selected for standardisation...

.

Description

File:DES-main-network.png|thumb|250px|Figure 1— The overall Feistel structure of DES
rect 0 130 639 229 Permuted Choice 1
rect 220 300 421 405 Feistel function
rect 220 594 421 701 Feistel function
rect 220 1037 421 1144 Feistel function
rect 220 1330 421 1437 Feistel function
rect 0 1478 639 1577 Permuted Choice 2
circle 50 351 26 XOR
circle 50 647 26 XOR
circle 50 1090 26 XOR
circle 50 1383 26 XOR

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 supplementary material

For reference, this article details the various tables referenced in the Data Encryption Standard block cipher.All bits and bytes are arranged in big endian order in this document. That is, bit number 1 is always the most significant bit....

.

DES is the archetypal block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

 — an algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 that takes a fixed-length string of plaintext

Plaintext

In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....

 bits and transforms it through a series of complicated operations into another ciphertext

Ciphertext

In cryptography, ciphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher...

 bitstring of the same length. In the case of DES, the block size

Block size (cryptography)

In modern cryptography, symmetric key ciphers are generally divided into stream ciphers and block ciphers. Block ciphers operate on a fixed length string of bits. The length of this bit string is the block size...

 is 64 bits. DES also uses a key

Key (cryptography)

In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...

 to customize the transformation, so that decryption can supposedly 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

Parity bit

A parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code....

, and are thereafter discarded. Hence the effective key length is 56 bits, and it is never quoted as such. Every 8th bit of the selected key is discarded, that is, positions 8, 16, 24, 32, 40, 48, 56, 64 are removed from the 64 bit key leaving behind only the 56 bit key.

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. Further comments on the usage of DES are contained in FIPS-74.

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

Permutation

In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

, 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.

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 ⊕ 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:

File:DES-f-function.png|thumb|250px|Figure 2—The Feistel function (F-function) of DES
rect 10 88 322 170 Expansion function
rect 9 340 77 395 Substitution box 1
rect 89 340 157 395 Substitution box 2
rect 169 340 237 395 Substitution box 3
rect 247 340 315 395 Substitution box 4
rect 327 340 395 395 Substitution box 5
rect 405 340 473 395 Substitution box 6
rect 485 340 553 395 Substitution box 7
rect 565 340 633 395 Substitution box 8
rect 9 482 630 565 Permutation
circle 319 232 21 XOR

1. Expansion — the 32-bit half-block is expanded to 48 bits using the expansion permutation, denoted E in the diagram, by duplicating half of the bits. The output consists of eight 6-bit(8*6=48bits) pieces, each containing a copy of 4 corresponding input bits, plus a copy of the immediately adjacent bit from each of the input pieces to either side.
2. Key mixing — the result is combined with a subkey using an XOR operation. 16 48-bit subkeys — one for each round — are derived from the main key using the key schedule
   Key schedule
   [[Image:DES-key-schedule.png|thumbnail|220px|The key schedule of DES [[Image:DES-key-schedule.png|thumbnail|220px|The key schedule of DES [[Image:DES-key-schedule.png|thumbnail|220px|The key schedule of DES ("[[Image:DES-key-schedule.png|thumbnail|220px|The key schedule of DES ("...
   
   (described below).
3. Substitution — after mixing in the subkey, the block is divided into eight 6-bit pieces before processing by the S-boxes
   Substitution box
   In cryptography, an S-Box is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext — Shannon's property of confusion...
   
   , 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
   Lookup table
   In computer science, a lookup table is a data structure, usually an array or associative array, often used to replace a runtime computation with a simpler array indexing operation. The savings in terms of processing time can be significant, since retrieving a value from memory is often faster than...
   
   . 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
   Permutation
   In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
   
   , the P-box. This is designed so that, after expansion, each S-box's output bits are spread across 6 different S boxes in the next round.

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

Confusion and diffusion

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Shannon in his paper Communication Theory of Secrecy Systems, published in 1949....

" respectively, a concept identified by Claude Shannon in the 1940s as a necessary condition for a secure yet practical cipher.

Key schedule

File:DES-key-schedule.png|thumb|250px|Figure 3— The key-schedule of DES
rect 96 28 298 58 Permuted choice 1
rect 127 122 268 155 Permuted choice 2
rect 127 216 268 249 Permuted choice 2
rect 127 357 268 390 Permuted choice 2
rect 127 451 268 484 Permuted choice 2
rect 96 91 127 116 Left shift by 1
rect 268 91 299 116 Left shift by 1
rect 96 185 127 210 Left shift by 1
rect 268 185 299 210 Left shift by 1
rect 96 326 127 351 Left shift by 2
rect 268 326 299 351 Left shift by 2
rect 96 419 127 444 Left shift by 1
rect 268 419 299 444 Left shift by 1

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

Parity bit

A parity bit is a bit that is added to ensure that the number of bits with the value one in a set of bits is even or odd. Parity bits are used as the simplest form of error detecting code....

 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 — the subkeys are in reverse order compared to encryption. Apart from that change, the process is the same as for encryption. The same 28 bits are passed to all rotation boxes.

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 number of known or chosen plaintexts to carry out, and are not a concern in practice.

Brute force attack

For any cipher, the most basic method of attack is brute force

Brute force attack

In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data. Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system that would make the task easier...

 — 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. As a result of discussions involving external consultants including the NSA, the key size was reduced from 128 bits to 56 bits to fit on a single chip.

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—or, at least, no implementations were publicly acknowledged. The vulnerability of DES was practically demonstrated in the late 1990s. In 1997, RSA Security

RSA Security

RSA, the security division of EMC Corporation, is headquartered in Bedford, Massachusetts, United States, and maintains offices in Australia, Ireland, Israel, the United Kingdom, Singapore, India, China, Hong Kong and Japan....

 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

DESCHALL Project

DESCHALL, short for DES Challenge, was the first group to publicly break a message which used the Data Encryption Standard , becoming the $10,000 winner of the first of the set of DES Challenges proposed by RSA Security in 1997...

, led by Rocke Verser, Matt Curtin

Matt Curtin

Matt Curtin is a computer scientist and entrepreneur in Columbus, Ohio best known for his work in cryptography and firewall systems. He is the founder of Interhack Corporation, first faculty advisor of , and lecturer in the Department of Computer Science and Engineering at The Ohio State...

, 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

Electronic Frontier Foundation

The Electronic Frontier Foundation is an international non-profit digital rights advocacy and legal organization based in the United States...

 (EFF), a cyberspace civil rights group, at the cost of approximately US$250,000 (see EFF DES cracker

EFF DES cracker

In cryptography, the EFF DES cracker is a machine built by the Electronic Frontier Foundation in 1998 to perform a brute force search of DES cipher's key space — that is, to decrypt an encrypted message by trying every possible key...

). 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.

The next confirmed DES cracker was the COPACOBANA machine built in 2006 by teams of the Universities of Bochum

Ruhr University

Ruhr University Bochum , located on the southern hills of central Ruhr area Bochum, was founded in 1962 as the first new public university in Germany since World War II...

 and Kiel

University of Kiel

The University of Kiel is a university in the city of Kiel, Germany. It was founded in 1665 as the Academia Holsatorum Chiloniensis by Christian Albert, Duke of Holstein-Gottorp and has approximately 23,000 students today...

, both in Germany

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

. Unlike the EFF machine, COPACOBANA consists of commercially available, reconfigurable integrated circuits. 120 of these Field-programmable gate array

Field-programmable gate array

A field-programmable gate array is an integrated circuit designed to be configured by the customer or designer after manufacturing—hence "field-programmable"...

s (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. 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. Adjusting for inflation over 8 years yields an even higher improvement of about 30x. Since 2007, SciEngines GmbH

SciEngines GmbH

SciEngines GmbH is a privately owned company. It has been founded late 2006 as a spin-off of the Universities of Bochum and Kiel, both in Germany. The company has been formed out of the team of the original COPACOBANA project. The project intended to create a platform for an affordable Custom...

, a spin-off company of the two project partners of COPACOBANA has enhanced and developed successors of COPACOBANA. In 2008 their COPACOBANA RIVYERA reduced the time to break DES to less than one day, using 128 Spartan-3 5000's. Currently SciEngines RIVYERA holds the record in brute-force breaking DES utilizing 128 Spartan-3 5000 FPGAs.

Attacks faster than brute-force

There are three attacks known that can break the full 16 rounds of DES with less complexity than a brute-force search: differential cryptanalysis

Differential cryptanalysis

Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output...

 (DC), linear cryptanalysis (LC), and Davies' attack

Davies' attack

In cryptography, is a dedicated statistical cryptanalysis method for attacking the Data Encryption Standard . The attack was originally created in 1987 by Donald Davies. In 1994, Eli Biham and Alex Biryukov made significant improvements to the technique. It is a known-plaintext attack based on the...

. However, the attacks are theoretical and are unfeasible to mount in practice; these types of attack are sometimes termed certificational weaknesses.

• Differential cryptanalysis
  Differential cryptanalysis
  Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output...
  
   was rediscovered in the late 1980s by Eli Biham
  Eli Biham
  Eli Biham is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion Israeli Institute of Technology Computer Science department. Starting from October 2008, Biham is the dean of the Technion Computer Science department, after serving for two years as chief of CS graduate...
  
   and Adi Shamir
  Adi Shamir
  Adi Shamir is an Israeli cryptographer. He is a co-inventor of the RSA algorithm , a co-inventor of the Feige–Fiat–Shamir identification scheme , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer...
  
  ; 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
  Linear cryptanalysis
  In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers...
  
   was discovered by Mitsuru Matsui
  Mitsuru Matsui
  is a Japanese cryptographer and senior researcher for Mitsubishi Electric Company. While researching error-correcting codes in 1990, Matsui was inspired by Biham and Shamir's differential cryptanalysis, and discovered the technique of linear cryptanalysis, published in 1993. Differential and linear...
  
  , 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 generalization of LC — multiple linear cryptanalysis — was suggested in 1994 (Kaliski and Robshaw), and was further refined by Biryukov and others. (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 (that is, 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 specialized technique for DES, first suggested by Donald Davies
  Donald Davies
  Donald Watts Davies, CBE FRS was a Welsh computer scientist who was one of the inventors of packet switching computer networking, and originator of the term.-Career history:...
  
   in the eighties, and improved by Biham and Biryukov
  Alex Biryukov
  Alex Biryukov is a cryptographer, currently an assistant professor at the University of Luxembourg. His notable work includes the design of the stream cipher LEX, as well as the cryptanalysis of numerous cryptographic primitives. In 1998, he developed impossible differential cryptanalysis together...
  
   (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, that is, versions of DES with fewer than 16 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 and others., 2002).

Minor cryptanalytic properties

DES exhibits the complementation property, namely that
where is the bitwise complement of denotes encryption with key and denote plaintext and ciphertext blocks respectively. The complementation property means that the work for a brute force attack

Brute force attack

In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data. Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system that would make the task easier...

 could be reduced by a factor of 2 (or a single bit) under a chosen-plaintext

Chosen-plaintext attack

A chosen-plaintext attack is an attack model for cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. The goal of the attack is to gain some further information which reduces the security of the...

 assumption.

DES also has four so-called weak keys. Encryption (E) and decryption (D) under a weak key have the same effect (see involution): or equivalently,
There are also six pairs of semi-weak keys. Encryption with one of the pair of semiweak keys, , operates identically to decryption with the other, : or equivalently,
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

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...

, or more precisely, the set (for all possible keys ) 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

Triple DES

In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....

 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

• Triple DES
  Triple DES
  In cryptography, Triple DES is the common name for the Triple Data Encryption Algorithm block cipher, which applies the Data Encryption Standard cipher algorithm three times to each data block....
  
  
• Skipjack (cipher)
  Skipjack (cipher)
  In cryptography, Skipjack is a block cipher—an algorithm for encryption—developed by the U.S. National Security Agency . Initially classified, it was originally intended for use in the controversial Clipper chip...
  
  
• Symmetric key algorithm

External links

• FIPS 46-3: The official document describing the DES standard (PDF); An older version in HTML
• COPACOBANA, a $10,000 DES cracker based on FPGAs by the Universities of Bochum and Kiel
• DES step-by-step presentation and reliable message encoding application
• A Fast New DES Implementation in Software - Biham
• On Multiple Linear Approximations
• RFC4772 : Security Implications of Using the Data Encryption Standard (DES)
• A simple DES / Triple DES implementation documentation