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Federal Information

Processing Standards Publication 180-2

2002 August 1

Announcing the

SECURE HASH STANDARD

Federal Information Processing Standards Publications (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

(Public Law 104-106), and the Computer Security Act of 1987 (Public Law 100-235).

1. Name of Standard: Secure Hash Signature Standard (SHS) (FIPS PUB 180-2).

2. Category of Standard: Computer Security Standard, Cryptography.

3. Explanation: This Standard specifies four secure hash algorithms - SHA-1, SHA-256,

SHA-384, and SHA-512 - for computing a condensed representation of electronic data

(message). When a message of any length < 2

bits (for SHA-1 and SHA-256) or < 2

128

bits (for

SHA-384 and SHA-512) is input to an algorithm, the result is an output called a message digest.

The message digests range in length from 160 to 512 bits, depending on the algorithm. Secure

hash algorithms are typically used with other cryptographic algorithms, such as digital signature

algorithms and keyed-hash message authentication codes, or in the generation of random

numbers (bits).

The four hash algorithms specified in this standard are called secure because, for a given

algorithm, it is computationally infeasible 1) to find a message that corresponds to a given

message digest, or 2) to find two different messages that produce the same message digest. Any

change to a message will, with a very high probability, result in a different message digest. This

will result in a verification failure when the secure hash algorithm is used with a digital signature

algorithm or a keyed-hash message authentication algorithm.

This standard supersedes FIPS 180-1, adding three algorithms that are capable of producing

larger message digests. The SHA-1 algorithm specified herein is the same algorithm that was

specified previously in FIPS 180-1, although some of the notation has been modified to be

consistent with the notation used in the SHA-256, SHA-384, and SHA-512 algorithms.

4. Approving Authority: Secretary of Commerce.

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

Technology (NIST), Information Technology Laboratory (ITL).

6. Applicability: This standard is applicable to all Federal departments and agencies for the

protection of sensitive unclassified information that is not subject to section 2315 of Title 10,

United States Code, or section 3502(2) of Title 44, United States Code. This standard shall be

implemented whenever a secure hash algorithm is required for Federal applications, including

use by other cryptographic algorithms and protocols. The adoption and use of this standard is

available to private and commercial organizations.

7. Specifications : Federal Information Processing Standard (FIPS) 180-2, Secure Hash

Standard (SHS) (affixed).

8. Implementations: The secure hash algorithms specified herein may be implemented in

software, firmware, hardware or any combination thereof. Only algorithm implementations that

are validated by NIST will be considered as complying with this standard. Information about the

planned validation program can be obtained at http://csrc.nist.gov/cryptval/ or from the National

Institute of Standards and Technology, Information Technology Laboratory, Attn: SHS

Validation, 100 Bureau Drive Stop 8930, Gaithersburg, MD 20899-8930.

9. Implementation Schedule: This standard becomes effective on February 1, 2003.

10. Patents: Implementations of the secure hash algorithms in this standard may be covered by

U.S. or foreign patents.

11. Export Control: Certain cryptographic devices and technical data regarding them are

subject to Federal export controls. Exports of cryptographic modules implementing this standard

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

the Bureau of Export Administration of the U.S. Department of Commerce. Applicable Federal

government export controls are specified in Title 15, Code of Federal Regulations (CFR) Part

740.17; Title 15, CFR Part 742; and Title 15, CFR Part 774, Category 5, Part 2.

12. Qualifications: While it is the intent of this standard to specify general security

requirements for generating a message digest, conformance to this standard does not assure that a

particular implementation is secure. The responsible authority in each agency or department

shall assure that an overall implementation provides an acceptable level of security. This

standard will be reviewed every five years in order to assess its adequacy.

13. Waiver Procedure. Under certain exceptional circumstances, the heads of Federal

agencies, or their delegates, may approve waivers to Federal Information Processing Standards

(FIPS). The heads of such agencies may redelegate such authority only to a senior official

designated pursuant to Section 3506(b) of Title 44, U.S. Code. Waivers shall be granted only

when compliance with this standard would

a. 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 that is not offset by government-

wide savings.

iii

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 that 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 Decision,

Information Technology Laboratory, 100 Bureau Drive, Stop 8900, Gaithersburg, MD 20899-

8900.

In addition, a 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

supporting and accompanying documents, with such deletions as the agency is authorized and

decides to make under Section 552(b) of Title 5, U.S. Code, shall be part of the procurement

documentation and retained by the agency.

14. Where to Obtain Copies of the Standard: This publication is available electronically by

accessing http://csrc.nist.gov/publications/. A list of other available computer security

publications, including ordering information, can be obtained from NIST Publications List 91,

which is available at the same web site. Alternatively, copies of NIST computer security

publications are available from: National Technical Information Service (NTIS), 5285 Port

Royal Road, Springfield, VA 22161.

Federal Information

Processing Standards Publication 180-2

2002 August 1

Specifications for the

SECURE HASH STANDARD

Table Of Contents

1. INTRODUCTION..............................................................................................................................................................3

2. DEFINITIONS.....................................................................................................................................................................4

2.1 GLOSSARY OF TERMS AND ACRONYMS....................................................................................................................4

2.2 ALGORITHM PARAMETERS, SYMBOLS, AND TERMS...............................................................................................4

2.2.1 Parameters........................................................................................................................................................4

2.2.2 Symbols..............................................................................................................................................................5

3. NOTATION AND CONVENTIONS.............................................................................................................................6

3.1 BIT STRINGS AND INTEGERS.......................................................................................................................................6

3.2 OPERATIONS ON WORDS.............................................................................................................................................7

4. FUNCTIONS AND CONSTANTS.................................................................................................................................9

4.1 FUNCTIONS....................................................................................................................................................................9

4.1.1 SHA-1 Functions..............................................................................................................................................9

4.1.2 SHA-256 Functions.........................................................................................................................................9

4.1.3 SHA-384 and SHA-512 Functions................................................................................................................9

4.2 CONSTANTS.................................................................................................................................................................10

4.2.1 SHA-1 Constants............................................................................................................................................10

4.2.2 SHA-256 Constants.......................................................................................................................................10

4.2.3 SHA-384 and SHA-512 Constants..............................................................................................................10

5. PREPROCESSING..........................................................................................................................................................12

5.1 PADDING THE MESSAGE ............................................................................................................................................12

5.1.1 SHA-1 and SHA-256......................................................................................................................................12

5.1.2 SHA-384 and SHA-512.................................................................................................................................12

5.2 PARSING THE PADDED MESSAGE .............................................................................................................................13

5.2.1 SHA-1 and SHA-256......................................................................................................................................13

5.2.2 SHA-384 and SHA-512.................................................................................................................................13

5.3 SETTING THE INITIAL HASH VALUE (H

(0)

)..............................................................................................................13

5.3.1 SHA-1...............................................................................................................................................................13

5.3.2 SHA-256..........................................................................................................................................................13

5.3.3 SHA-384..........................................................................................................................................................14

5.3.4 SHA-512..........................................................................................................................................................14

6. SECURE HASH ALGORITHMS ................................................................................................................................15

6.1 SHA-1..........................................................................................................................................................................15

6.1.1 SHA-1 Preprocessing....................................................................................................................................15

6.1.2 SHA-1 Hash Computation............................................................................................................................15

6.1.3 Alternate Method for Computing a SHA-1 Message Digest...................................................................17

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