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FIPS PUB 46-2

Supersedes FIPS PUB 46-1

1988 January 22

Federal Information

Processing Standards Publication 46-2

1993 December 30

Announcing the Standard for

DATA ENCRYPTION STANDARD (DES)

(The Foreword, Abstract, and Key Words

can be found at the end of this document.)

Federal Information Processing Standards Publications (FIPS PUBS) are issued by

the National Bureau of Standards in accordance with section 111 (f) (2) of the

Federal Property and Administrative Services Act of 1949, as amended, Public Law

89-306 (79 Stat 1127), Executive Order 11717 (38 FR 12315, dated May 11, 1973),

and Part 6 of Title 15 Code of Federal Regulations.

1. Name of Standard. Data Encryption Standard (DES).

2. Category of Standard. Computer Security.

3. Explanation. The Data Encryption Standard (DES) specifies a FIPS approved

cryptographic algorithm as required by FIPS 140-1. This publication provides a

complete description of a mathematical algorithm for encrypting (enciphering)

and decrypting (deciphering) binary coded information. Encrypting data converts

it to an unintelligible form called cipher. Decrypting cipher converts the data

back to its original form called plaintext. The algorithm described in this

standard specifies both enciphering and deciphering operations which are based

on a binary number called a key.

A key consists of 64 binary digits ("O"s or "1"s) of which 56 bits are randomly

generated and used directly by the algorithm. The other 8 bits, which are not

used by the algorithm, are used for error detection. The 8 error detecting bits

are set to make the parity of each 8-bit byte of the key odd, i.e., there is an

odd number of "1"s in each 8-bit byte1. Authorized users of encrypted computer

data must have the key that was used to encipher the data in order to decrypt

it. The encryption algorithm specified in this standard is commonly known among

those using the standard. The unique key chosen for use in a particular

application makes the results of encrypting data using the algorithm unique.

Selection of a different key causes the cipher that is produced for any given

set of inputs to be different. The cryptographic security of the data depends on

the security provided for the key used to encipher and decipher the data.

Data can be recovered from cipher only by using exactly the same key used to

encipher it. Unauthorized recipients of the cipher who know the algorithm but do

not have the correct key cannot derive the original data algorithmically.

However, anyone who does have the key and the algorithm can easily decipher the

cipher and obtain the original data. A standard algorithm based on a secure key

thus provides a basis for exchanging encrypted computer data by issuing the key

used to encipher it to those authorized to have the data.

Data that is considered sensitive by the responsible authority, data that has a

high value, or data that represents a high value should be cryptographically

protected if it is vulnerable to unauthorized disclosure or undetected

modification during transmission or while in storage. A risk analysis should be

performed under the direction of a responsible authority to determine potential

threats. The costs of providing cryptographic protection using this standard as

well as alternative methods of providing this protection and their respective

costs should be projected. A responsible authority then should make a decision,

based on these analyses, whether or not to use cryptographic protection and this

standard.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 Sometimes keys are generated in an encrypted form. A random 64-bite number is

generated and defined to be the cipher formed by the encryption of a key using a

key encrypting key. In this case the parity bits of the encrypted key cannot be

set until after the key is decrypted.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

4. Approving Authority. Secretary of Commerce.

5. Maintenance Agency. U.S. Department of Commerce, National Institute of

Standards and Technology, Computer Systems Laboratory.

6. Applicability. This standard may be used by Federal departments and agencies

when the following conditions apply:

An authorized official or manager responsible for data security or the

security of any computer system decides that cryptographic protection is

required; and

2. The data is not classified according to the National Security Act of

1947, as amended, or the Atomic Energy Act of 1954, as amended.

Federal agencies or departments which use cryptographic devices for

protecting data classified according to either of these acts can use those

devices for protecting unclassified data in lieu of the standard.

Other FIPS approved cryptographic algorithms may be used in addition to, or

in lieu of, this standard when implemented in accordance with FIPS 140-1.

In addition, this standard may be adopted and used by non-Federal Government

organizations. Such use is encouraged when it provides the desired security

for commercial and private organizations.

7. Applications. Data encryption (cryptography) is utilized in various

applications and environments. The specific utilization of encryption and

the implementation of the DES will be based on many factors particular to

the computer system and its associated components. In general, cryptography

is used to protect data while it is being communicated between two points or

while it is stored in a medium vulnerable to physical theft. Communication

security provides protection to data by enciphering it at the transmitting

point and deciphering it at the receiving point. File security provides

protection to data by enciphering it when it is recorded on a storage medium

and deciphering it when it is read back from the storage medium. In the

first case, the key must be available at the transmitter and receiver

simultaneously during communication. In the second case, the key must be

maintained and accessible for the duration of the storage period. FIPS 171

provides approved methods for managing the keys used by the algorithm

specified in this standard.

8. Implementations. Cryptographic modules which implement this standard

shall conform to the requirements of FIPS 140-1. The algorithm specified in

this standard may be implemented in software, firmware, hardware, or any

combination thereof. The specific implementation may depend on several

factors such as the application, the environment, the technology used, etc.

Implementations which may comply with this standard include electronic

devices (e.g., VLSI chip packages), micro-processors using Read Only Memory

(ROM), Programmable Read Only Memory (PROM), or Electronically Erasable Read

Only Memory (EEROM), and mainframe computers using Random Access Memory

(RAM). When the algorithm is implemented in software or firmware, the

processor on which the algorithm runs must be specified as part of the

validation process. Implementations of the algorithm which are tested and

validated by NIST will be considered as complying with the standard. Note

that FIPS 140-1 places additional requirements on cryptographic modules for

Government use. Information about devices that have been validated and

procedures for testing and validating equipment for conformance with this

standard and FIPS 140-1 are available from the National Institute of

Standards and Technology, Computer Systems Laboratory, Gaithersburg, MD

20899.

9. Export Control. Cryptographic devices and technical data regarding them

are subject to Federal Government export controls as specified in Title 22,

Code of Federal Regulations, Parts 120 through 128. Some exports of

cryptographic modules implementing this standard and technical data

regarding them must comply with these Federal regulations and be licensed by

the U.S. Department of State. Other exports of cryptographic modules

implementing this standard and technical data regarding them fall under the

licensing authority of the Bureau of Export Administration of the U.S.

Department of Commerce. The Department of Commerce is responsible for

licensing cryptographic devices used for authentication, access control,

proprietary software, automatic teller machines (ATMs), and certain devices

used in other equipment and software. For advice concerning which agency has

licensing authority for a particular cryptographic device, please contact

the respective agencies.

10. Patents. Cryptographic devices implementing this standard may be covered

by U.S. and foreign patents issued to the International Business Machines

Corporation. However, IBM has granted nonexclusive, royalty-free licenses

under the patents to make, use and sell apparatus which complies with the

standard. The terms, conditions and scope of the licenses are set out in

notices published in the May 13, 1975 and August 31, 1976 issues of the

Official Gazette of the United States Patent and Trademark Office (934 O.G.

452 and 949 O.G. 1717).

11. Alternative Modes of Using the DES. FIPS PUB 81, DES Modes of Operation,

describes four different modes for using the algorithm described in this

standard. These four modes are called the Electronic Codebook (ECB) mode,

the Cipher Block Chaining (CBC) mode, the Cipher Feedback (CFB) mode, and

the Output Feedback (OFB) mode. ECB is a direct application of the DES

algorithm to encrypt and decrypt data; CBC is an enhanced mode of ECB which

chains together blocks of cipher text; CFB uses previously generated cipher

text as input to the DES to generate pseudorandom outputs which are combined

with the plaintext to produce cipher, thereby chaining together the

resulting cipher; OFB is identical to CFB except that the previous output of

the DES is used as input in OFB while the previous cipher is used as input

in CFB. OFB does not chain the cipher.

12. Implementation of this standard. This standard became effective July

1977. It was reaffirmed in 1983, 1988, and 1993. It applies to all Federal

agencies, contractors of Federal agencies, or other organizations that

process information (using a computer or telecommunications system) on

behalf of the Federal Government to accomplish a Federal function. Each

Federal agency or department may issue internal directives for the use of

this standard by their operating units based on their data security

requirement determinations. FIPS 46-2 which revises the implementation of

the Data Encryption Algorithm to include software, firmware, hardware, or

any combination thereof, is effective June 30, 1994. This revised standard

may be used in the interim period before the effective date.

NIST provides technical assistance to Federal agencies in implementing data

encryption through the issuance of guidelines and through individual

reimbursable projects. The National Security Agency assists Federal

departments and agencies in communications security for classified

applications and in determining specific security requirements. Instructions

and regulations for procuring data processing equipment utilizing this

standard are included in the Federal Information Resources Management

Regulation (FIRMR) Subpart 201-8.111-1.

13. Specifications. Federal Information Processing Standard (FIPS) 46-2,

Data Encryption Standard (DES) (affixed).

14. Cross Index.

a. Federal Information Resources Management Regulations (FIRMR) subpart

201.20.303, Standards, and subpart 201.39.1002, Federal Standards.

b. FIPS PUB 31, Guidelines to ADP Physical Security and Risk Management.

c. FIPS PUB 41, Computer Security Guidelines for Implementing the

Privacy Act of 1974.

d. FIPS PUB 65, Guideline for Automatic Data Processing Risk Analysis.

e. FIPS PUB 73, Guidelines for Security of Computer Applications.

f. FIPS PUB 74, Guidelines for Implementing and Using the NBS Data

Encryption Standard.

g. FIPS PUB 81, DES Modes of Operation.

h. FIPS PUB 87, Guidelines for ADP Contingency Planning.

i. FIPS PUB 112, Password Usage.

j. FIPS PUB 113, Computer Data Authentication.

k. FIPS PUB 140-1, Security Requirements for Cryptographic Modules.

l. FIPS PUB 171, Key Management Using ANSI X9.17.

m. Other FIPS and Federal Standards are applicable to the implementation

and use of this standard. In particular, the Code for Information

Interchange, Its Representations, Subsets, and Extensions (FIPS PUB 1-2)

and other related data storage media or data communications standards

should be used in conjunction with this standard. A list of currently

approved FIPS may be obtained from the National Institute of Standards

and Technology, Computer Systems Laboratory, Gaithersburg, MD 20899.

15. Qualifications. The cryptographic algorithm specified in this standard

transforms a 64-bit binary value into a unique 64-bit binary value based on

a 56-bit variable. If the complete 64-bit input is used (i.e., none of the

input bits should be predetermined from block to block) and if the 56-bit

variable is randomly chosen, no technique other than trying all possible

keys using known input and output for the DES will guarantee finding the

chosen key. As there are over 70,000,000,000,000,000 (seventy quadrillion)

possible keys of 56 bits, the feasibility of deriving a particular key in

this way is extremely unlikely in typical threat environments. Moreover, if

the key is changed frequently, the risk of this event is greatly diminished.

However, users should be aware that it is theoretically possible to derive

the key in fewer trials (with a correspondingly lower probability of success

depending on the number of keys tried) and should be cautioned to change the

key as often as practical. Users must change the key and provide it a high

level of protection in order to minimize the potential risks of its

unauthorized computation or acquisition. The feasibility of computing the

correct key may change with advances in technology.

A more complete description of the strength of this algorithm against

various threats is contained in FIPS PUB 74, Guidelines for Implementing and

Using the NBS Data Encryption Standard.

When correctly implemented and properly used, this standard will provide a

high level of cryptographic protection to computer data. NIST, supported by

the technical assistance of Government agencies responsible for

communication security, has determined that the algorithm specified in this

standard will provide a high level of protection for a time period beyond

the normal life cycle of its associated equipment. The protection provided

by this algorithm against potential new threats will be reviewed within 5

years to assess its adequacy (See Special Information Section). In addition,

both the standard and possible threats reducing the security provided

through the use of this standard will undergo continual review by NIST and

other cognizant Federal organizations. The new technology available at that

time will be evaluated to determine its impact on the standard. In addition,

the awareness of any breakthrough in technology or any mathematical weakness

of the algorithm will cause NIST to reevaluate this standard and provide

necessary revisions.

At the next review (1998), the algorithm specified in this standard will be

over twenty years old. NIST will consider alternatives which offer a higher

level of security. One of these alternatives may be proposed as a

replacement standard at the 1998 review.

16. Comments. Comments and suggestions regarding this standard and its use

are welcomed and should be addressed to the National Institute of Standards

and Technology, Attn: Director, Computer Systems Laboratory, Gaithersburg,

MD 20899.

17. Waiver Procedure. Under certain exceptional circumstances, the heads of

Federal departments and agencies may approve waivers to Federal Information

Processing Standards (FIPS). The head of such agency may redelegate such

authority only to a senior official designated pursuant to section 3506(b)

of Title 44, United States Code. Waiver shall be granted only when:

a. Compliance with a standard would adversely affect the accomplishment

of the mission of an operator of a Federal computer system; or

b. Compliance with a standard would cause a major adverse financial

impact on the operator which is not offset by Government-wide savings.

Agency heads may act upon a written waiver request containing the

information detailed above. Agency heads may also act without a written

waiver request when they determine that conditions for meeting the standard

cannot be met. Agency heads may approve waivers only by a written decision

which explains the basis on which the agency head made the required

finding(s). A copy of each decision, with procurement sensitive or

classified portions clearly identified, shall be sent to: National Institute

of Standards and Technology; ATTN: FIPS Waiver Decisions, Technology

Building, Room B-154, Gaithersburg, MD 20899.

In addition, notice of each waiver granted and each delegation of authority

to approve waivers shall be sent promptly to the Committee on Government

Operations of the House of Representatives and the Committee on Government

Affairs of the Senate and shall be published promptly in the Federal

Register.

When the determination on a waiver applies to the procurement of equipment

and/or services, a notice of the waiver determination must be published in

the Commerce Business Daily as a part of the notice of solicitation for

offers of an acquisition or, if the waiver determination is made after that

notice is published, by amendment to such notice.

A copy of the waiver, any supporting documents, the document approving the

waiver and any accompanying documents, with such deletions as the agency is

authorized and decides to make under 5 United States Code Section 552(b),

shall be part of the procurement documentation and retained by the agency.

18. Special Information. In accordance with the Qualifications Section of

this standard, reviews of this standard have been conducted every 5 years

since its adoption in 1977. The standard was reaffirmed during each of those

reviews. This revision to the text of the standard contains changes which

allow software implementations of the algorithm and which permit the use of

other FIPS approved cryptographic algorithms.

19. Where to Obtain Copies of the Standard. Copies of this publication are

for sale by the National Technical Information Service, U.S. Department of

Commerce, Springfield, VA 22161. When ordering, refer to Federal Information

Processing Standards Publication 46-2 (FIPS PUB 46-2), and identify the

title. When microfiche is desired, this should be specified. Prices are

published by NTIS in current catalogs and other issuances. Payment may be

made by check, money order, deposit account or charged to a credit card

accepted by NTIS.

FIPS PUB 44-2

Supersedes FIPS PUB 46-1

1988 January 22

Federal Information

Processing Standards Publication 46-2

1993 December 30

Specifications for

DATA ENCRYPTION STANDARD

The Data Encryption Standard (DES) shall consist of the following Data

Encryption Algorithm to be implemented in special purpose electronic

devices. These devices shall be designed in such a way that they may be used

in a computer system or network to provide cryptographic protection to

binary coded data. The method of implementation will depend on the

application and environment. The devices shall be implemented in such a way

that they may be tested and validated as accurately performing the

transformations specified in the following algorithm.

DATA ENCRYPTION ALGORITHM

Introduction

The algorithm is designed to encipher and decipher blocks of data consisting

of 64 bits under control of a 64-bit key.** Deciphering must be accomplished

by using the same key as for enciphering, but with the schedule of

addressing the key bits altered so that the deciphering process is the

reverse of the enciphering process. A block to be enciphered is subjected to

an initial permutation IP, then to a complex key-dependent computation and

finally to a permutation which is the inverse of the initial permutation

IP-1. The key-dependent computation can be simply defined in terms of a

function f, called the cipher function, and a function KS, called the key

schedule. A description of the computation is given first, along with

details as to how the algorithm is used for encipherment. Next, the use of

the algorithm for decipherment is described. Finally, a definition of the

cipher function f is given in terms of primitive functions which are called

the selection functions Si and the permutation function P. Si, P and KS of

the algorithm are contained in the Appendix.

The following notation is convenient: Given two blocks L and R of bits, LR

denotes the block consisting of the bits of L followed by the bits of R.

Since concatenation is associative, B1B2...B8, for example, denotes the

block consisting of the bits of B1 followed by the bits of B2...followed by

the bits of B8.

** Blocks are composed of bits numbered from left to right, i.e., the left

most bit of a block is bit one.

Figure 1. Enciphering computation.

Enciphering

A sketch of the enciphering computation is given in Figure 1.

The 64 bits of the input block to be enciphered are first subjected to the

following permutation, called the initial permutation IP:

IP

58 50 42 34 26 18 10 2

60 52 44 36 28 20 12 4

62 54 46 38 30 22 14 6

64 56 48 40 32 24 16 8

57 49 41 33 25 17 9 1

59 51 43 35 27 19 11 3

61 53 45 37 29 21 13 5

63 55 47 39 31 23 15 7

That is the permuted input has bit 58 of the input as its first bit, bit 50

as its second bit, and so on with bit 7 as its last bit. The permuted input

block is then the input to a complex key-dependent computation described

below. The output of that computation, called the preoutput, is then

subjected to the following permutation which is the inverse of the initial

permutation:

IP-1

40 8 48 16 56 24 64 32

39 7 47 15 55 23 63 31

38 6 46 14 54 22 62 30

37 5 45 13 53 21 61 29

36 4 44 12 52 20 60 28

35 3 43 11 51 19 59 27

34 2 42 10 50 18 58 26

33 1 41 9 49 17 57 25

That is, the output of the algorithm has bit 40 of the preoutput block as

its first bit, bit 8 as its second bit, and so on, until bit 25 of the

preoutput block is the last bit of the output.

The computation which uses the permuted input block as its input to produce

the preoutput block consists, but for a final interchange of blocks, of 16

iterations of a calculation that is described below in terms of the cipher

function f which operates on two blocks, one of 32 bits and one of 48 bits,

and produces a block of 32 bits.

Let the 64 bits of the input block to an iteration consist of a 32 bit block

L followed by a 32 bit block R. Using the notation defined in the

introduction, the input block is then LR.

Let K be a block of 48 bits chosen from the 64-bit key. Then the output L'R'

of an iteration with input LR is defined by:

(1) L' = R

R' = L(+)f(R,K)

where (+) denotes bit-by-bit addition modulo 2.

As remarked before, the input of the first iteration of the calculation is

the permuted input block. If L'R' is the output of the 16th iteration then

R'L' is the preoutput block. At each iteration a different block K of key

bits is chosen from the 64-bit key designated by KEY.

With more notation we can describe the iterations of the computation in more

detail. Let KS be a function which takes an integer n in the range from 1 to

16 and a 64-bit block KEY as input and yields as output a 48-bit block Kn

which is a permuted selection of bits from KEY. That is

(2) Kn = KS(n,KEY)

with Kn determined by the bits in 48 distinct bit positions of KEY. KS is

called the key schedule because the block K used in the n'th iteration of

(1) is the block Kn determined by (2).

As before, let the permuted input block be LR. Finally, let L() and R() be

respectively L and R and let Ln and Rn be respectively L' and R' of (1) when

L and R are respectively Ln-1 and Rn-1 and K is Kn; that is, when n is in

the range from 1 to 16,

(3) Ln = Rn-1

Rnn = Ln-1(+)f(Rn-1,Kn)

The preoutput block is then R16L16.

The key schedule KS of the algorithm is described in detail in the Appendix.

The key schedule produces the 16 Kn which are required for the algorithm.

Deciphering

The permutation IP-1 applied to the preoutput block is the inverse of the

initial permutation IP applied to the input. Further, from (1) it follows

that:

(4) R = L'

L = R' (+) f(L',K)

Consequently, to decipher it is only necessary to apply the very same

algorithm to an enciphered message block, taking care that at each iteration

of the computation the same block of key bits K is used during decipherment

as was used during the encipherment of the block. Using the notation of the

previous section, this can be expressed by the equations:

(5) Rn-1 = Ln

Ln-1 = Rn (+) f(Ln,Kn)

where now R16L16 is the permuted input block for the deciphering calculation

and L() and R() is the preoutput block. That is, for the decipherment

calculation with R16L16 as the permuted input, K16 is used in the first

iteration, K15 in the second, and so on, with K1 used in the 16th iteration.

The Cipher Function f

A sketch of the calculation of f(R,K) is given in Figure 2.

Figure 2. Calculation of f(R,K).

Let E denote a function which takes a block of 32 bits as input and yields a

block of 48 bits as output. Let E be such that the 48 bits of its output,

written as 8 blocks of 6 bits each, are obtained by selecting the bits in

its inputs in order according to the following table:

E BIT-SELECTION TABLE

32 1 2 3 4 5

4 5 6 7 8 9

8 9 10 11 12 13

12 13 14 15 16 17

16 17 18 19 20 21

20 21 22 23 24 25

24 25 26 27 28 29

28 29 30 31 32 1

Thus the first three bits of E(R) are the bits in positions 32, 1 and 2 of R

while the last 2 bits of E(R) are the bits in positions 32 and 1.

Each of the unique selection functions S1,S2,...,S8, takes a 6-bit block as

input and yields a 4-bit block as output and is illustrated by using a table

containing the recommended S1:

S1

Column Number

Row

No. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7

1 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8

2 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0

3 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13

If S1 is the function defined in this table and B is a block of 6 bits, then

S1(B)is determined as follows: The first and last bits of B represent in

base 2 a number in the range 0 to 3. Let that number be i. The middle 4 bits

of B represent in base 2 a number in the range 0 to 15. Let that number be

j. Look up in the table the number in the i'th row and j'th column. It is a

number in the range 0 to 15 and is uniquely represented by a 4 bit block.

That block is the output S1(B) of S1 for the input B. For example, for input

011011 the row is 01, that is row 1, and the column is determined by 1101,

that is column 13. In row 1 column 13 appears 5 so that the output is 0101.

Selection functions S1,S2,...,S8 of the algorithm appear in the Appendix.

The permutation function P yields a 32-bit output from a 32-bit input by

permuting the bits of the input block. Such a function is defined by the

following table:

P

16 7 20 21

29 12 28 17

1 15 23 26

5 18 31 10

2 8 24 14

32 27 3 9

19 13 30 6

22 11 4 25

The output P(L) for the function P defined by this table is obtained from

the input L by taking the 16th bit of L as the first bit of P(L), the 7th

bit as the second bit of P(L), and so on until the 25th bit of L is taken as

the 32nd bit of P(L). The permutation function P of the algorithm is

repeated in the Appendix.

Now let S1,...,S8 be eight distinct selection functions, let P be the

permutation function and let E be the function defined above.

To define f(R,K) we first define B1,...,B8 to be blocks of 6 bits each for

which

(6) B1B2...B8 = K(+)E(R)

The block f(R,K) is then defined to be

(7)

P(S1(B1)S2(B2)...S

8(B8))

Thus K(+)E(R) is first divided into the 8 blocks as indicated in (6). Then

each Bi is taken as an input to Si and the 8 blocks (S1(B1)S2(B2)...S8(B8)

of 4 bits each are consolidated into a single block of 32 bits which forms

the input to P. The output (7) is then the output of the function f for the

inputs R and K.

APPENDIX

PRIMITIVE FUNCTIONS FOR THE DATA ENCRYPTION ALGORITHM

The choice of the primitive functions KS, S1,...,S8 and P is critical to the

strength of an encipherment resulting from the algorithm. Specified below is

the recommended set of functions, describing S1,...,S8 and P in the same way

they are described in the algorithm. For the interpretation of the tables

describing these functions, see the discussion in the body of the algorithm.

The primitive functions S1,...,S8 are:

S1

14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7

O 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8

4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0

15 12 8 2 4 9 1 7 5 11 3 14 10 O 6 13

S2

15 1 8 14 6 11 3 4 9 7 2 13 12 O 5 10

3 13 4 7 15 2 8 14 12 0 1 10 6 9 11 5

0 14 7 11 10 4 13 1 5 8 12 6 9 3 2 15

13 8 10 1 3 15 4 2 11 6 7 12 0 5 14 9

S3

10 0 9 14 6 3 15 5 1 13 12 7 11 4 2 8

13 7 O 9 3 4 6 10 2 8 5 14 12 11 15 1

13 6 4 9 8 15 3 0 11 1 2 12 5 10 14 7

1 10 13 0 6 9 8 7 4 15 14 3 11 5 2 12

S4

7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15

13 8 11 5 6 15 O 3 4 7 2 12 1 10 14 9

10 6 9 0 12 11 7 13 15 1 3 14 5 2 8 4

3 15 O 6 10 1 13 8 9 4 5 11 12 7 2 14

S5

2 12 4 1 7 10 11 6 8 5 3 15 13 O 14 9

14 11 2 12 4 7 13 1 5 0 15 10 3 9 8 6

4 2 1 11 10 13 7 8 15 9 12 5 6 3 O 14

11 8 12 7 1 14 2 13 6 15 O 9 10 4 5 3

S6

12 1 10 15 9 2 6 8 O 13 3 4 14 7 5 11

10 15 4 2 7 12 9 5 6 1 13 14 O 11 3 8

9 14 15 5 2 8 12 3 7 0 4 10 1 13 11 6

4 3 2 12 9 5 15 10 11 14 1 7 6 0 8 13

S7

4 11 2 14 15 0 8 13 3 12 9 7 5 10 6 1

13 0 11 7 4 9 1 10 14 3 5 12 2 15 8 6

1 4 11 13 12 3 7 14 10 15 6 8 0 5 9 2

6 11 13 8 1 4 10 7 9 5 0 15 14 2 3 12

S8

13 2 8 4 6 15 11 1 10 9 3 14 5 0 12 7

1 15 13 8 10 3 7 4 12 5 6 11 0 14 9 2

7 11 4 1 9 12 14 2 0 6 10 13 15 3 5 8

2 1 14 7 4 10 8 13 15 12 9 0 3 5 6 11

The primitive function P is:

16 7 20 21

29 12 28 17

1 15 23 26

5 18 31 10

2 8 24 14

32 27 3 9

19 13 30 6

22 11 4 25

Recall that Kn, for 1<= n <= 16, is the block of 48 bits in (2) of the

algorithm. Hence, to describe KS, it is sufficient to describe the

calculation of Kn from KEY for n = 1, 2,..., 16. That calculation is

illustrated in Figure 3. To complete the definition of KS it is therefore

sufficient to describe the two permuted choices, as well as the schedule of

left shifts. One bit in each 8-bit byte of the KEY may be utilized for error

detection in key generation, distribution and storage. Bits 8, 16,..., 64

are for use in assuring that each byte is of odd parity.

Permuted choice 1 is determined by the following table:

PC-1

57 49 41 33 25 17 9

1 58 50 42 34 26 18

10 2 59 51 43 35 27

19 11 3 60 52 44 36

63 55 47 39 31 23 15

7 62 54 46 38 30 22

14 6 61 53 45 37 29

21 13 5 28 20 12 4

The table has been divided into two parts, with the first part determining

how the bits of C() are chosen, and the second part determining how the bits

of D() are chosen. The bits of KEY are numbered 1 through 64. The bits of

C() are respectively bits 57, 49, 41,..., 44 and 36 of KEY, with the bits of

D() being bits 63, 55, 47,..., 12 and 4 of KEY.

With C() and D() defined, we now define how the blocks Cn and Dn are

obtained from the blocks Cn-1 and Dn-1, respectively, for n = 1, 2,..., 16.

That is accomplished by adhering to the following schedule of left shifts of

the individual blocks:

Figure 3. Key schedule calculation.

Iteration Number of

Number Left Shifts

1 1

2 1

3 2

4 2

5 2

6 2

7 2

8 2

9 1

10 2

11 2

12 2

13 2

14 2

15 2

16 1

For example, C3 and D3 are obtained from C2 and D2, respectively, by two

left shifts, and C16 and D16 are obtained from C15 and D15, respectively, by

one left shift. In all cases, by a single left shift is meant a rotation of

the bits one place to the left, so that after one left shift the bits in the

28 positions are the bits that were previously in positions 2, 3,..., 28, 1.

Permuted choice 2 is determined by the following table:

PC-2

14 17 11 24 1 5

3 28 15 6 21 10

23 19 12 4 26 8

16 7 27 20 13 2

41 52 31 37 47 55

30 40 51 45 33 48

44 49 39 56 34 53

46 42 50 36 29 32

Therefore, the first bit of Kn is the 14th bit of CnDn, the second bit the

17th, and so on with the 47th bit the 29th, and the 48th bit the 32nd.

The Foreword, Abstract, and Key Words follow:

FIPS PUB 46-2

FEDERAL INFORMATION

PROCESSING STANDARDS PUBLICATION

1993 December 30

U.S. DEPARTMENT OF COMMERCE/National Institute of Standards and Technology

DATA ENCRYPTION STANDARD (DES)

U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary

Technology Administration, Mary L. Good, Undersecretary for Technlogy

National Institute of Standards and Technology, Arati Prabhakar, Director

Foreword

The Federal Information Processing Standards Publication Series of the

National Bureau of Standards (NBS) is the official publication relating to

standards, guidelines, and documents adopted and promulgated under the

provisions of Public Law 89-306 (Brooks Act) and under Part 6 of Title 15,

Code of Federal Regulations. These legislative and executive mandates have

given the Secretary of Commerce important responsibilities for improving the

utilization and management of computers and automatic data processing in the

Federal Government. To carry out the Secretary's responsibilities, the NBS,

through its Institute for Computer Sciences and Technology, provides

leadership, technical guidance, and coordination of Government efforts in

the development of standards, guide-lines and documents in these areas.

Comments concerning Federal Information Processing Standards Publications

are welcomed and should be addressed to the Director, Institute for Computer

Sciences and Technology, National Bureau of Standards, Gaithersburg, MD

20899.

James H. Burrows, Director

Institute for Computer Sciences and Technology

Abstract

The selective application of technological and related procedual safeguards

is an important responsibility of every Federal organization in providing

adequate security to its electronic data systems. This publication specifies

a cryptographic algorithm which may be used by Federal organizations to

protect sensitive data. Protection of data during transmission or while in

storage may be necessary to maintain the confidentiality and integrity of

the information represented by the data. The algorithm uniquely defines the

mathematical steps required to transform data into a cryptographic cipher

and also to transform the cipher back to the original form. The Data

Encryption Standard is being made available for use by Federal agencies

within the context of a total security program consisting of physical

security procedures, good information management practices, and computer

system/network access controls. This revision supersedes FIPS 46-1 in its

entirety.

Key words: computer security; data encryption standard; encryption; Federal

Information Processing Standard (FIPS); security.

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