26 June 1998
Source: http://www.itl.nist.gov/div897/pubs/fip81.htm

FIPS PUB 81

Federal Information
Processing Standards Publication 81
1980 December 2
Announcing the Standard for

# DES MODES OF OPERATION

- See Important Change Notice at the end of this document.
  (The Foreword, Abstract, and Key Words
  can be found at the end of this document.)
  [See Second Change Notice]

##### Federal Information Processing Standards Publications (FIPS PUBS) are issued by the National Institute of Standards and Technology after approval by the Secretary of Commerce pursuant to Section 111(d) of the Federal Property and Administrative Services Act of 1949, as amended by the Computer Security Act of 1987, Public Law 100-235.

1. Name of Standard. DES Modes of Operation.

2. Category of Standard. ADP Operations, computer security.

3. Explanation. The Federal Data Encryption Standard (DES) (FIPS 46) specifies a crypto-graphic algorithm to be used for the cryptographic protection of sensitive, but unclassified, computer data. This FIPS defines four modes of operation for the DES which may be used in a wide variety of applications. The modes specify how data will be encrypted (cryptographically protected) and decrypted (returned to original form). The modes included in this standard are the Electronic Codebook (ECB) mode, the Cipher Block Chaining (CBC) mode, the Cipher Feedback (CFB) mode, and the Output Feedback (OFB) mode.

The body of this standard provides specifications of the recommended modes of operation but does not specify the necessary and sufficient conditions for their secure implementation in a particular application. This standard specifies the numbering of data bits, how the bits are encrypted and decrypted, and the data paths and the data processing necessary for encrypting and decrypting data or messages.

This standard is based on (and references) the DES and provides the next level of detail necessary for providing compatibility among DES equipment. This standard anticipates the development of a set of application standards which reference it such as communication security standards, data storage standards, password protection standards and key management standards. Cryptographic system designers or security application designers must select one or more of the possible modes of operation for implementing and using the DES in a cryptographic system or security application. The Appendices to this standard provide tutorial information on the modes of operation and examples for validating their correct implementation. The Appendices are guidelines and are not mandatory requirements of this standard.

4. Approving Authority. Secretary of Commerce.

5. Maintenance Agency. U.S. Department of Commerce, National Institute of Standards and Technology, Computer Systems Laboratory.

6. Related Documents.

  FIPS PUB 46, "Data Encryption Standard," January 15, 1977.
  (Proposed) Fedreal Standard 1026, "Telcommunications: Interoperability Requirements".
  (Proposed) Federal Standard 1027, "Telcommunications: Security Requirements for use of the Data Encryption Standard," August 5, 1980, draft.

7. Applicability. This standard shall be used by Federal departments and agencies when procuring equipment or services which implement the Data Encryption Standard and which are intended for use in the cryptographic protection of sensitive, but unclassified, computer data. This standard may be used by anyone desiring to implement and use the Data Encryption Standard. The selection of one of the specified modes of operation will depend on the particular application being considered.

8. Specifications. Federal Information Processing Standard (FIPS 81) DES Modes of Operation (affixed).

9. Qualifications. The DES modes of operation described in this standard are based upon information provided by many sources within the Federal Government and private industry.

These modes are presently being implemented in cryptographic equipment containing DES devices. However, a standard of this nature must, of necessity, remain flexible enough to adapt to advancements and innovations in science and technology. As such, this standard should not be construed as being either exhaustive or static. It will be reviewed every five years in order to incorporate new implementations whose technical or economic merit justify the issuance of a revised standard. FIPS 46 requires implementation of the DES algorithm in electronic devices when used by Federal departments and agencies. The DES, itself, must therefore be in hardware or firmware for Federal applications. However, the modes of operation specified in this standard may be implemented in software, hardware, or firmware.

10. 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 121 through 128. Cryptographic devices implementing this standard and technical data regarding them must comply with these Federal regulations.

11. Patents. Cryptographic equipment implementing this standard may be covered by U.S. and foreign patents.

12. Implementation Schedule. This standard becomes effective on June 2, 1981.

13. Waivers. Heads of agencies may request that the requirements of this standard be waived in instances where it can be clearly demonstrated that there are appreciable performance or cost advantages to be gained and when the overall interests of the Federal Government are best served by granting the requested waiver. Such waiver requests will be reviewed by and are subject to the approval of the Secretary of Commerce. The waiver request must specify anticipated performance and cost advantages in the justification for the waiver.

Forty-five days should be allowed for review and response by the Secretary of Commerce. Waiver requests shall be submitted to the Secretary of Commerce, Washington, DC 20230, and labeled as a Request for a Waiver to this Federal Information Processing Standard. No agency shall take any action to deviate from this standard prior to the receipt of a waiver approval from the Secretary of Commerce. No agency shall implement or procure equipment using a DES mode of operation not conforming to this standard unless a waiver has been approved.

14. Where to Obtain Copies. 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 81 (FIPS PUB 81), and title. When microfiche is desired, this should be specified. Payment may be made by check, money order, or deposit account.

FIPS PUB 81

Federal Information
Processing Standards Publication 81
1980 December 2

Specifications for

# DES MODES OF OPERATION

                                    CONTENTS

    1.  INTRODUCTION
        1.1  Definitions, Abbreviations, and Conventions
    2.  ELECTRONIC CODEB00K (ECB) MODE
    3.  CIPHER BLOCK CHAINING (CBC) MODE
    4.  CIPHER FEEDBACK (CFB) MODE
    5.  OUTPUT FEEDBACK (OFB) MODE

    FIGURES
    (The figures for this document are not available at this time.)
    Figure 1.       Electronic Codebook (ECB) Mode
    Figure 2.       Cipher Block Chaining (CBC) Mode
    Figure 3.       K-Bit Cipher Feedback (CFB) Mode
    Figure 4.       K-Bit Output Feedback (OFB) Mode
    Figure A1:      Des Mappings

    TABLES
    Table B1.  An Example of the Electronic Codebook (ECB) Mode
    Table C1.  An Example of the Cipher Block Chaining (CBC) Mode
    Table D1.  An Example of the 1-Bit Cipher Feedback (CFB) Mode
    Table D2.  An Example of the 8-Bit Cipher Feedback (CFB) Mode
    Table D3.  An Example of the 64-Bit Cipher Feedback (CFB) Mode
    Table D4.  An Example of the 7-Bit Cipher Feedback Alternative Mode
    Table D5.  An Example of the 56-Bit Cipher Feedback Alternative Mode
    Table E1.  An Example of the 1-Bit Output Feedback (OFB) Mode
    Table E2.  An Example of the 8-Bit Output Feedback (OFB) Mode
    Table F1.  An Example of the Cipher Block Chaining (CBC) Mode for
                      Authenticationn
    Table F2.  An Example of the Cipher Feedback (CFB) Mode for
                       Authentication

    APPENDICES
    Appendix A.     General Information
    Appendix B.     Electronic Codebook (ECB) Mode
    Appendix C.     Cipher Block Chaining (CBC) Mode
    Appendix D.     Cipher Feedback (CFB) Mode
    Appendix E.     Output Feedback (OFB) Mode
    Appendix F.     DES Authentication Technique

I. Introduction. Binary data may be cryptographically protected (encrypted) using devices implementing the algorithm specified in the Data Encryption Standard (DES) (FIPS PUB 46) in conjunction with a cryptographic key. The cryptographic key controls the encryption process and the identical key must also be used in the decryption process to obtain the original data. Since the DES is publicly defined, cryptographic security depends on the secrecy of the cryptographic key.

The binary format of a cryptographic key is:

(B1,B2,...,B7,P1,B8,...B14,P2,B15,...,B49,P7,B50,...,B56,P8)

where (B1,B2,...,B56) are the independent bits of a DES key and (PI,P2,...,P8) are reserved for parity bits computed on the preceding seven independent bits and set so that the parity of the octet is odd, i.e., there is an odd number of "1" bits in the octet.

The hexadecimal format of a cryptographic key is:

(H1H2 H3H4 ... H15H16)

where (H1,H2,... ,H16) are hexadecimal characters from the set (O,1,...,9,A,B,C,D,E,F). The embedded blanks in the format are optional and lower case letters may be used in place of the upper case letters. This standard assumes that a cryptographic key has been entered into a DES device prior to encryption or decryption.

1.1 Definitions, Abbreviations, and Conventions. The following definitions, abbreviations and conventions shall be used throughout this standard:

  BIT: A binary digit denoted as a "0" or a

  BINARY VECTOR: A sequence of bits.

  BLOCK: A binary vector consisting of sixty-four bits numbered from the left as 1, 2, . 64 and denoted as (B1,B2,...,364).

  CBC:Ciplier Block Chaining.

  CFB:Cipher Feedback.

  CIPHER TEXT: Encrypted data.

  CRYPTOGRAPHIC KEY: A 64-bit parameter consisting of 56 independent bits and 8 parity bits used in a DES device to control the encrypt and decrypt operations. (Synonyms: KEY, KEY VARIABLE).

  DATA UNIT: A binary vector of K bits that is encrypted as an entity and denoted as (D1,D2,...,DK) where K = 1,2,...,64 and where D1,D2,...,DK represent bits.

  DECRYPTION: The process of changing cipher text into plain text.
  Verb: DECRYPT. (Synonym: DECIPHER).

  DECRYPT STATE: The state of a DES device executing the deciphering operation specified in FIPS PUB 46.

  DES: Data Encryption Standard; specified in FIPS PUB 46.

  DES DEVICE: The electronic component used to implement the DES algorithm, typically an integrated circuit chip or a micro-computer with the DES algorithm specified in a read-only memory program.

  DES INPUT BLOCK: A block that is entered into the DES device for either encryption or decryption. The input block shall be designated (I1,I2,...,I64) where I1,12,...,164 represent bits.

  DES OUTPUT BLOCK: A block that is the Final result of an encryption or decryption opertion of a DES device. The output block shall be designated (01,02,... ,064) where 01,02,... ,064 represent bits.

  ECB: Electronic Codebook.

  ENCRYPTION:The process of changing plain text into cipher text.
  Verb: ENCRYPT. (Synonym: ENCIPHER).

  ENCRYPT STATE: The state of a DES device executing the enciphering operation specified in FIPS PUB 46.

  EXCLUSIVE-OR OPERATION: The bit-by-bit modulo-2 addition of two binary vectors of equal length. This operation is represented by a " " in this standard.

  INITIALIZATION VECTOR (IV): A binary vector used in the initial input block in the CFB and OFB modes and as the randomizing block that is exclusive- ORed with the first data block in the CBC mode.

  LEAST SIGNIFICANT BIT(S): The right-most bit(s) of a binary vector. (Synonym: Low order bit(s)).

  MESSAGE (MSG): A logical data entity consisting of a sequence of data units (e.g., bits, octets, characters, fixed length numbers) that is encrypted as an entity.

  MOST SIGNIFICANT BIT(S): The left-most bit(s) of a binary vector. (Synonym: High order bit(s)).

  OCTET: A group of eight binary digits numbered from left to right: B1,B2,...,B8.

  OFB: Output Feedback.

  PLAIN TEXT: Unencrypted data.

2. Electronic Codebook (ECB) Mode. The Electronic Codebook (ECB) mode is defined as follows (Figure 1). In ECB encryption, a plain text data block (D1,D2,...,D64) is used directly as the DES input block (11,12,... ,164). The input block is processed through a DES device in the encrypt state. The resultant output block (01,02,...,064) is used directly as cipher text (C1,C2,...,C64) or may be used in subsequent ADP applications.

In ECB decryption, a cipher text block (C1,C2,...,C64) is used directly as the DES input block (I1,I2,...,164). The input block is then processed through a DES device in the decrypt state. The resultant output block (O1,O2,...,064) is the plain text (D1,D2,. ..,D64) or may be used in subsequent ADP applications.

The ECB decryption process is the same as the ECB encryption process except that the decrypt state of the DES device is used rather than the encrypt state.

3. Cipher Block Chaining (CBC) Mode. The Cipher Block Chaining (CBC) mode is defined as follows (Figure 2). A message to be encrypted is divided into blocks. In CBC encryption, the first DES input block is formed by exclusive-ORing the first block of a message with a 64-bit initialization vector (IV), i.e., (I1,I2,...,I64) = (IV1 D1,IV2 D2,...,IV64 D64). The input block is processed through a DES device in the encrypt state, and the resulting output block is used as the cipher text, i.e., (C1,C2,... ,C64) = (01,02,.. ,064).

This first cipher text block is then exclusive-ORed with the second plain text data block to produce the second DES input block, i.e., (I1,I2,...,I64) = (C1 D1,C2 D2,...,C64 64). Note that I and D now refer to the second block. The second input block is processed through the DES device in the encrypt state to produce the second cipher text block. This encryption process continues to "chain" successive cipher and plain text blocks together until the last plain text block in the message is encrypted. If the message does not consist of an integral number of data blocks, then the final partial data block should be encrypted in a manner specified for the application. One such method is described in Appendix C of this standard.

In CBC decryption, the first cipher text block of an encrypted message is used as the input block and is processed through a DES device in the decrypt state, i.e., (I1,12,...,164) = (C1,C2,...,C64). The resulting output block, which equals the original input block to the DES during encryption, is exclusive-ORed with the IV (must be same as that used during encryption) to produce the first plain text block, i.e., (D1,D2,...,D64)= (O1 IV1,O2 IV2,...,O64 IV64).

The second cipher text block is then used as the input block and is processed through the DES in the decrypt state and the resulting output block is exclusive-ORed with the first cipher text block to produce the second plain text data block, i.e., (D1,D2,...,D64) = (O1 C1,02 C2,...,064 C64). Note that again the D and O refer to the second block. The CBC decryption process continues in this manner until the last complete cipher text block has been decrypted. Cipher text representing a partial data block must be decrypted in a manner as specified for the application.

4. Cipher Feedback (CFB) Node. The Cipher Feedback (CFB) mode is defined as follows (Figure 3). A message to be encrypted is divided into data units each containing K bits (K = 1,2,... ,64). In both the CFB encrypt and decrypt operations, an initialization vector (IV) of length L is used. The IV is placed in the least significant bits of the DES input block with the unused bits set to "0's," i.e., (I1,12,...,164) - (0,0,...,0,IV1,IV2,IVL).

This input block is processed through the DES device in the encrypt state to produce an output block. During encryption, cipher text is produced by exclusive-ORing a K-bit plain text data unit with the most significant K bits of the output block, i.e., (C1,C2,...,CK) - (D1 01,D2 02,... ,DK 0K). Similarly, during decryption, plain text is produced by exclusive-ORing a K-bit unit of cipher text with the most significant K bits of the output block, i.e., (DI,D2,...,DK) - (CI 1C2 02,. .. ,CK 0K).

In both cases the unused bits of the DES output block are discarded. In both cases the next input block is created by discarding the most signif icant K bits of the previous input block, shifting the remaining bats K positions to the left and then inserting the K bits of cipher text just produced in the encryption operation or just used in the decrypt operation into the least significant bit positions, i.e., (I1,12,...,164) = (I[K+1l,I[K+21,...,164,CI,C2,...,CK). This input block is then processed through the DES device in the encrypt state to produce the next output block. This process continues until the entire plain text message has been encrypted or until the entire cipher text message has been decrypted.

The CFB mode may operate on data units of length l through 64 inclusive. K-bit CFB is defined to be the CFB mode operating on data units of length K for K - 1,2,... ,64. For each operation of the DES device one K-bit unit of plain text produces one K-bit unit of cipher text or one K-bit unit of cipher text produces one K-bit unit of plain text.

An acceptable alternative for 8-bit CFB when enciphering 7-bit entities using an 8-bit feedback path is to insert a "1" bit in bit position one of the 8-bit feedback path, i.e., ("1",C1,C2,... ,C7). This results in a "1" always being placed in bit location 57 of the DES input block. This alternative is called the 7-bit CFB(a) mode of operation.

5. Output Feedback (OFB) Node. The Output Feedback (OFB) mode is defined as follows (Figure 4). A message to be encrypted is divided into data units each containing K bits (K = 1,2,...,64). In both the OFB encrypt and decrypt operations, an initialization vector (IV) of length L is used. The IV is placed in the least significant bits of the DES input block with the unused bits set to "O's," i.e., (I1,12,...,164) = (0,0,...,0,IV1,IV2,...,IVL). This input block is processed through the DES device in the encrypt state to produce an output block. During encryption, cipher text is produced by exclusive-ORing a K-bit plain text data unit with the most significant K bits of the output block, i.e., (C1,C2,...,CK) = (D1 O1,D2 O2,... ,DK OK).

Similarly, during decryption, plain text is produced by exclusive-ORing a K-bit unit of cipher text with the most significant K bits of the output block, i.e., (D1,D2,...,DK) = (C1 01,C2 02,...,CK 0K).

In both cases the unused bits of the DES output block are discarded. In both cases the next input block is created by discarding the most significant K bits of the previous input block, shifting the remaining bits K positions to the left and then inserting the K bits of output just used into the least significant bit positions, i.e., (Il,12,...,164) = I[K+1], I[K+21, ..., I64, 01, 02,...,OK). This input block is then processed through the DES device in the encrypt state to produce the next output block.

This process continues until the entire plain text message has been encrypted or until the entire cipher text message has been decrypted.

The OFB mode may operate on data units of length 1 through 64 inclusive. K-bit OFB is defined to be the 0FB mode operating on data units of length K for K = 1,2,...,64. For each operation of the DES device one K-bit unit of plain text produces one K-bit unit of cipher text or one K-bit unit of cipher text produces one K-bit unit of plain text.

APPENDIX A

GENERAL INFORMATION

The National Bureau of Standards issued Federal Information Processing Standards Publication 46 (FIPS PUB 46) in 1977. That standard specifies a cryptographic algorithm, commonly called the Data Encryption Standard (DES) algorithm, to be used within the Federal Government for the cryptographic protection of sensitive, but unclassified, computer data.

The DES algorithm was developed by the International Business Machines Corporation (IBM) and submitted to the National Bureau of Standards during an NBS public solicitation for cryptographic algorithms to be used in a Federal Information Processing Standard. Several methods for incorporating this algorithm into a cryptographic system are possible.

These methods, external to the DES algorithm, have come to be called the "modes of operation." Four modes, called the Electronic Codebook (ECB) mode, the Cipher Block Chaining (CBC) mode, the Cipher Feedback (CFB) mode, and the Output Feedback (OFB) mode, are specified in this standard.

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 pseudo-random outputs which are combined with the plain text to produce cipher text, thereby chaining together the resulting cipher text; OFB is identical to CFB except that the previous output of the DES is used as input in OFB while the previous cipher text is used as input in CFB. OFB does not chain the cipher text. The proposed FIPS specifies these four modes because they are capable of providing acceptable levels of protection for all anticipated unclassified Federal ADP encryption applications.

Unencrypted data is called plain text. Encryption (also called enciphering) is the process of transforming plain text into cipher text. Decryption (also called deciphering) is the inverse transformation. The encryption and decryption processes are performed according to a set of rules, called an algorithm, that is typically based on a parameter called a key. The key is usually the only parameter that must be provided to or by the users of a cryptographic system and must be kept secret. The period of time over which a particular key is used to encrypt or decrypt data is called its cryptoperiod.

Mathematically, the DES maps the set of all possible 64-bit vectors onto itself. See Figure A1. There are 2T64 (2 raised to the 64th power) elements in this set, including all binary numbers from O up to, but not including, 2f64.

The DES cryptographic key allows a user to select any one of 2t56 possible invertible mappings, i.e., transformations that are one-to-one. Selecting a key selects one of the mappings. When using the DES in ECB mode and any particular key, each input is mapped onto a unique output in encryption and this output is mapped back onto the input in decryption. The DES is an iterative, block, product cipher system (i.e., encryption algorithm). A product cipher system mixes transposition and substitution operations in an alternating manner.

Because the DES algorithm maps a 64-bit input block onto a 64-bit output block the DES is called a block cipher system. Iterative refers to the use of the output of an operation as the input for another iteration of the same procedure. The DES internally uses sixteen iterations of a pair of transposition and substitution operations to encrypt or decrypt an input block. A complete specification of the DES algorithm is found in FIPS PUB 46.

Two categories of methods for incorporating the DES in a cryptographic system are block methods and stream methods. In a block method, the DES input block is (or is a simple function of) the plain text to be encrypted and the DES output block is the cipher text.

A stream method is based on generating a pseudo-random binary stream of bits, and then using the exclusive-OR binary operation to combine this pseudo-random sequence with the plain text to produce the cipher text. Since the exclusive-OR operator is its own binary inverse, the same pseudo-random binary stream is used for both the encryption of plain text, P, and the decryption of cipher text, C. If 0 is the pseudo-random binary stream, then C = P 0 and inversely, P = C.

APPENDIX B

ELECTRONIC CODEBOOK (ECB) MODE

The Electronic Codebook (ECB) mode is a basic, block, cryptographic method which transforms 64 bits of input to 64 bits of output u specified in FIPS PUB 46.

The analogy to a codebook arises because the same plain text block always produces the same cipher text block for a given cryptographic key. Thus a list (or codebook) of plain text blocks and corresponding cipher text blocks theoretically could be constructed for any given key. In electronic implementation the codebook entries are calculated each time for the plain text to be encrypted and, inversely, for the cipher text to be decrypted.

Since each bit of an ECB output block is a complex function of all 64 bits of the input block and all 56 independent (non-parity) bits of the cryptographic key, a single bit error in either a cipher text block or the non-parity key bits used for decryption will cause the decrypted plain text block to have an average error rate of fifty percent. However, an error in one ECB cipher text block will not affect the decryption of other blocks, i.e., there is no error extension between ECB blocks.

If block boundaries are lost between encryption and decryption (e.~., a bit slip), then synchronization between the encryption and decryption operations will be lost until correct block boundaries are reestablished. The results of all decryption operations will be incorrect until this occurs.

Since the ECB mode is a 64-bit block cipher, an ECB device must encrypt data in integral multiples of sixty-four bits. If a user has less than sixty- four bits to encrypt, then the least significant bits of the unused portion of the input data block must be padded, e.g., filled with random or pseudo- random bits, prior to ECB encryption. The corresponding decrypting device must then discard these padding bits after decryption of the cipher text block.

The same input block always produces the same output block under a fixed keg in ECB mode. If this is undesirable in a particular application, the CBC, CFB or OFB modes should be used. An example of the ECB mode is given in Table B1.

TABLE B1

AN EXAMPLE OF THE ELECTRONIC CODEBOOK (ECB) MODE

The ECB mode in the encrypt state has been selected.
Cryptographic Key = 0123456789abcdef

The plain text is the ASCII code for "Now is the time for all ." These seven-bit characters are written in hexadecimal notation
(0,b7,b6,...,b1).

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 4e6f772069732074 | 4e6f772069732074 | 3fa40e8a984d4315 | 3fa40e8a984d4815

2. 68652074696d652o | 68652074696d652o | 6a271787ab8883f9 | 6a271787ab8883f9

3. 666f7220616c6c20 | 666f7220616c6c20 | 893d51ec4b563b53 | 893d51ec4b563b53

The ECB mode in the decrypt state has been selected.

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 3fa40e8a984d4815 | 3fa40e8a984d4815 | 4e6f772o69732o74 | 4e6f772069732074

2. 6a271787ab8883f9 | 6a271787ab8883f9 | 68652074696d6520 | 68652074696d6520

3. 893d51ec4b563b53 | 893d51ec4b563b53 | 666f7220616c6c20 | 666f7220616c6c20

APPENDIX C

CIPHER BLOCK CHAINING (CBC) MODE

CBC is a block cipher system in which the first plain text data block is exclusive-ORed with a block of pseudo-random data prior to being processed through the DES. The resulting cipher text block is then exclusive-ORed with the next plain text data block to form the next input block to the DES, thus chaining together blocks of cipher text. The chaining of cipher text blocks provides an error extension characteristic which is valuable in protecting against fraudulent data alteration. A CBC authentication technique is described in Appendix F.

The CBC mode produces the same cipher text whenever the same plain text is encrypted using the same key and IV. Users who are concerned about this characteristic should incorporate a unique identifier (e.g., a one-up counter) at the beginning of each CBC message within a cryptographic period in order to insure unique cipher text. If the key and the IV are the same and no identifier precedes each message, messages that have the same beginning will have the same cipher text when encrypted in the CBC mode until the blocks that differ in the two messages are encrypted.

Since the CBC mode is a block method of encryption, it must operate on 64-bit data blocks. Partial data blocks (blocks of less than 64 bits) require special handling. One method of encrypting a final partial data block of a message is described below. Others may be defined for special applications.

The following method may be used for applications where the length of the cipher text can be greater than the length of the plain text. In this case the final partial data block of a message is padded in the least significant bits positions with "0"s, "1"s or pseudo- random bits. The decryptor will have to know when and to what extent padding has occurred This can be accomplished explicitly, e.g., using a padding indicator, or implicitly, e.g., using constant length transactions.

The padding indicator will depend on the data being encrypted. If the data is pure binary, then the partial data block should be left justified in the input block and the unused bits of the block set to the complement of the last data bit, i.e., if the last data bit of the message is "0" then "1"s are used as padding bits and if the last data bit is "1" then "0"s are used. The input block is then encrypted.

The resulting output block is the cipher text. The cipher text message must be marked as being padded so that the decryptor can reverse the padding process, remove the padding bits and produce the original plain text. The decryptor scans the decrypted padded block and discards the least significant bits that are all identical. If the data consists of bytes (e.g., 8-bit ASCII characters) then the padding indicator should be a character denoting the number of padding bytes, including itself, and should be placed in the least significant byte of the input block before encrypting. For example if there are five ASCII data characters in the final partial block of a message to be encrypted, then an ASCII "3" is put in the least significant byte of the input block (any pad characters may be used in the other two pad positions) before encryption. Again the cipher text message must be marked as being padded.

In the CBC mode, one or more bit errors within a single cipher text block will affect the decryption of two blocks (the block in which the error occurs and the succeeding block). If the errors occur in the n-th cipher text block, then each bit of the n-th plain text block will have an average error rate of fifty percent. The (n+1)st plain text block will have only those bits in error which correspond directly to the cipher text bits in error.

Block synchronization between encrypt and decrypt operations is required for the CBC mode. If bits are added or are lost in a cipher text block so that block boundaries are lost between the encryption and decryptinn operations, then synchronization is lost. However, cryptographic synchronization will automatically be reestablished 64 bits after block boundaries have been established. This property is known as self-synchronization.

An example of the CBC mode is given in Table C1.

TABLE C1

AN EXAMPLE OF THE CIPHER BLOCK CHAINING (CBC) MODE

The CBC mode in the encrypt state has been selected.
Cryptographic Key = 0123456789abcdef

Initialization Vector = 1234567890abcdef

The plain text is the ASCII code for "Now is the time for all ." These seven- bit characters are written in hexadecimal notation (0,b7,b6,...b1).

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 4e6f772069732074 | 5c5b2158f9d8ed9b | e5c7cdde872bf27c | e5c7cdde872bf27c

2. 68652074696d6520 | 8da2edaaee46975c | 43e934008c389c0f | 43e934008c389c0f

3. 666f7220616c6c20 | 25864620ed54f02f | 683788499a7c05f6 | 683788499a7c05f6

The CBC mode in the decrypt state has been selected.

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. e5c7cdde872bf27c | e5c7cdde872bf27c | 5c5b2158f9d8ed9b | 4e6f772069732074

2. 43e934008c389c0f | 43e934008c389c0f | 8da2edaaee46975c | 68652074696d6520

3. 683788499a7c05f6 | 683788499a7c05f6 | 25864620ed54f02f | 666f7220616c6c20

APPENDIX D

CIPHER FEEDBACK (CFB) MODE

The CFB mode is a stream method of encryption in which the DES is used to generate pseudorandom bits which are exclusive-ORed with binary plain text to form cipher text. The cipher text is fed back to form the next DES input block. Identical messages that are encrypted using the CFB mode and different IVs will have different cipher texts. IVs that are shorter than 64 bits should be put in the least significant bits of the first DES input block and the unused, most significant, bits initialized to "0's."

In the CFB mode, errors in any K-bit unit of cipher text will affect the decryption of the garbled cipher text and also the decryption of succeeding cipher text until the bits in error have been shifted out of the CFB input block. The first af fected K-bit unit of plain text will be garbled in exactly those places where the cipher text is in error. Succeeding decrypted plain text will have an average error rate of fifty percent until all errors have been shifted out of the DES input block. Assuming no additional errors are encountered during this time, the correct plain text will then be obtained.

If K-bit boundaries are lost during decryption, then cryptographic synchronization will be lost until cryptographic initialization is performed or until 64 bits after the K-bit boundaries have been reestablished.

The encryption and decryption processes in the CFB mode both use the encrypt state of the DES. Examples of 1, 8, and 64-bit CFB mode are given in Tables D1, D2, and D3, respectively.

The 7-bit CFB alternative mode is defined in the standard in order to encipher and decipher 7-bit codes and still use an 8-bit feedback path. Most commercial implementations of the DES are designed to efficiently handle 8-bit bytes of data and key. Most computer and communication systems of recent architecture are also designed to efficiently handle full 8-bit bytes. However, some systems use the most significant bit as a parity bit. These systems often generate the parity bit during transmission and check its validity during reception. In such systems the parity bit on cipher text would be automatically modified during transmission. In this case, the encryption and decryption processes must operate independently of the parity bits and the 7-bit CFB (a) mode should be used. If the encryptor and the decryptor both set the most significant bit of the 8-bit cipher byte to be a "1" bit in the feedback, the systems are compatible. Holding no more than eight bits of the DES input constant provides an acceptable level of security for government applications.

An extension of this technique is useful in applications requiring very efficient use of the DES device. If several 7-bit data units are to be enciphered simultaneously, then a "l". bit may be put in the most significant bit position of each 8-bit byte of the feedback path. This extension of the 7-bit CFB alternative mode should be called the K-bit CFB (a) for K= 14, 21, 28, 35, 42, 49, and 56 for implementations which encipher, respectively, 2, 3, 4, 5, 6, 7, and 7-bit data units simultaneously. These alternatives provide an acceptable level of security for government applications.

Examples of 7 and 56-bit CFB (a) mode are given in tables D4 and D5, respectively.

TABLE D1

AN EXAMPLE OF THE 1-BIT CIPHER FEEDBACK (CFB) MODE

The 1-bit CFB mode in the encrypt state has been selected.

Cryptographic Key = 0123456789abcdef

Initialization Vector = 1234567890abcdef

The plain text is the binary vector (010011100110111101110111). The DES input and output blocks are written in hexadecimal notation. The represents bit-by-bit, modulo 2 addition.

    TIME   DES INPUT BLOCK  DES OUTPUT BLOCK         P      0    = C

    1      1234567890abcdef bd661569ae874e25         0     1     = 1
    2      2468acf121579bdf 48b3169c1fac7a10         1     0     = 1
    3      48d159e242af37bf 0a0143394c9959fe         0     0     = 0
    4      91a2b3c4855e6f7e 6d52f55fd8bo2711         0     0     = 0
    5      234567890abcdefc 3a38debb3a2fa892         1     0     = 1
    6      468acf121579bdf9 719b70bd3dce7acc         1     0     = 1
    7      8d159e242af37bf3 81809c230adc0d23         1     1     = 0
    8      1a2b3c4855e6f7e6 83d14a6da6926604         0     1     = 1
    9      34567890abcdefcd 311e9dc8d6d52d8a         0     0     = 0
    10     68acf121579bdf9a db47c7feb6fc4272         1     1     = 0
    11     d159e242af37bf34 b73850afa3b8ed89         1     1     = 0
    12     a2b3c4855e6f7e68 f5fb19ddoos9o8oo         0     1     = 1
    13     4567890abcdefcd1 0f4351a9bbffe5a5         1     0     = 1
    14     8acf121579bdf9a3 769593c58e20d41b         1     0     = 1
    15     159e242af37bf347 0e949d3f3a293d64         1     0     = 1
    16     2b3c4855e6f7e68f 921eb7ffeacd0db9         1     1     = 0
    17     567890abcdefcd1e d2ad109c8895fb95         0     1     = 1
    18     acf121579bdf9a3d 3c36317828a9bd04         1     0     = 1
    19     59e242af37bf347b e7248586e7e4ecac         1     1     = 0
    20     b3c4855e6f7e68f6 f9a58e16a7597c5e         1     1     = 0
    21     67890abcdefcd1ec e939fdf63d177946         0     1     = 1
    22     cf121579bdf9a3d9 f325eac046bad58d         1     1     = 0
    23     9e242af37bf347b2 8385a6d975ffdbba         1     1     = 0
    24     3c4855e6f7e68f64 70a54baceae7ba6b         1     0     = 1

TABLE D2

AN EXAMPLE OF THE 8-BIT CIPHER FEEDBACK (CFB) MODE

The 8-bit CFB mode in the encrypt state has been selected.

Cryptographic Key - 0123456789abcdef

Initialization Vector = 1234567890abcdef

The plain text is the ASCII code for "Now is the." These seven-bit characters are written in hexadecimal notation (0,b7,b6,...b1). The represents bit-by-bit, modulo 2 addition.

    TIME   DES INPUT BLOCK  DES OUTPUT BLOCK              P      0    = C

    1     1234567890abcdef bd661569ae874e25               4e      bd  = f3
    2     34567890abcdeff3 7039546f9a0f6330               6f      70  = 1f
    3     567890abcdeff31f ad1b78b0bb371be7               77      ad  = da
    4     7890abcdeff31fda 2735b01d5ca31f7                20      27  = 07
    5     90abcdeff31fda07 68863426e397685d               69      68  = 01
    6     abcdeff31fda0701 6798240e8c6b685f               73      67  = 14
    7     cdeff31fda070114 421feefb3f8ca64f               20      42  = 62
    8     eff31fda07011462 9a169a9b50666575               74      9a  = ee
    9     f31fda07011462ee 703b1799be9a5748               68      70  = 18
    10    1fda07011462ee18 1a4aee195be70077               65      1a  = 7f

The 8-bit GFB mode in the decrypt state has been selected.

    TIME   DES INPUT BLOCK  DES OUTPUT BLOCK              C      0    = P

    1     1234567890abcdef bd661569ae874e25               f3      bd  = 4e
    2     34567890abcdeff3 7039546f9a0f6330               1f      70  = 6f
    3     567890abcdeff31f ad1b78b0bb371be7               da      ad  = 77
    4     7890abcdeff31fda 27350b01d5ca31f7               07      27  = 20
    5     90abcdeff31fda07 68863426e397685d               01      68  = 69
    6     abcdeff31fda0701 6798240e8c6b685f               14      67  = 73
    7     cdeff31fda070114 421feefb3f8ca64f               62      42  = 20
    8     eff31fda07011462 9a169a9b50666575               ee      9a  = 74
    9     f31fdaf17011462ee 703b1799be9a5748              18      70  = 68
    10    1fda07011462ee18 1a4aee195be70077               7f      1a  = 65

TABLE D3

AN EXAMPLE OF ThE 64-BIT CIPHER FEEDBACK (CFB) MODE

The 64-bit CFB mode in the encrypt state has been selected.

Cryptographic Key - 0123456789abcdef

Initialization Vector - 1234567890abcdef

The plain text is the ASCII code for "Now is the time for all ." These seven- bit characters are written in hexadecimal notation (0,b7,b6,...,b1).

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 4e6f772069732o74 | 1234567890abcdef | bd661569ae874e25 | f3096249c7f46e51

2. 68652o74696d6s20 | f3096249c7f46e51 | cefba3ef73ff92a4 | a69e839b1a92f784

3. 666f7220616c6c20 | a69e839b1a92f784 | 65290313e8e2ca02 | 03467133898ea622

The 64-bit CFB mode in the decrypt state hu been selected.

      TIME PLAIN         CIPHER TEXT  DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. f3096249c7f46e51 | 234567890abcdef | bd661569ae874e25 | 4e6f772069732074

2. a69e839b1a92f784 | f3096249e7f46e51 | cefba3ef73ff92a4 | 68652o74696d6520

3. 03467133898ea622 | a69e839b1a92f784 | 65290313e8e2ca02 | 666f7220616c6c20

TABLE D4

AN EXAMPLE OF THE 7-BIT CIPHER FEEDBACK ALTERNATIVE MODE

The 7-bit CFB(a) mode in the encrypt state has been selected.
Cryptographic
Key - 0123456789abcdef
Initiaiization Vector - 1234567890abcdef
The plain text is the ASCII code for "Now is the." These seven-bit characters are written in hexadecimal notation (0, b7, b6,...b1). The represents bit-by-bit, modulo 2 addition.

    TIME   DES INPUT BLOCK  DES OUTPUT BLOCK             P  + 0   = C

    1      1234567890abcdef bd661569ae874e25             4e   bd  = 73
    2      34567890abcdeff3 7039546f9a0f6330             6f   70  = 1f
    3      567890abcdeff39f e86e0d3772221b21             77   e8  = 1f
    4      7890abcdeff39f9f cbb91f82946f3a68             20   cb  = 6b
    5      90abcdeff39f9feb 9faf68acc9d1c4f9             69   9f  = 76
    6      abcdeff39f9febf6 bf7e7edc468df70f             73   bf  = 4c
    7      cdeff39f9febf6cc 6a555c03e8c20cea             20   6a  = 4a
    8      eff39f9febf6ccca d8bb411744869e4a             74   d8  = 2c
    9      f39f9febf6cccaac e656f81f3f1a8c28             68   e6  = 0e
    10     9f9febf6cccaac8e cd1883fe15bf7c26             65   cd  = 28

The 7-bit CFB(a) mode in the decrypt state has been selected.

    TIME   DES INPUT BLOCK  DES OUTPUT BLOCK             C       0 = P

    1      1234567890abcdef bd661569ae874e25             73      bd= 4e
    2      34567890abcdeff3 7039546f9a0f6330             1f      70= 6f
    3      56789Oabcdeff39f e86eOd3772221b21             1f      8 = 77
    4      7890abcdeff39f9f cbb91f82946f3a68             6b      cb= 20
    5      90abcdeff39f9feb 9faf68acc9d1c4f9             76      9f= 69
    6      abcdeff39f9febf6 bf7e7edc468df70f             4c      bf= 73
    7      cdeff39f9febf6cc 6a555cO3e8c20cea             4a      6a= 20
    8      eff39f9febf6ccca d8bb411744869e4a             2c      d8= 74
    9      f39f9febf6cccaac e656f8f3f31a8c28             Oe      e6= 68
    10     9f9febf6cccaac8e cd1883fe15bf7c26             28      cd= 65

TABLE D5

AN EXAMPLE OF THE 56-BIT CIPHER FEEDBACK ALTERNATIVE MODE

The 56-bit CFB(a) mode in the encrypt state has been selected.

Cryptographic Key - 0123456789abcdef

Initialization Vector - 1234567890abcdef

The plain text is the ASCII code for "Now is the time for all " These seven- bit characters are written in hexadecimal notation (0, b7, b6,. .b1).

      TIME PLAIN     CIPHER TEXT      DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 4e6f772069732074 | 1234567890abcdef | bd661569ae874e25 | 7309624947746e51

2. 68652074696d6520 | f389e2c9c7f4eed1 | 8988dd3d6b71f76b | 616d7d49021c24b

3. 666f7220616c6c20 | e1edfdc9829c92cb | 314a61d117be7e4d | 572513717652126d

The 56-bit CFB(a) mode in the decrypt state has been selected.

      TIME PLAIN     CIPHER TEXT      DES INPUT     DES UTPUT
         TEXT                           BLOCK         BLOCK

1. 7309624947746e51 | 1234567890abcdef | bd661569ae874e25 | 4e6f772069732074

2. 616d7d49021c124b | f389e2c9c7f4eed1| 8988dd3d6b71f76b| 68652074696d6520

3. 572513717652126d | e1edfdc9829c92cb | 314a61d117be7e4d | 666f7220616c6c20

APPENDIX E

OUTPUT FEEDBACK (OFB) MODE

The Output Feedback (OFB) mode is an additive stream cipher in which errors in the cipher text are not extended to cause additional errors in the decrypted plain text. One bit in error in the cipher text causes only one bit to be in error in the decrypted plain text. Therefore, this mode cannot be used for data authentication but is useful in applications where a few errors in the decrypted plain text are acceptable.

In the OFB mode, the same K bits of the DES output block that are used to encrypt a K-bit unit of plain text are fed back for the next input block. This feedback is completely independent of all plain text and all cipher text. As a result, there is no error extension in OFB mode.

If cryptographic synchronization is lost in the OFB mode, then cryptographic initialization must be performed. The OFB mode is not a self-synchronizing cryptographic mode.

Examples of 1-bit OFB and 8-bit OFB are given in Tables El and E2, respectively.

TABLE E1

AN EXAMPLE OF THE 1-BIT OUTPUT FEEDBACK (OFB) MODE

The 1-bit OFB mode in the encrypt state has been selected.

Cryptographic Key - 0123456789abcdef

Initialization Vector - 1234567890abcdef

The plain text is the binary vector (010011100110111101110111). The represents bit-by- bit, modulo 2 addition.

    TIME   DES INPUT BLOCK   DES OUTPUT BLOCK    P     0     = C

    1     1234567890abcdef   bd661569ae874e25    0     1     = 1
    2     2468acf121579bdf   48b3169c1fac7a10    1     0     = 1
    3     48d159e242af37be   8879ea93c63d77a5    0     1     = 1
    4     91a2b3c4855e6f7d   0d36e16101e86d61    0     0     = 0
    5     234567890abcdefa   e9eab8cfc00f4ac3    1     1     = 0
    6     468acf121579bdf5   9d41640f97df7904    1     1     = 0
    7     8d159e242af37beb   32f72fd1899eda45    1     0     = 1
    8     1a2b3c4855e6f7d6   ca2a095d20f4e769    0     1     = 1
    9     34567890abcdefad   de869588355e1041    0     1     = 1
    10    68acf121579bdf5b   11245e6a8720ddce    1     0     = 1
    11    d159e242af37beb6   836b0be324094a97    1     1     = 0
    12    a2b3c4855e6f7d6d   c07714703b296a5a    0     1     = 1
    13    4567890abcdefadb   bf6380ecc496d599    1     1     = 0
    14    8acf121579bdf5b7   96ed6856969aef13    1     1     = 0
    15    159e242af37beb6f   3823feaa3d170085    1     0     = 1
    16    2b3c4855e6f7d6de   2d57dc0c899d6700    1     0     = 1
    17    567890abcdefadbc   2fe1c261c0e1a302    0     0     = 0
    18    acf121579bdf5b78   778ad641faa047d0    1     0     = 1
    19    59e242af37beb6f0   f66ae4359eec3755    1     1     = 0
    20    b3c4855e6f7d6de1   cd0bda27e32a13da    1     1     = 0
    21    67890abcdefadbc3   9f71f74488551801    0     1     = 1
    22    cf121579bdf5b787   a62e89aa6b85be74    1     1     = 0
    23    9e242af37beb6f0f   7b0b2e1de987b804    1     0     = 1
    24    3c4855e6f7d6de1e   7f41b5ef07c3ea29    1     0     = 1

TABLE E2

AN EXAMPLE OF THE 8-BIT OUTPUT FEEDBACK (OFB) MODE

The 8-bit OFB mode in the encrypt state has been selected.

Cryptographic Key - 0123456789abcdef

Initialization Vector - 1234567890abcdef

The plain text is the ASCII code for "Now is the." These seven-bit characters are written in hexadecimal notation (0,b7,b6,.. .,b1). The represents bit-by-bit, modulo 2 addition.

    TIME   DES INPUT BLOCK       DES OUTPUT BLOCK  P         0 = C

    1     1234567890abcdef       bd661569ae874e25  4e        bd =f3
    2     34567890abcdefbd       25e73b5d4cbd2359  6f        25 =4a
    3     567890abcdefbd25       5f97oo7o5s3623do  77        5f =28
    4     7890abcdefbd255f       704ad48bf9eec8fa  20        70 =50
    5     90abcdefbd255f7o       a0b1a091bb7875s3  69        a0 =c9
    6     abcdefbd255f7oao       b58127681139ee7f  73        b5 =c6
    7     cdefbd255f70a0b5       694d556ef5806a65  20        69 =49
    8     efbd255f70a0b569       f1885324299132a2  74        f1 =85
    9     bd255f70a0b569f1       be639ff6d7b74bo4  68        be =d6
    10    255f70a0b569f1be       e17b6ae22b4bad65  65        e1= 84

The 8-bit OFB mode in the decrypt state has been selected.

    TIME   DES INPUT BLOCK       DES OUTPUT BLOCK  C         0 = P

    1     1234567890abcdef       bd661569ae874e25  f3        bd = 4e
    2     34567890abcdefbd       25e73b5d4cbd2359  4a        25 = 6f
    3     567890abcdefbd25       5f97oo7oss3623do  28        5f = 77
    4     7890abcdefbd255f       704ad48bf9eec8fa  50        70 = 20
    5     90abcdefbd255f7o       a0b1a091bb787553  c9        a0 = 69
    6     abcdefbd255f70ao       b58127681139ee7f  c6        b5 = 73
    7     cdefbd255f7oa0b5       694d556ef5806a65  49        69 = 20
    8     efbd255f70aob569       f1885324299132a2  85        f1 = 74
    9     bd255f70a0b569f1       be639ff6d7b74b04  d6        be = 68
    10    255f70a0b569f1be       e17b6ae22b4bad65  84        e1 = 65

APPENDIX F

DES AUTHENTICATION TECHNIQUE

The DES can be used for message (data) authentication. A Message Authentication Code (MAC) is generated (computed) as a cryptographic function of the message (data). The MAC is then stored or transmitted with the data. Only those knowing the secret key can recompute the DEAD for the received message and verify that the message has not been modified by comparing the computed DEAD with the stored or transmitted DEAD. An unauthorized recipient of the data who does not possess the key cannot modify the data and generate a new DEAD to correspond with the modified data. This technique is useful in applications which require maintaining data integrity but which do not require protecting the data from disclosure. For example, computer programs may be stored in plain text form with a computed DEAD appended to the program file. The program may be read and executed without decryption. However, when the integrity of the program is questioned, a MAC can be computed on the program file and compared with the one stored in the file. If the two MAC's are identical and the cryptographic key used to generate the MAC has been protected, then the program file has not been modified.

A MAC may be generated using either the CBC or the CFB mode. In CBC authentication, a message is encrypted in the normal CBC manner but the cipher text is discarded. Messages which terminate in partial data blocks must be padded on the right (LSB) with zeros. In CBC authentication, the most significant M bits of the final output block are used as the MAC, where M is the number of bits in the MAC.

In CFB authentication, a message is encrypted in the normal CFB manner except that the cipher text is discarded. After encrypting the final K bits of data and feeding the resulting cipher text back into the DES input block, the DES device is operated one more time and the most significant M bits of the resulting DES output block are used as the MAC.

In both CBC and CFB authentication, a MAC should be used that is as long as practical. Since a MAC is an error detection code (which is computed using cryptographic techniques), a long MAC is desirable. Bit manipulation within a message using a MAC of length M will be detectable with a probability of 1- (1/2N). Concluding that a message has not been modified is based upon this probability. The proposed Federal Standard 1026 requires M to be at least 24 for Federal telecommunication applications. Financial transaction application standards are recommending M to be 32. Application designers should select M to optimize security and efficiency requirements.

In ADP communications security applications a message numbering and verifying system should be used to protect against insertion of false messages, deletion of valid messages, and replay of a previously valid message. The combined use of a unique Message Identifier (MID) and a MAC achieves these security objectives in addition to protecting the message against message modification. If the data source MAC and the data destination MAC are in agreement and if the MID agrees with the value expected by the receiver, then these four security objectives have been accomplished. The MID should be unique and deterministic for each message transmitted between a sender and receiver. The uniqueness may be achieved through the use of a simple binary counter.

Examples of the MAC calculation using CBC and 8-bit CFB are given in Tables F1 and F2, respectively.

TABLE F1

AN EXAMPLE OF THE CIPHER BLOCK CHAINING (CBC) MODE FOR AUTHENTICATION

The CBC mode in the encrypt state has been selected.

Cryptographic Key 0123456789abcdef

Initialization Vector - 1234S67890abcdef

The plain text is the ASCII code for "7654321 Now is the time for ." These seven-bit characters are written in hexadecimal notation (0,b7,b6,..b1).

    TIME  PLAIN TEXT         DES INPUT          DES OUTPUT
    3736353433323120    25O2634ca399fccf   b9916b8ee4c3da64
    4e6f772O69732O74    f7felcae8dbOfalo   b4f44e3cbefb9948
    68652O74696d6520    dc916e48d796fc68   4S2l388fa59ae67d
    666f7220OOOOO0OO    234e4aafa59ae67d   058d2e77e86O62733

    32-bit MAC is selected.

    TEXT                     MAC
    3736353433323l204e6f772068732074686S2O74696d652O666f722O58d2e77e

TABLE F2

AN EXAMPLE OF THE CIPHER FEEDBACK (CFB) MODE FOR AUTHENTICATION

The 8-bit CFB mode in the encrypt state has been selected.

Cryptographic Key -123456789abcdef

Initialization Vector - 1234S67890abcdef

    TIME   DES INPUT BLOCK       DES OUTPUT BLOCK  P     0 = C

        1    23456789Oabcdef   bd661569ae874e25   37    bd = 8a
        2    3456789Oabcdef8a  b156f27e4O84b3e1   36    b1= 87
        3    5789Oabcdef8a87   346594a9f532e7ef   35    34 = 01
        4    789Oabcdef8a87o1  ed228c3dObo87e56   34    ed = d9
        5    9Oabcdef8a87O1d9  12fffb7d10c59f6e   33 +  12 = 21
        6    abcdef8a87o1d921  O2de319634551992   32 +  02 = 30
        7    cdef8a8701d92130  be3ee94f5b0d9337   31 +  be = 8f
        8    ef8a87o1d9213o8f  15a8855f3e99o8b3   20 +  15 = 35
        9    8a8701d9213O8f35  3af549c9c870562c   4e +  3a = 74
        10   87o1d9213o8f3574  d2b323ada61cdeoo   6f +  d2 = bd
        11   O1d9213o8f3574bd  6977832969dbbeba   77 +  69 = 1e
        12   d9213O8f3574bd1e  5473999aba6c9813   20 +  54 = 74
        13   21308f3574bd1e74  9db2dcb11bcefd56   69 + 9d = f4
        14   308f3574bd1e74f4  41dd4dfde3648513   73 +  41 = 32
        15   8f3574bd1e74f432  349de10f1d65672o   20 +  34 = 14
        16   3574bd1e74f43214  0384e72851495e94   74 +  03 = 77
        17   74bd1e74f4321477  64aeb25d7a54bb91   68 +  64 = 0c
        18   bd1e74f4321477oc  IfO7839f59391e53   65 +  1f = 7a
        19   Ie74f4321477oc7a  I4d3c21640e42157   20 +  14 = 34
        20   74f4321477Oc7a34  fb7a853aadb39183   74 +  fb = 8f
        21   f4321477Oc7a348f  edee83bOao7afcd4   69 +  ed = 84
        22   3214770c7a348f84  5065694b1a1b765c   6d +  50 = 3d
        23   I477oc7a348f843d  68ec7ad3602e91c2   65 +  68 = Od
        24   77Oc7a348f843d0d  28f5c32ae7b4495f   20 +  28 = 08
        25   Oc7a348f843dodo8  523d79cb8d3eb462   66 +  52 = 34
        26   7a348f843d0d 834  dd5816fac447o533   6f +  dd = b2
        27   348f843d0d0834b2  b61ec6Of26c3b29a   72 +  b6 = c4
        28   8f843dOdO834b2c4  daca26833o988a7d   20 +  da = fa
        29   843d0dO834b2c4fa  cd6474O3bc9oc4c4

32-bit MAC selected.

    TEXT     MAC
    37363534333231204e6f77206873207468652074696d6520666f7220cd647403

The Foreword, Abstract, and Key Words follow:

FIPS PUB 81
FEDERAL INFORMATION
PROCESSING STANDARDS PUBLICATION
1980 December 2
U.S. DEPARTMENT OF COMMERCE/National Institute of Standards and Technology

##
DES MODES OF OPERATION

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick , Secretary
National Institute of Standards and Technology, Ernest Ambler, Director

Foreword

The Federal Information Processing Standards Publication Series of the National Institute of Standards and Technology (NIST) is the official publication relating to standards and guidelines adopted and promulgated under the provisions of Section 111(d) of the Federal Property and Administrative Services Act of 1949 as amended by the Computer Security Act of 1987, Public Law 100-235. These mandates have given the Secretary of Commerce and NIST important responsibilities for improving the utilization and management of computers and related telecommunications systems in the Federal Government. The NIST, through its Computer Systems Laboratory, provides leadership, technical guidance, and coordination of Government efforts in the development of standards and guidelines in these areas.
Comments concerning Federal Information Processing Standards Publications are welcomed and should be addressed to the Director, Computer Systems Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899.
James H. Burrows, Director
Computer Systems Laboratory

Abstract

The Federal Data Encryption Standard (DES) (FIPS 46) specifies a cryptographic algorithm to be used for the Cryptographic protection of sensitive, but unclassified, computer data. This FIPS defines four modes of operation for the DES which may be used in a wide variety of applications. The modes specify how data will be encrypted (cryptographically protected) and decrypted (returned to original form). The modes included in this standard are the Electronic Codebook (ECB) mode, the Cipher Block Chaining (CBC) mode, the Cipher Feedback (CF3) mode, and the Output Feedback (OFB) mode.
Key words:Computer security; cryptography; data security; DES; encryption; Federal Information Processing Standards; modes of operation.

## Important FIPS 81 Change Notice

U.S. DEPARTMENT OF COMMERENCE
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
Gaithersburg, MD 20899

DATE OF CHANGE: 1981 November 20

FIPS PBULICATION CHANGE NOTICE
TITLE OF PUBLICATION

#
DES MODES OF OPERATION

This office has a record of your interest in receiving changes to the above FIPS PUB. The change(s) indicated below have been provided by the Maintenance Agency for this publication and will be included in the next published revision to this FIPS PUB. Questions or requests for additional information should be addressed to the Maintenance Agency:
Department Of Commerce
National Institute of Standards and Technology
Computer Systems Laboratory
Washington, D.C. 20234
CHANGE ITEM(S)
PAGE SECTION PARA. LINE(S) ORIGINAL CHANGE

    8         4         3     All      An acceptable    Replace with (a) below
    16        5               All      The 7-bit CFB    Replace with (a) below
    16        6               2,4      7-bit            8-bit
    16        6               5        14,21,28,35,42,  16,24,32,40,48,
                                       49, and 56       56, and 64
    16        6               6        and 7-bit        and 8, 8-bit
    16        7               1        7 and 56-bit     8 and 64-bit
    20                        2,3      7-BIT            8-BIT
    20                        13       7-BIT            8-BIT
    21                        2,3      56-BIT           64-BIT
    21                        13       56-BIT           64-BIT

    a)       An acceptable alternative for 7-bit CFB that uses an 8-bit
             feedback path while enciphering 7-bit data units is the 7-bit
             CFB(a) mode of operation.  This alternative always inserts a
             "1" in bit position one of the 8-bit feedback path so that the
             feedback is of the form (1 ,C1 ,C2,C3,C4,C5,CS,C7).  The
             cipher is represented as a 7-bit entity of the fom
             (C1,C2,C3,C4,C5,C6,C7).

             An acceptable alternative for 8-bit CFB when enciphering 8-bit
             data units composed of a non-information bit followed by a 7-
             bit code (e.g., p,b7,b6,b5,b4,b3,b2,b1) is the 8-bit CFB(a)
             mode of operation.  This alternative is similar to the 8-bit
             CFB except that a "1" bit is always inserted in bit position
             one of the 8-bit feedback path so that the feedback is of the
             form (1, C2, C3,C4,CE,C6,C7,C8).  The cipher is represented
    as
             an 8-bit entity of the form (C1,C2,C3,C4,C5,C6,C7,C8) or
             (0,C2, C3,C4,C5,C6,C7,C8) or (1,C2,C3,C4,C5,C6,C7,C8) or
             (P,C2,C3,C4,C5,C6,C7,C8) where P is a cipher parity bit.

    (b) The 7-bit CFB(a) mode is defined in the standard in order
             to encipher and decipher 7-bit data units and still use an 8-
             bit feedback path.

             Most computer and communication systems are designed to
             efficiently handle full 8-bit bytes. When using 7-bit codes
             the eighth bit of the byte is often used as a parity bit so
             that the byte is of the form (p,b7,b6,b5,b4,b3,b2,b1).  These
             systems often generate the parity bit during transmission and
             check its validity during reception.  In such systems the
             parity bit on cipher text would be automatically modified
             during transmission.  In this cases the encryption and
             decryption processes must operate independently of the parity
             bits and the 8-bit CFB(a) mode should be used.

             NOTE: These changes are provided-to make the specification of
             the 7-bit CFB(a) mode consistent with that specified in a
             proposed American National Standard for the Modes of
              Operation of the Data Encryption Algorithm.  The 8-bit CFB(a)
              mode and its extensions are defined in FIPS PUB 81 so that they
              may be used in many application standards.

Source: http://csrc.nist.gov/fips/change81.wp5 (WordPerfect)

U.S. Department of Commerce
National Institute of Standards and Technology

FIPS Publication Change Notice

FIPS PUB 81, DES Modes of Operation
Change No.: 2
Date of Change: 1996 May 31

Change Items:

This change notice provides editorial changes, updated references to documents and organizations, a correction to Figure 3, and additional guidance to agencies regarding the 64-bit Output Feedback Mode to FIPS 81, DES Modes of Operation. These changes are considered to be included whenever reference is made to the publication.

This change notice should be filed with FIPS 81.

Attachment

4 pages

1. There is a correction to Figure 3 on Page 9, which diagrams the flow for k-bit CFB mode. In the decryption state, it is the k bits of cipher text which should be fed back into the rightmost k bits of the input block; a line segment should extend from the cipher text box to the line that points to the input block. The leftmost k bits of the output block should only be fed into the exclusive-OR function with the k bits of cipher text. These bits from the output block should not be fed back into the input block. The corrected diagram for Figure 3 is shown here:

2. After the publication of FIPS 81, it was discovered that when less than 64 bits of feedback are used in the OFB mode (paragraph 5, p. 8), there is a risk of generating short cycles. That is, when the same key is used, and multiple encryptions or decryptions have occurred, then the resulting output block may be equal to an input block from a previous iteration. If that occurs, then further encryption or decryption using the same key will result in a repetition of previously generated output and input blocks. This increases the risk of a cryptanalyst recovering the original plain text. Because of this short cycle property, NIST does not support the use of the OFB mode for any amount of feedback less than 64 bits. Note that this short cycle property is not a problem with the DES algorithm, and would occur using any block cipher in a similar manner.

Tables E1 and E2 in Appendix E are accurate examples for using the OFB mode with 1- and 8-bits of feedback. However, only 64-bits of feedback should be used, as stated above. Table E3 should be added, which gives an example for using 64-bits of feedback:

Table E3 An Example of the 64-bit Output Feedback Mode The 64-bit OFB mode in the encrypt state has been selected. Cryptographic Key = 0123456789abcdef Initialization Vector = 1234567890abcdef

The plain text is the ASCII code for:

> "We the people of the United States, in order to "

These seven-bit characters are written in hexadecimal notation (0, b7, b6,. . ., b1). The "(+)" represents bit-by-bit, modulo 2 addition. Note that all 64 bits of the DES output block are exclusive-ORed with the 64 bits of plain text.

    TIME   DES INPUT BLOCK   DES OUTPUT BLOCK  (+)         P         =        C

     1     1234567890abcdef  bd661569ae874e25  (+)  5765207468652070 = ea03351dc6e26e55

     2     ea03351dc6e26e55  f75b04e2a914a8b9  (+)  656f706c65206f66 = 9234748ecc34c7df

     3     9234748ecc34c7df  d459dee65c9c67aa  (+)  2074686520556e69 = f42db6837cc909c3

     4     f42db6837cc909c3  dc1d0251dd29af70  (+)  7465642053746174 = a87866718e5dce04

     5     a87866718e5dce04  7890b81ad467a062  (+)  65732c20696e206f = 1de3943abd09800d

     6     1de3943abd09800d  baa00ff9674763ba  (+)  7264657220746f20 = c8c46a8b47330c9a

In addition, the following editorial changes and updates are made to the Announcement Section of FIPS 81, DES Modes of Operation.

The introductory paragraph is updated as follows:

Federal Information Processing Standards (FIPS PUBS) are issued by the National Institute of Standards and Technology (NIST) after approval by the Secretary of Commerce pursuant to Section 5131 of the Information Technology Management Reform Act of 1996 and the Computer Security Act of 1987, Public Law 104-106.

Paragraph 3, Explanation; Paragraph 6, Related Documents; and Paragraph 9, Qualifications; are updated as follows:

All references to FIPS 46 are changed to FIPS 46-2, Data Encryption Standard, December 30, 1993.

Paragraph 5. Maintenance Agency. is updated as follows:

U.S. Department of Commerce, National Institute of Standards and Technology (NIST), Computer Systems Laboratory.

Paragraph 6, Related Documents, is updated as follows

Delete references to Proposed Federal Standards 1026 and 1027. Add reference to FIPS 140-1, Security Requirements for Cryptographic Modules, January 11, 1994.

Paragraph 9, Qualifications, is updated as follows:

The DES modes of operation described in this standard are based upon information provided by many sources within the Federal Government and private industry. These modes are presently being implemented in cryptographic equipment containing DES devices. However, a standard of this nature must, of necessity, remain flexible enough to adapt to advancements and innovations in science and technology. As such, this standard should not be construed as being either exhaustive or static. It will be reviewed every five years in order to incorporate new implementations whose technical or economic merit justify the issuance of a revised standard. FIPS 46-2 requires implementation of the DES algorithm when agencies determine that cryptographic protection is required for unclassified information. FIPS 46-2 and this standard may be implemented in hardware, software, or firmware, or any combination thereof. Cryptographic modules which implement this standard shall conform to the requirements of FIPS 140-1.

Paragraph 10, Export Control, is updated as follows:

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 131 (International Traffic of Arms Regulations -- ITAR). 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.

Paragraph 12, Implementation Schedule, is updated as follows:

This standard became effective on June 2, 1981.

Paragraph 13, Waivers, is updated as follows:

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 re-delegate such authority only to a senior official designated pursuant to section 3506(a) of Title 44, U.S. Code. Waivers 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. 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 such decision, with procurement sensitive or classified portions clearly identified, shall be sent to: National Institute of Standards and Technology; ATTN: FIPS Waiver Decisions, Building 820, Room 509; 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 Reform and Oversight of the House of Representatives and the Committee on Governmental 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 supporting and accompanying documents, with such deletions as the agency is authorized and decides to make under 5 U.S.C. Section 552(b), shall be part of the procurement documentation and retained by the agency.

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