FIPS 180-1 - Secure Hash Standard

FIPS PUB 180-1
Supersedes FIPS PUB 180
1993 May 11

Federal Information
Processing Standards Publication 180-1
1995 April 17
Announcing the Standard for

# SECURE HASH STANDARD

(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 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.

Name of Standard: Secure Hash Standard.
Category of Standard: Computer Security.
Explanation: This Standard specifies a Secure Hash Algorithm, SHA-1, for computing a condensed representation of a message or a data file. When a message of any length < 264 bits is input, the SHA-1 produces a 160-bit output called a message digest. The message digest can then be input to the Digital Signature Algorithm (DSA) which generates or verifies the signature for the message. Signing the message digest rather than the message often improves the efficiency of the process because the message digest is usually much smaller in size than the message. The same hash algorithm must be used by the verifier of a digital signature as was used by the creator of the digital signature.
The SHA-1 is called secure because it is computationally infeasible to find a message which corresponds to a given message digest, or to find two different messages which produce the same message digest. Any change to a message in transit will, with very high probability, result in a different message digest, and the signature will fail to verify. SHA-1 is a technical revision of SHA (FIPS 180). A circular left shift operation has been added to the specifications in section 7, line b, page 9 of FIPS 180 and its equivalent in section 8, line c, page 10 of FIPS 180. This revision improves the security provided by this standard. The SHA-1 is based on principles similar to those used by Professor Ronald L. Rivest of MIT when designing the MD4 message digest algorithm ("The MD4 Message Digest Algorithm," Advances in Cryptology - CRYPTO '90 Proceedings, Springer-Verlag, 1991, pp. 303-311), and is closely modelled after that algorithm.
Figure 1: Using the SHA-1 with the DSA
Approving Authority: Secretary of Commerce.
Maintenance Agency: U.S. Department of Commerce, National Institute of Standards and Technology, Computer Systems Laboratory.
Applicability: This standard is applicable to all Federal departments and agencies for the protection of 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 is required for use with the Digital Signature Algorithm (DSA) as specified in the Digital Signature Standard (DSS) and whenever a secure hash algorithm is required for Federal applica- tions. Private and commercial organizations are encouraged to adopt and use this standard.
Applications: The SHA-1 may be used with the DSA in electronic mail, electronic funds transfer, software distribution, data storage, and other applications which require data integrity assurance and data origin authentication. The SHA-1 may also be used whenever it is necessary to generate a condensed version of a message.
Implementations: The SHA-1 may be implemented in software, firmware, hardware, or any combination thereof. Only implementations of the SHA-1 that are validated by NIST will be considered as complying with this standard. Information about the requirements for validating implementations of this standard can be obtained from the National Institute of Standards and Technology, Computer Systems Laboratory, Attn: SHS Validation, Gaithersburg, MD 20899.
Export Control: Implementations of this standard are subject to FederalGovernment export controls as specified in Title 15, Code of Federal Regulations, Parts 768 through 799. Exporters are advised to contact the Department of Commerce, Bureau of Export Administration for more information.
Patents: Implementations of the SHA-1 in this standard may be covered by U.S. and foreign patents.
Implementation Schedule: This standard becomes effective October 2, 1995.
Specifications: Federal Information Processing Standard (FIPS 180-1) Secure Hash Standard (affixed).
Cross Index:

  a. FIPS PUB 46-2, Data Encryption Standard.
  b. FIPS PUB 73, Guidelines for Security of Computer Applications.
  c. FIPS PUB 140-1, Security Requirements for Cryptographic Modules.
  d. FIPS PUB 186, Digital Signature Standard.
  e. Federal Informations Resources Management Regulations (FIRMR) subpart 201.20.303, Standards, and subpart 201.39.1002, Federal Standards.

Objectives: The objectives of this standard are to:

  a. Specify the secure hash algorithm required for use with the Digital Signature Standard (FIPS 186) in the generation and verification of digital signatures;
  b. Specify the secure hash algorithm to be used whenever a secure hash algorithm is required for Federal applications; and
  c. Encourage the adoption and use of the specified secure hash algorithm by private and commercial organizations.

Qualifications: While it is the intent of this standard to specify a secure hash algorithm, 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.
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.
  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 180-1 (FIPSPUB180-1), 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 180-1
  Supersedes FIPS PUB 180
  1993 May 11

  Federal Information
  Processing Standards Publication 180-1
  1995 April 17
  Specifications for

  # SECURE HASH STANDARD

  1. INTRODUCTION
  The Secure Hash Algorithm (SHA-1) is required for use with the Digital Signature Algorithm (DSA) as specified in the Digital Signature Standard (DSS) and whenever a secure hash algorithm is required for federal applica- tions. For a message of length < 2^64 bits, the SHA-1 produces a 160-bit condensed representation of the message called a message digest. The message digest is used during generation of a signature for the message. The SHA-1 is also used to compute a message digest for the received version of the message during the process of verifying the signature. Any change to the message in transit will, with very high probability, result in a different message digest, and the signature will fail to verify.
  The SHA-1 is designed to have the following properties: it is computationally infeasible to find a message which corresponds to a given message digest, or to find two different messages which produce the same message digest.
  2. BIT STRINGS AND INTEGERS
  The following terminology related to bit strings and integers will be used:
    a. A hex digit is an element of the set {0, 1, ... , 9, A, ... , F}. A hex digit is the representation of a 4-bit string. Examples: 7 = 0111, A = 1010.
    b. A word equals a 32-bit string which may be represented as a sequence of 8 hex digits. To convert a word to 8 hex digits each 4-bit string is converted to its hex equivalent as described in (a) above. Example:
    1010 0001 0000 0011 1111 1110 0010 0011 = A103FE23.
    c. An integer between 0 and 232 - 1 inclusive may be represented as a word. The least significant four bits of the integer are represented by the right-most hex digit of the word representation. Example: the integer 291 = 28+25+21+20 = 256+32+2+1 is represented by the hex word, 00000123.
    If z is an integer, 0 <= z < 264, then z = 232x + y where 0 <= x < 232 and 0 <= y < 232. Since x and y can be represented as words X and Y, respectively, z can be represented as the pair of words (X,Y).
    d. block = 512-bit string. A block (e.g., B) may be represented as a sequence of 16 words.
  3. OPERATIONS ON WORDS
  The following logical operators will be applied to words:
    a. Bitwise logical word operations

        X ^ Y         =  bitwise logical "and" of  X and Y.

        X \/ Y        =  bitwise logical "inclusive-or" of X and Y.

        X XOR Y       =  bitwise logical "exclusive-or" of X and Y.

        ~ X           =  bitwise logical "complement" of X.

    Example:

                    01101100101110011101001001111011
              XOR   01100101110000010110100110110111
                    --------------------------------
                =   00001001011110001011101111001100

    b. The operation X + Y is defined as follows: words X and Y represent integers x and y, where 0 <= x < 232 and 0 <= y < 232. For positive integers n and m, let n mod m be the remainder upon dividing n by m. Compute
      z = (x + y) mod 232.
    Then 0 <= z < 232. Convert z to a word, Z, and define Z = X + Y.
    c. The circular left shift operation Sn(X), where X is a word and n is an integer with 0 <= n 32, is defined by
      Sn(X) = (X << n) OR (X >> 32-n).
    In the above, X << n is obtained as follows: discard the left-most n bits of X and then pad the result with n zeroes on the right (the result will still be 32 bits). X >> n is obtained by discarding the right-most n bits of X and then padding the result with n zeroes on the left. Thus Sn(X) is equivalent to a circular shift of X by n positions to the left.
  4. MESSAGE PADDING
  The SHA-1 is used to compute a message digest for a message or data file that is provided as input. The message or data file should be considered to be a bit string. The length of the message is the number of bits in the message (the empty message has length 0). If the number of bits in a message is a multiple of 8, for compactness we can represent the message in hex. The purpose of message padding is to make the total length of a padded message a multiple of 512. The SHA-1 sequentially processes blocks of 512 bits when computing the message digest. The following specifies how this padding shall be performed. As a summary, a "1" followed by m "0"s followed by a 64-bit integer are appended to the end of the message to produce a padded message of length 512 * n. The 64-bit integer is l, the length of the original message. The padded message is then processed by the SHA-1 as n 512-bit blocks.
  Suppose a message has length l < 264. Before it is input to the SHA-1, the message is padded on the right as follows:
    a. "1" is appended. Example: if the original message is "01010000", this is padded to "010100001".
    b. "0"s are appended. The number of "0"s will depend on the original length of the message. The last 64 bits of the last 512-bit block are reserved for the length l of the original message.
      Example: Suppose the original message is the bit string
      01100001 01100010 01100011 01100100 01100101.
      After step (a) this gives
      01100001 01100010 01100011 01100100 01100101 1.
      Since l = 40, the number of bits in the above is 41 and 407 "0"s are appended, making the total now 448. This gives (in hex)
        61626364 65800000 00000000 00000000
        00000000 00000000 00000000 00000000
        00000000 00000000 00000000 00000000
        00000000 00000000.
      c. Obtain the 2-word representation of l, the number of bits in the original message. If l < 232 then the first word is all zeroes. Append these two words to the padded message.
        Example: Suppose the original message is as in (b). Then l = 40 (note that l is computed before any padding). The two-word representation of 40 is hex 00000000 00000028. Hence the final padded message is hex
          61626364 65800000 00000000 00000000
          00000000 00000000 00000000 00000000
          00000000 00000000 00000000 00000000
          00000000 00000000 00000000 00000028.
      The padded message will contain 16 * n words for some n > 0. The padded message is regarded as a sequence of n blocks M1 , M2, ... , Mn, where each Mi contains 16 words and M1 contains the first characters (or bits) of the message.
      5. FUNCTIONS USED
      A sequence of logical functions f0, f1,..., f79 is used in the SHA-1. Each ft, 0 <= t <= 79, operates on three 32-bit words B, C, D and produces a 32-bit word as output. ft(B,C,D) is defined as follows: for words B, C, D,
        ft(B,C,D) = (B AND C) OR ((NOT B) AND D) ( 0 <= t <= 19)
        ft(B,C,D) = B XOR C XOR D (20 <= t <= 39)
        ft(B,C,D) = (B AND C) OR (B AND D) OR (C AND D) (40 <= t <= 59)
        ft(B,C,D) = B XOR C XOR D (60 <= t <= 79).
      6. CONSTANTS USED
      A sequence of constant words K(0), K(1), ... , K(79) is used in the SHA-1. In hex these are given by
        K = 5A827999 ( 0 <= t <= 19)
        Kt = 6ED9EBA1 (20 <= t <= 39)
        Kt = 8F1BBCDC (40 <= t <= 59)
        Kt = CA62C1D6 (60 <= t <= 79).
      7. COMPUTING THE MESSAGE DIGEST
      The message digest is computed using the final padded message. The computation uses two buffers, each consisting of five 32-bit words, and a sequence of eighty 32-bit words. The words of the first 5-word buffer are labeled A,B,C,D,E. The words of the second 5-word buffer are labeled H0, H1, H2, H3, H4. The words of the 80-word sequence are labeled W0, W1,..., W79. A single word buffer TEMP is also employed.
      To generate the message digest, the 16-word blocks M1, M2,..., Mn defined in Section 4 are processed in order. The processing of each Mi involves 80 steps.
      Before processing any blocks, the {Hi} are initialized as follows: in hex,
        H0 = 67452301
        H1 = EFCDAB89
        H2 = 98BADCFE
        H3 = 10325476
        H4 = C3D2E1F0.
      Now M1, M2, ... , Mn are processed. To process Mi, we proceed as follows:
        a. Divide Mi into 16 words W0, W1, ... , W15, where W0 is the left-most word.
        b. For t = 16 to 79 let Wt = S1(Wt-3 XOR Wt-8 XOR Wt- 14 XOR Wt-16).
        c. Let A = H0, B = H1, C = H2, D = H3, E = H4.
        d. For t = 0 to 79 do
          TEMP = S5(A) + ft(B,C,D) + E + Wt + Kt;
          E = D; D = C; C = S30(B); B = A; A = TEMP;
        e. Let H0 = H0 + A, H1 = H1 + B, H2 = H2 + C, H3 = H3 + D, H4 = H4 + E.
      After processing Mn, the message digest is the 160-bit string represented by the 5 words
        H0 H1 H2 H3 H4.
      8. ALTERNATE METHOD OF COMPUTATION
      The above assumes that the sequence W0, ... , W79 is implemented as an array of eighty 32-bit words. This is efficient from the standpoint of minimization of execution time, since the addresses of Wt-3, ... ,Wt-16 in step (b) are easily computed. If space is at a premium, an alternative is to regard { Wt } as a circular queue, which may be implemented using an array of sixteen 32-bit words W[0], ... W[15]. In this case, in hex let MASK = 0000000F. Then processing of Mi is as follows:
        a. Divide Mi into 16 words W[0], ... , W[15], where W[0] is the left-most word.
        b. Let A = H0, B = H1, C = H2, D = H3, E = H4.
        c. For t = 0 to 79 do
          s = t ^ MASK;
          if (t >= 16) W[s] = S1(W[(s + 13) ^ MASK] XOR W[(s + 8) AND MASK] XOR W[(s + 2) ^ MASK] XOR W[s]);
          TEMP = S5(A) + ft(B,C,D) + E + W[s] + Kt;
          E = D; D = C; C = S30(B); B = A; A = TEMP;
        d. Let H0 = H0 + A, H1 = H1 + B, H2 = H2 + C, H3 = H3 + D, H4 = H4 + E.
      9. COMPARISON OF METHODS
      The methods of Sections 7 and 8 yield the same message digest. Although using the method of Section 8 saves sixty-four 32-bit words of storage, it is likely to lengthen execution time due to the increased complexity of the address computations for the { W[t] } in step (c). Other computation methods which give identical results may be implemented in conformance with the standard.
    APPENDIX A. A SAMPLE MESSAGE AND ITS MESSAGE DIGEST
    This appendix is for informational purposes only and is not required to meet the standard.
    Let the message be the ASCII binary-coded form of "abc", i.e.,
      01100001 01100010 01100011.
    This message has length l = 24. In step (a) of Section 4, we append "1". In step (b) we append 423 "0"s. In step (c) we append hex 00000000 00000018, the 2-word representation of 24. Thus the final padded message consists of one block, so that n = 1 in the notation of Section 4.
    The initial hex values of {Hi} are
    H0 = 67452301
    H1 = EFCDAB89
    H2 = 98BADCFE
    H3 = 10325476
    H4 = C3D2E1F0.
    Start processing block 1. The words of block 1 are
    W[0] = 61626380
    W[1] = 00000000
    W[2] = 00000000
    W[3] = 00000000
    W[4] = 00000000
    W[5] = 00000000
    W[6] = 00000000
    W[7] = 00000000
    W[8] = 00000000
    W[9] = 00000000
    W[10] = 00000000
    W[11] = 00000000
    W[12] = 00000000
    W[13] = 00000000
    W[14] = 00000000
    W[15] = 00000018.
    The hex values of A,B,C,D,E after pass t of the "for t = 0 to 79" loop (step (d) of Section 7 or step (c) of Section 8) are

                    A           B           C           D           E

        t =  0: 0116FC33    67452301    7BF36AE2    98BADCFE    10325476
        t =  1: 8990536D    0116FC33    59D148C0    7BF36AE2    98BADCFE
        t =  2: A1390F08    8990536D    C045BF0C    59D148C0    7BF36AE2
        t =  3: CDD8E11B    A1390F08    626414DB    C045BF0C    59D148C0
        t =  4: CFD499DE    CDD8E11B    284E43C2    626414DB    C045BF0C
        t =  5: 3FC7CA40    CFD499DE    F3763846    284E43C2    626414DB
        t =  6: 993E30C1    3FC7CA40    B3F52677    F3763846    284E43C2
        t =  7: 9E8C07D4    993E30C1    0FF1F290    B3F52677    F3763846
        t =  8: 4B6AE328    9E8C07D4    664F8C30    0FF1F290    B3F52677
        t =  9: 8351F929    4B6AE328    27A301F5    664F8C30    0FF1F290
        t = 10: FBDA9E89    8351F929    12DAB8CA    27A301F5    664F8C30
        t = 11: 63188FE4    FBDA9E89    60D47E4A    12DAB8CA    27A301F5
        t = 12: 4607B664    63188FE4    7EF6A7A2    60D47E4A    12DAB8CA
        t = 13: 9128F695    4607B664    18C623F9    7EF6A7A2    60D47E4A
        t = 14: 196BEE77    9128F695    1181ED99    18C623F9    7EF6A7A2
        t = 15: 20BDD62F    196BEE77    644A3DA5    1181ED99    18C623F9
        t = 16: 4E925823    20BDD62F    C65AFB9D    644A3DA5    1181ED99
        t = 17: 82AA6728    4E925823    C82F758B    C65AFB9D    644A3DA5
        t = 18: DC64901D    82AA6728    D3A49608    C82F758B    C65AFB9D
        t = 19: FD9E1D7D    DC64901D    20AA99CA    D3A49608    C82F758B
        t = 20: 1A37B0CA    FD9E1D7D    77192407    20AA99CA    D3A49608
        t = 21: 33A23BFC    1A37B0CA    7F67875F    77192407    20AA99CA
        t = 22: 21283486    33A23BFC    868DEC32    7F67875F    77192407
        t = 23: D541F12D    21283486    0CE88EFF    868DEC32    7F67875F
        t = 24: C7567DC6    D541F12D    884A0D21    0CE88EFF    868DEC32
        t = 25: 48413BA4    C7567DC6    75507C4B    884A0D21    0CE88EFF
        t = 26: BE35FBD5    48413BA4    B1D59F71    75507C4B    884A0D21
        t = 27: 4AA84D97    BE35FBD5    12104EE9    B1D59F71    75507C4B
        t = 28: 8370B52E    4AA84D97    6F8D7EF5    12104EE9    B1D59F71
        t = 29: C5FBAF5D    8370B52E    D2AA1365    6F8D7EF5    12104EE9
        t = 30: 1267B407    C5FBAF5D    A0DC2D4B    D2AA1365    6F8D7EF5
        t = 31: 3B845D33    1267B407    717EEBD7    A0DC2D4B    D2AA1365
        t = 32: 046FAA0A    3B845D33    C499ED01    717EEBD7    A0DC2D4B
        t = 33: 2C0EBC11    046FAA0A    CEE1174C    C499ED01    717EEBD7
        t = 34: 21796AD4    2C0EBC11    811BEA82    CEE1174C    C499ED01
        t = 35: DCBBB0CB    21796AD4    4B03AF04    811BEA82    CEE1174C
        t = 36: 0F511FD8    DCBBB0CB    085E5AB5    4B03AF04    811BEA82
        t = 37: DC63973F    0F511FD8    F72EEC32    085E5AB5    4B03AF04
        t = 38: 4C986405    DC63973F    03D447F6    F72EEC32    085E5AB5
        t = 39: 32DE1CBA    4C986405    F718E5CF    03D447F6    F72EEC32
        t = 40: FC87DEDF    32DE1CBA    53261901    F718E5CF    03D447F6
        t = 41: 970A0D5C    FC87DEDF    8CB7872E    53261901    F718E5CF
        t = 42: 7F193DC5    970A0D5C    FF21F7B7    8CB7872E    53261901
        t = 43: EE1B1AAF    7F193DC5    25C28357    FF21F7B7    8CB7872E
        t = 44: 40F28E09    EE1B1AAF    5FC64F71    25C28357    FF21F7B7
        t = 45: 1C51E1F2    40F28E09    FB86C6AB    5FC64F71    25C28357
        t = 46: A01B846C    1C51E1F2    503CA382    FB86C6AB    5FC64F71
        t = 47: BEAD02CA    A01B846C    8714787C    503CA382    FB86C6AB
        t = 48: BAF39337    BEAD02CA    2806E11B    8714787C    503CA382
        t = 49: 120731C5    BAF39337    AFAB40B2    2806E11B    8714787C
        t = 50: 641DB2CE    120731C5    EEBCE4CD    AFAB40B2    2806E11B
        t = 51: 3847AD66    641DB2CE    4481CC71    EEBCE4CD    AFAB40B2
        t = 52: E490436D    3847AD66    99076CB3    4481CC71    EEBCE4CD
        t = 53: 27E9F1D8    E490436D    8E11EB59    99076CB3    4481CC71
        t = 54: 7B71F76D    27E9F1D8    792410DB    8E11EB59    99076CB3
        t = 55: 5E6456AF    7B71F76D    09FA7C76    792410DB    8E11EB59
        t = 56: C846093F    5E6456AF    5EDC7DDB    09FA7C76    792410DB
        t = 57: D262FF50    C846093F    D79915AB    5EDC7DDB    09FA7C76
        t = 58: 09D785FD    D262FF50    F211824F    D79915AB    5EDC7DDB
        t = 59: 3F52DE5A    09D785FD    3498BFD4    F211824F    D79915AB
        t = 60: D756C147    3F52DE5A    4275E17F    3498BFD4    F211824F
        t = 61: 548C9CB2    D756C147    8FD4B796    4275E17F    3498BFD4
        t = 62: B66C020B    548C9CB2    F5D5B051    8FD4B796    4275E17F
        t = 63: 6B61C9E1    B66C020B    9523272C    F5D5B051    8FD4B796
        t = 64: 19DFA7AC    6B61C9E1    ED9B0082    9523272C    F5D5B051
        t = 65: 101655F9    19DFA7AC    5AD87278    ED9B0082    9523272C
        t = 66: 0C3DF2B4    101655F9    0677E9EB    5AD87278    ED9B0082
        t = 67: 78DD4D2B    0C3DF2B4    4405957E    0677E9EB    5AD87278
        t = 68: 497093C0    78DD4D2B    030F7CAD    4405957E    0677E9EB
        t = 69: 3F2588C2    497093C0    DE37534A    030F7CAD    4405957E
        t = 70: C199F8C7    3F2588C2    125C24F0    DE37534A    030F7CAD
        t = 71: 39859DE7    C199F8C7    8FC96230    125C24F0    DE37534A
        t = 72: EDB42DE4    39859DE7    F0667E31    8FC96230    125C24F0
        t = 73: 11793F6F    EDB42DE4    CE616779    F0667E31    8FC96230
        t = 74: 5EE76897    11793F6F    3B6D0B79    CE616779    F0667E31
        t = 75: 63F7DAB7    5EE76897    C45E4FDB    3B6D0B79    CE616779
        t = 76: A079B7D9    63F7DAB7    D7B9DA25    C45E4FDB    3B6D0B79
        t = 77: 860D21CC    A079B7D9    D8FDF6AD    D7B9DA25    C45E4FDB
        t = 78: 5738D5E1    860D21CC    681E6DF6    D8FDF6AD    D7B9DA25
        t = 79: 42541B35    5738D5E1    21834873    681E6DF6    D8FDF6AD.

    Block 1 has been processed. The values of {Hi} are
    H0 = 67452301 + 42541B35 = A9993E36
    H1 = EFCDAB89 + 5738D5E1 = 4706816A
    H2 = 98BADCFE + 21834873 = BA3E2571
    H3 = 10325476 + 681E6DF6 = 7850C26C
    H4 = C3D2E1F0 + D8FDF6AD = 9CD0D89D.
    Message digest = A9993E36 4706816A BA3E2571 7850C26C 9CD0D89D
  APPENDIX B. A SECOND SAMPLE MESSAGE AND ITS MESSAGE DIGEST
  This appendix is for informational purposes only and is not required to meet the standard.
  Let the message be the binary-coded form (cf. Appendix A) of the ASCII string
  "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq".
  Since each of the 56 characters is converted to 8 bits, the length of the message is l = 448. In step (a) of Section 4, we append "1". In step (b) we append 511 "0"s. In step (c) we append the 2-word representation of 448, i.e., hex 00000000 000001C0. This gives n = 2.
  The initial hex values of {Hi} are
  H0 = 67452301
  H1 = EFCDAB89
  H2 = 98BADCFE
  H3 = 10325476
  H4 = C3D2E1F0.
  Start processing block 1. The words of block 1 are
  W[0] = 61626364
  W[1] = 62636465
  W[2] = 63646566
  W[3] = 64656667
  W[4] = 65666768
  W[5] = 66676869
  W[6] = 6768696A
  W[7] = 68696A6B
  W[8] = 696A6B6C
  W[9] = 6A6B6C6D
  W[10] = 6B6C6D6E
  W[11] = 6C6D6E6F
  W[12] = 6D6E6F70
  W[13] = 6E6F7071
  W[14] = 80000000
  W[15] = 00000000.
  The hex values of A,B,C,D,E after pass t of the "for t = 0 to 79" loop (step (d) of Section 7 or step (c) of Section 8) are

                  A           B           C           D           E

      t =  0: 0116FC17    67452301    7BF36AE2    98BADCFE    10325476
      t =  1: EBF3B452    0116FC17    59D148C0    7BF36AE2    98BADCFE
      t =  2: 5109913A    EBF3B452    C045BF05    59D148C0    7BF36AE2
      t =  3: 2C4F6EAC    5109913A    BAFCED14    C045BF05    59D148C0
      t =  4: 33F4AE5B    2C4F6EAC    9442644E    BAFCED14    C045BF05
      t =  5: 96B85189    33F4AE5B    0B13DBAB    9442644E    BAFCED14
      t =  6: DB04CB58    96B85189    CCFD2B96    0B13DBAB    9442644E
      t =  7: 45833F0F    DB04CB58    65AE1462    CCFD2B96    0B13DBAB
      t =  8: C565C35E    45833F0F    36C132D6    65AE1462    CCFD2B96
      t =  9: 6350AFDA    C565C35E    D160CFC3    36C132D6    65AE1462
      t = 10: 8993EA77    6350AFDA    B15970D7    D160CFC3    36C132D6
      t = 11: E19ECAA2    8993EA77    98D42BF6    B15970D7    D160CFC3
      t = 12: 8603481E    E19ECAA2    E264FA9D    98D42BF6    B15970D7
      t = 13: 32F94A85    8603481E    B867B2A8    E264FA9D    98D42BF6
      t = 14: B2E7A8BE    32F94A85    A180D207    B867B2A8    E264FA9D
      t = 15: 42637E39    B2E7A8BE    4CBE52A1    A180D207    B867B2A8
      t = 16: 6B068048    42637E39    ACB9EA2F    4CBE52A1    A180D207
      t = 17: 426B9C35    6B068048    5098DF8E    ACB9EA2F    4CBE52A1
      t = 18: 944B1BD1    426B9C35    1AC1A012    5098DF8E    ACB9EA2F
      t = 19: 6C445652    944B1BD1    509AE70D    1AC1A012    5098DF8E
      t = 20: 95836DA5    6C445652    6512C6F4    509AE70D    1AC1A012
      t = 21: 09511177    95836DA5    9B111594    6512C6F4    509AE70D
      t = 22: E2B92DC4    09511177    6560DB69    9B111594    6512C6F4
      t = 23: FD224575    E2B92DC4    C254445D    6560DB69    9B111594
      t = 24: EEB82D9A    FD224575    38AE4B71    C254445D    6560DB69
      t = 25: 5A142C1A    EEB82D9A    7F48915D    38AE4B71    C254445D
      t = 26: 2972F7C7    5A142C1A    BBAE0B66    7F48915D    38AE4B71
      t = 27: D526A644    2972F7C7    96850B06    BBAE0B66    7F48915D
      t = 28: E1122421    D526A644    CA5CBDF1    96850B06    BBAE0B66
      t = 29: 05B457B2    E1122421    3549A991    CA5CBDF1    96850B06
      t = 30: A9C84BEC    05B457B2    78448908    3549A991    CA5CBDF1
      t = 31: 52E31F60    A9C84BEC    816D15EC    78448908    3549A991
      t = 32: 5AF3242C    52E31F60    2A7212FB    816D15EC    78448908
      t = 33: 31C756A9    5AF3242C    14B8C7D8    2A7212FB    816D15EC
      t = 34: E9AC987C    31C756A9    16BCC90B    14B8C7D8    2A7212FB
      t = 35: AB7C32EE    E9AC987C    4C71D5AA    16BCC90B    14B8C7D8
      t = 36: 5933FC99    AB7C32EE    3A6B261F    4C71D5AA    16BCC90B
      t = 37: 43F87AE9    5933FC99    AADF0CBB    3A6B261F    4C71D5AA
      t = 38: 24957F22    43F87AE9    564CFF26    AADF0CBB    3A6B261F
      t = 39: ADEB7478    24957F22    50FE1EBA    564CFF26    AADF0CBB
      t = 40: D70E5010    ADEB7478    89255FC8    50FE1EBA    564CFF26
      t = 41: 79BCFB08    D70E5010    2B7ADD1E    89255FC8    50FE1EBA
      t = 42: F9BCB8DE    79BCFB08    35C39404    2B7ADD1E    89255FC8
      t = 43: 633E9561    F9BCB8DE    1E6F3EC2    35C39404    2B7ADD1E
      t = 44: 98C1EA64    633E9561    BE6F2E37    1E6F3EC2    35C39404
      t = 45: C6EA241E    98C1EA64    58CFA558    BE6F2E37    1E6F3EC2
      t = 46: A2AD4F02    C6EA241E    26307A99    58CFA558    BE6F2E37
      t = 47: C8A69090    A2AD4F02    B1BA8907    26307A99    58CFA558
      t = 48: 88341600    C8A69090    A8AB53C0    B1BA8907    26307A99
      t = 49: 7E846F58    88341600    3229A424    A8AB53C0    B1BA8907
      t = 50: 86E358BA    7E846F58    220D0580    3229A424    A8AB53C0
      t = 51: 8D2E76C8    86E358BA    1FA11BD6    220D0580    3229A424
      t = 52: CE892E10    8D2E76C8    A1B8D62E    1FA11BD6    220D0580
      t = 53: EDEA95B1    CE892E10    234B9DB2    A1B8D62E    1FA11BD6
      t = 54: 36D1230A    EDEA95B1    33A24B84    234B9DB2    A1B8D62E
      t = 55: 776C3910    36D1230A    7B7AA56C    33A24B84    234B9DB2
      t = 56: A681B723    776C3910    8DB448C2    7B7AA56C    33A24B84
      t = 57: AC0A794F    A681B723    1DDB0E44    8DB448C2    7B7AA56C
      t = 58: F03D3782    AC0A794F    E9A06DC8    1DDB0E44    8DB448C2
      t = 59: 9EF775C3    F03D3782    EB029E53    E9A06DC8    1DDB0E44
      t = 60: 36254B13    9EF775C3    BC0F4DE0    EB029E53    E9A06DC8
      t = 61: 4080D4DC    36254B13    E7BDDD70    BC0F4DE0    EB029E53
      t = 62: 2BFAF7A8    4080D4DC    CD8952C4    E7BDDD70    BC0F4DE0
      t = 63: 513F9CA0    2BFAF7A8    10203537    CD8952C4    E7BDDD70
      t = 64: E5895C81    513F9CA0    0AFEBDEA    10203537    CD8952C4
      t = 65: 1037D2D5    E5895C81    144FE728    0AFEBDEA    10203537
      t = 66: 14A82DA9    1037D2D5    79625720    144FE728    0AFEBDEA
      t = 67: 6D17C9FD    14A82DA9    440DF4B5    79625720    144FE728
      t = 68: 2C7B07BD    6D17C9FD    452A0B6A    440DF4B5    79625720
      t = 69: FDF6EFFF    2C7B07BD    5B45F27F    452A0B6A    440DF4B5
      t = 70: 112B96E3    FDF6EFFF    4B1EC1EF    5B45F27F    452A0B6A
      t = 71: 84065712    112B96E3    FF7DBBFF    4B1EC1EF    5B45F27F
      t = 72: AB89FB71    84065712    C44AE5B8    FF7DBBFF    4B1EC1EF
      t = 73: C5210E35    AB89FB71    A10195C4    C44AE5B8    FF7DBBFF
      t = 74: 352D9F4B    C5210E35    6AE27EDC    A10195C4    C44AE5B8
      t = 75: 1A0E0E0A    352D9F4B    7148438D    6AE27EDC    A10195C4
      t = 76: D0D47349    1A0E0E0A    CD4B67D2    7148438D    6AE27EDC
      t = 77: AD38620D    D0D47349    86838382    CD4B67D2    7148438D
      t = 78: D3AD7C25    AD38620D    74351CD2    86838382    CD4B67D2
      t = 79: 8CE34517    D3AD7C25    6B4E1883    74351CD2    86838382.

  Block 1 has been processed. The values of {Hi} are
  H0 = 67452301 + 8CE34517 = F4286818
  H1 = EFCDAB89 + D3AD7C25 = C37B27AE
  H2 = 98BADCFE + 6B4E1883 = 0408F581
  H3 = 10325476 + 74351CD2 = 84677148
  H4 = C3D2E1F0 + 86838382 = 4A566572.
  Start processing block 2. The words of block 2 are
  W[0] = 00000000
  W[1] = 00000000
  W[2] = 00000000
  W[3] = 00000000
  W[4] = 00000000
  W[5] = 00000000
  W[6] = 00000000
  W[7] = 00000000
  W[8] = 00000000
  W[9] = 00000000
  W[10] = 00000000
  W[11] = 00000000
  W[12] = 00000000
  W[13] = 00000000
  W[14] = 00000000
  W[15] = 000001C0.
  The hex values of A,B,C,D,E after pass t of the for "t = 0 to 79" loop (step (d) of Section 7 or step (c) of Section 8) are

                  A           B           C           D           E

      t =  0: 2DF257E9    F4286818    B0DEC9EB    0408F581    84677148
      t =  1: 4D3DC58F    2DF257E9    3D0A1A06    B0DEC9EB    0408F581
      t =  2: C352BB05    4D3DC58F    4B7C95FA    3D0A1A06    B0DEC9EB
      t =  3: EEF743C6    C352BB05    D34F7163    4B7C95FA    3D0A1A06
      t =  4: 41E34277    EEF743C6    70D4AEC1    D34F7163    4B7C95FA
      t =  5: 5443915C    41E34277    BBBDD0F1    70D4AEC1    D34F7163
      t =  6: E7FA0377    5443915C    D078D09D    BBBDD0F1    70D4AEC1
      t =  7: C6946813    E7FA0377    1510E457    D078D09D    BBBDD0F1
      t =  8: FDDE1DE1    C6946813    F9FE80DD    1510E457    D078D09D
      t =  9: B8538ACA    FDDE1DE1    F1A51A04    F9FE80DD    1510E457
      t = 10: 6BA94F63    B8538ACA    7F778778    F1A51A04    F9FE80DD
      t = 11: 43A2792F    6BA94F63    AE14E2B2    7F778778    F1A51A04
      t = 12: FECD7BBF    43A2792F    DAEA53D8    AE14E2B2    7F778778
      t = 13: A2604CA8    FECD7BBF    D0E89E4B    DAEA53D8    AE14E2B2
      t = 14: 258B0BAA    A2604CA8    FFB35EEF    D0E89E4B    DAEA53D8
      t = 15: D9772360    258B0BAA    2898132A    FFB35EEF    D0E89E4B
      t = 16: 5507DB6E    D9772360    8962C2EA    2898132A    FFB35EEF
      t = 17: A51B58BC    5507DB6E    365DC8D8    8962C2EA    2898132A
      t = 18: C2EB709F    A51B58BC    9541F6DB    365DC8D8    8962C2EA
      t = 19: D8992153    C2EB709F    2946D62F    9541F6DB    365DC8D8
      t = 20: 37482F5F    D8992153    F0BADC27    2946D62F    9541F6DB
      t = 21: EE8700BD    37482F5F    F6264854    F0BADC27    2946D62F
      t = 22: 9AD594B9    EE8700BD    CDD20BD7    F6264854    F0BADC27
      t = 23: 8FBAA5B9    9AD594B9    7BA1C02F    CDD20BD7    F6264854
      t = 24: 88FB5867    8FBAA5B9    66B5652E    7BA1C02F    CDD20BD7
      t = 25: EEC50521    88FB5867    63EEA96E    66B5652E    7BA1C02F
      t = 26: 50BCE434    EEC50521    E23ED619    63EEA96E    66B5652E
      t = 27: 5C416DAF    50BCE434    7BB14148    E23ED619    63EEA96E
      t = 28: 2429BE5F    5C416DAF    142F390D    7BB14148    E23ED619
      t = 29: 0A2FB108    2429BE5F    D7105B6B    142F390D    7BB14148
      t = 30: 17986223    0A2FB108    C90A6F97    D7105B6B    142F390D
      t = 31: 8A4AF384    17986223    028BEC42    C90A6F97    D7105B6B
      t = 32: 6B629993    8A4AF384    C5E61888    028BEC42    C90A6F97
      t = 33: F15F04F3    6B629993    2292BCE1    C5E61888    028BEC42
      t = 34: 295CC25B    F15F04F3    DAD8A664    2292BCE1    C5E61888
      t = 35: 696DA404    295CC25B    FC57C13C    DAD8A664    2292BCE1
      t = 36: CEF5AE12    696DA404    CA573096    FC57C13C    DAD8A664
      t = 37: 87D5B80C    CEF5AE12    1A5B6901    CA573096    FC57C13C
      t = 38: 84E2A5F2    87D5B80C    B3BD6B84    1A5B6901    CA573096
      t = 39: 03BB6310    84E2A5F2    21F56E03    B3BD6B84    1A5B6901
      t = 40: C2D8F75F    03BB6310    A138A97C    21F56E03    B3BD6B84
      t = 41: BFB25768    C2D8F75F    00EED8C4    A138A97C    21F56E03
      t = 42: 28589152    BFB25768    F0B63DD7    00EED8C4    A138A97C
      t = 43: EC1D3D61    28589152    2FEC95DA    F0B63DD7    00EED8C4
      t = 44: 3CAED7AF    EC1D3D61    8A162454    2FEC95DA    F0B63DD7
      t = 45: C3D033EA    3CAED7AF    7B074F58    8A162454    2FEC95DA
      t = 46: 7316056A    C3D033EA    CF2BB5EB    7B074F58    8A162454
      t = 47: 46F93B68    7316056A    B0F40CFA    CF2BB5EB    7B074F58
      t = 48: DC8E7F26    46F93B68    9CC5815A    B0F40CFA    CF2BB5EB
      t = 49: 850D411C    DC8E7F26    11BE4EDA    9CC5815A    B0F40CFA
      t = 50: 7E4672C0    850D411C    B7239FC9    11BE4EDA    9CC5815A
      t = 51: 89FBD41D    7E4672C0    21435047    B7239FC9    11BE4EDA
      t = 52: 1797E228    89FBD41D    1F919CB0    21435047    B7239FC9
      t = 53: 431D65BC    1797E228    627EF507    1F919CB0    21435047
      t = 54: 2BDBB8CB    431D65BC    05E5F88A    627EF507    1F919CB0
      t = 55: 6DA72E7F    2BDBB8CB    10C7596F    05E5F88A    627EF507
      t = 56: A8495A9B    6DA72E7F    CAF6EE32    10C7596F    05E5F88A
      t = 57: E785655A    A8495A9B    DB69CB9F    CAF6EE32    10C7596F
      t = 58: 5B086C42    E785655A    EA1256A6    DB69CB9F    CAF6EE32
      t = 59: A65818F7    5B086C42    B9E15956    EA1256A6    DB69CB9F
      t = 60: 7AAB101B    A65818F7    96C21B10    B9E15956    EA1256A6
      t = 61: 93614C9C    7AAB101B    E996063D    96C21B10    B9E15956
      t = 62: F66D9BF4    93614C9C    DEAAC406    E996063D    96C21B10
      t = 63: D504902B    F66D9BF4    24D85327    DEAAC406    E996063D
      t = 64: 60A9DA62    D504902B    3D9B66FD    24D85327    DEAAC406
      t = 65: 8B687819    60A9DA62    F541240A    3D9B66FD    24D85327
      t = 66: 083E90C3    8B687819    982A7698    F541240A    3D9B66FD
      t = 67: F6226BBF    083E90C3    62DA1E06    982A7698    F541240A
      t = 68: 76C0563B    F6226BBF    C20FA430    62DA1E06    982A7698
      t = 69: 989DD165    76C0563B    FD889AEF    C20FA430    62DA1E06
      t = 70: 8B2C7573    989DD165    DDB0158E    FD889AEF    C20FA430
      t = 71: AE1B8E7B    8B2C7573    66277459    DDB0158E    FD889AEF
      t = 72: CA1840DE    AE1B8E7B    E2CB1D5C    66277459    DDB0158E
      t = 73: 16F3BABB    CA1840DE    EB86E39E    E2CB1D5C    66277459
      t = 74: D28D83AD    16F3BABB    B2861037    EB86E39E    E2CB1D5C
      t = 75: 6BC02DFE    D28D83AD    C5BCEEAE    B2861037    EB86E39E
      t = 76: D3A6E275    6BC02DFE    74A360EB    C5BCEEAE    B2861037
      t = 77: DA955482    D3A6E275    9AF00B7F    74A360EB    C5BCEEAE
      t = 78: 58C0AAC0    DA955482    74E9B89D    9AF00B7F    74A360EB
      t = 79: 906FD62C    58C0AAC0    B6A55520    74E9B89D    9AF00B7F.

  Block 2 has been processed. The values of {Hi} are
  H0 = F4286818 + 906FD62C = 84983E44
  H1 = C37B27AE + 58C0AAC0 = 1C3BD26E
  H2 = 0408F581 + B6A55520 = BAAE4AA1
  H3 = 84677148 + 74E9B89D = F95129E5
  H4 = 4A566572 + 9AF00B7F = E54670F1.
  Message digest = 84983E44 1C3BD26E BAAE4AA1 F95129E5 E54670F1

APPENDIX C. A THIRD SAMPLE MESSAGE AND ITS MESSAGE DIGEST
This appendix is for informational purposes only and is not required to meet the standard.
Let the message be the binary-coded form of the ASCII string which consists of 1,000,000 repetitions of "a".
Message digest = 34AA973C D4C4DAA4 F61EEB2B DBAD2731 6534016F

The Foreword, Abstract, and Key Words follow:

FIPS PUB 180-1
FEDERAL INFORMATION
PROCESSING STANDARDS PUBLICATION
1995 April 17
U.S. DEPARTMENT OF COMMERCE/National Institute of Standards and Technology

##
SECURE HASH STANDARD

U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary
National Institute of Standards and Technology, Arati Prabhakar, 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
This standard specifies a Secure Hash Algorithm (SHA-1) which can be used to generate a condensed representation of a message called a message digest. The SHA-1 is required for use with the Digital Signature Algorithm (DSA) as specified in the Digital Signature Standard (DSS) and whenever a secure hash algorithm is required for Federal applications. The SHA-1 is used by both the transmitter and intended receiver of a message in computing and verifying a digital signature.
Key words: computer security; digital signatures; Federal Information Processing Standard (FIPS); hash algorithm.