Internet Engineering Task Force (IETF) D. Eastlake 3rd Request for Comments: 6234 Huawei Obsoletes: 4634 T. Hansen Updates: 3174 AT&T Labs Category: Informational May 2011 ISSN: 2070-1721 US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF) Abstract The United States of America has adopted a suite of Secure Hash Algorithms (SHAs), including four beyond SHA-1, as part of a Federal Information Processing Standard (FIPS), namely SHA-224, SHA-256, SHA-384, and SHA-512. This document makes open source code performing these SHA hash functions conveniently available to the Internet community. The sample code supports input strings of arbitrary bit length. Much of the text herein was adapted by the authors from FIPS 180-2. This document replaces RFC 4634, fixing errata and adding code for an HMAC-based extract-and-expand Key Derivation Function, HKDF (RFC 5869). As with RFC 4634, code to perform SHA-based Hashed Message Authentication Codes (HMACs) is also included. Status of This Memo This document is not an Internet Standards Track specification; it is published for informational purposes. This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Not all documents approved by the IESG are a candidate for any level of Internet Standard; see Section 2 of RFC 5741. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc6234. Eastlake & Hansen Informational [Page 1]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Copyright Notice Copyright (c) 2011 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Eastlake & Hansen Informational [Page 2]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Table of Contents 1. Overview of Contents ............................................4 2. Notation for Bit Strings and Integers ...........................5 3. Operations on Words .............................................6 4. Message Padding and Parsing .....................................8 4.1. SHA-224 and SHA-256 ........................................8 4.2. SHA-384 and SHA-512 ........................................9 5. Functions and Constants Used ...................................10 5.1. SHA-224 and SHA-256 .......................................10 5.2. SHA-384 and SHA-512 .......................................11 6. Computing the Message Digest ...................................12 6.1. SHA-224 and SHA-256 Initialization ........................12 6.2. SHA-224 and SHA-256 Processing ............................13 6.3. SHA-384 and SHA-512 Initialization ........................14 6.4. SHA-384 and SHA-512 Processing ............................15 7. HKDF- and SHA-Based HMACs ......................................17 7.1. SHA-Based HMACs ...........................................17 7.2. HKDF ......................................................17 8. C Code for SHAs, HMAC, and HKDF ................................17 8.1. The Header Files ..........................................21 8.1.1. The .h file ........................................21 8.1.2. stdint-example.h ...................................29 8.1.3. sha-private.h ......................................29 8.2. The SHA Code ..............................................30 8.2.1. sha1.c .............................................30 8.2.2. sha224-256.c .......................................39 8.2.3. sha384-512.c .......................................51 8.2.4. usha.c .............................................73 8.3. The HMAC Code .............................................79 8.4. The HKDF Code .............................................84 8.5. The Test Driver ...........................................91 9. Security Considerations .......................................123 10. Acknowledgements .............................................123 11. References ...................................................124 11.1. Normative References ....................................124 11.2. Informative References ..................................124 Appendix: Changes from RFC 4634...................................126 Eastlake & Hansen Informational [Page 3]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 1. Overview of Contents This document includes specifications for the United States of America (USA) Federal Information Processing Standard (FIPS) Secure Hash Algorithms (SHAs), code to implement the SHAs, code to implement HMAC (Hashed Message Authentication Code, [RFC2104]) based on the SHAs, and code to implement HKDF (HMAC-based Key Derivation Function, [RFC5869]) based on HMAC. Specifications for HMAC and HKDF are not included as they appear elsewhere in the RFC series [RFC2104] [RFC5869]. NOTE: Much of the text below is taken from [SHS], and the assertions of the security of the hash algorithms described therein are made by the US Government, the author of [SHS], not by the listed authors of this document. See also [RFC6194] concerning the security of SHA-1. The text below specifies Secure Hash Algorithms, SHA-224 [RFC3874], SHA-256, SHA-384, and SHA-512, for computing a condensed representation of a message or a data file. (SHA-1 is specified in [RFC3174].) When a message of any length < 2^64 bits (for SHA-224 and SHA-256) or < 2^128 bits (for SHA-384 and SHA-512) is input to one of these algorithms, the result is an output called a message digest. The message digests range in length from 224 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 authentication codes, the generation of random numbers [RFC4086], or in key derivation functions. The algorithms specified in this document are called secure because it is computationally infeasible to (1) find a message that corresponds to a given message digest, or (2) find two different messages that produce the same message digest. Any change to a message in transit will, with 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. The code provided herein supports input strings of arbitrary bit length. SHA-1's sample code from [RFC3174] has also been updated to handle input strings of arbitrary bit length. Permission is granted for all uses, commercial and non-commercial, of this code. This document obsoletes [RFC4634], and the changes from that RFC are summarized in the Appendix. Eastlake & Hansen Informational [Page 4]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 ASN.1 OIDs (Object Identifiers) for the SHA algorithms, taken from [RFC4055], are as follows: id-sha1 OBJECT IDENTIFIER ::= { iso(1) identified-organization(3) oiw(14) secsig(3) algorithms(2) 26 } id-sha224 OBJECT IDENTIFIER ::= {{ joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistalgorithm(4) hashalgs(2) 4 } id-sha256 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistalgorithm(4) hashalgs(2) 1 } id-sha384 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistalgorithm(4) hashalgs(2) 2 } id-sha512 OBJECT IDENTIFIER ::= { joint-iso-itu-t(2) country(16) us(840) organization(1) gov(101) csor(3) nistalgorithm(4) hashalgs(2) 3 } Section 2 below defines the terminology and functions used as building blocks to form these algorithms. Section 3 describes the fundamental operations on words from which these algorithms are built. Section 4 describes how messages are padded up to an integral multiple of the required block size and then parsed into blocks. Section 5 defines the constants and the composite functions used to specify the hash algorithms. Section 6 gives the actual specification for the SHA-224, SHA-256, SHA-384, and SHA-512 functions. Section 7 provides pointers to the specification of HMAC keyed message authentication codes and to the specification of an extract-and-expand key derivation function based on HMAC. Section 8 gives sample code for the SHA algorithms, for SHA-based HMACs, and for HMAC-based extract-and-expand key derivation function. 2. Notation for 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 or 64-bit string that may be represented as a sequence of 8 or 16 hex digits, respectively. To convert a word to hex digits, each 4-bit string is converted to its hex equivalent as described in (a) above. Example: Eastlake & Hansen Informational [Page 5]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 1010 0001 0000 0011 1111 1110 0010 0011 = A103FE23. Throughout this document, the "big-endian" convention is used when expressing both 32-bit and 64-bit words, so that within each word the most significant bit is shown in the leftmost bit position. c. An integer may be represented as a word or pair of words. An integer between 0 and 2^32 - 1 inclusive may be represented as a 32-bit word. The least significant four bits of the integer are represented by the rightmost hex digit of the word representation. Example: the integer 291 = 2^8+2^5+2^1+2^0 = 256+32+2+1 is represented by the hex word 00000123. The same holds true for an integer between 0 and 2^64-1 inclusive, which may be represented as a 64-bit word. If Z is an integer, 0 <= z < 2^64, then z = (2^32)x + y where 0 <= x < 2^32 and 0 <= y < 2^32. Since x and y can be represented as words X and Y, respectively, z can be represented as the pair of words (X,Y). Again, the "big-endian" convention is used and the most significant word is in the leftmost word position for values represented by multiple-words. d. block = 512-bit or 1024-bit string. A block (e.g., B) may be represented as a sequence of 32-bit or 64-bit words. 3. Operations on Words The following logical operators will be applied to words in all four hash operations specified herein. SHA-224 and SHA-256 operate on 32-bit words while SHA-384 and SHA-512 operate on 64-bit words. In the operations below, x<<n is obtained as follows: discard the leftmost n bits of x and then pad the result with n zeroed bits on the right (the result will still be the same number of bits). Similarly, x>>n is obtained as follows: discard the rightmost n bits of x and then prepend the result with n zeroed bits on the left (the result will still be the same number of bits). a. Bitwise logical word operations X AND Y = bitwise logical "and" of X and Y. X OR Y = bitwise logical "inclusive-or" of X and Y. Eastlake & Hansen Informational [Page 6]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 X XOR Y = bitwise logical "exclusive-or" of X and Y. NOT 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 w-bit integers x and y, where 0 <= x < 2^w and 0 <= y < 2^w. For positive integers n and m, let n mod m be the remainder upon dividing n by m. Compute z = (x + y) mod 2^w. Then 0 <= z < 2^w. Convert z to a word, Z, and define Z = X + Y. c. The right shift operation SHR^n(x), where x is a w-bit word and n is an integer with 0 <= n < w, is defined by SHR^n(x) = x>>n d. The rotate right (circular right shift) operation ROTR^n(x), where x is a w-bit word and n is an integer with 0 <= n < w, is defined by ROTR^n(x) = (x>>n) OR (x<<(w-n)) e. The rotate left (circular left shift) operation ROTL^n(x), where x is a w-bit word and n is an integer with 0 <= n < w, is defined by ROTL^n(X) = (x<<n) OR (x>>(w-n)) Note the following equivalence relationships, where w is fixed in each relationship: ROTL^n(x) = ROTR^(w-n)(x) ROTR^n(x) = ROTL^(w-n)(x) Eastlake & Hansen Informational [Page 7]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 4. Message Padding and Parsing The hash functions specified herein are 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 for SHA-224 and SHA-256 or a multiple of 1024 for SHA-384 and SHA-512. The following specifies how this padding shall be performed. As a summary, a "1" followed by m "0"s followed by a 64-bit or 128-bit integer are appended to the end of the message to produce a padded message of length 512*n or 1024*n. The appended integer is the length of the original message. The padded message is then processed by the hash function as n 512-bit or 1024-bit blocks. 4.1. SHA-224 and SHA-256 Suppose a message has length L < 2^64. Before it is input to the hash function, 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. K "0"s are appended where K is the smallest, non-negative solution to the equation ( L + 1 + K ) mod 512 = 448 c. Then append the 64-bit block that is L in binary representation. After appending this block, the length of the message will be a multiple of 512 bits. 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 Eastlake & Hansen Informational [Page 8]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Since L = 40, the number of bits in the above is 41 and K = 407 "0"s are appended, making the total now 448. This gives the following in hex: 61626364 65800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 The 64-bit representation of L = 40 is hex 00000000 00000028. Hence the final padded message is the following hex 61626364 65800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000028 4.2. SHA-384 and SHA-512 Suppose a message has length L < 2^128. Before it is input to the hash function, 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. K "0"s are appended where K is the smallest, non-negative solution to the equation ( L + 1 + K ) mod 1024 = 896 c. Then append the 128-bit block that is L in binary representation. After appending this block, the length of the message will be a multiple of 1024 bits. 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 Eastlake & Hansen Informational [Page 9]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Since L = 40, the number of bits in the above is 41 and K = 855 "0"s are appended, making the total now 896. This gives the following in hex: 61626364 65800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 The 128-bit representation of L = 40 is hex 00000000 00000000 00000000 00000028. Hence the final padded message is the following hex: 61626364 65800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000028 5. Functions and Constants Used The following subsections give the six logical functions and the table of constants used in each of the hash functions. 5.1. SHA-224 and SHA-256 SHA-224 and SHA-256 use six logical functions, where each function operates on 32-bit words, which are represented as x, y, and z. The result of each function is a new 32-bit word. CH( x, y, z) = (x AND y) XOR ( (NOT x) AND z) MAJ( x, y, z) = (x AND y) XOR (x AND z) XOR (y AND z) BSIG0(x) = ROTR^2(x) XOR ROTR^13(x) XOR ROTR^22(x) BSIG1(x) = ROTR^6(x) XOR ROTR^11(x) XOR ROTR^25(x) SSIG0(x) = ROTR^7(x) XOR ROTR^18(x) XOR SHR^3(x) SSIG1(x) = ROTR^17(x) XOR ROTR^19(x) XOR SHR^10(x) Eastlake & Hansen Informational [Page 10]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 SHA-224 and SHA-256 use the same sequence of sixty-four constant 32-bit words, K0, K1, ..., K63. These words represent the first 32 bits of the fractional parts of the cube roots of the first sixty- four prime numbers. In hex, these constant words are as follows (from left to right): 428a2f98 71374491 b5c0fbcf e9b5dba5 3956c25b 59f111f1 923f82a4 ab1c5ed5 d807aa98 12835b01 243185be 550c7dc3 72be5d74 80deb1fe 9bdc06a7 c19bf174 e49b69c1 efbe4786 0fc19dc6 240ca1cc 2de92c6f 4a7484aa 5cb0a9dc 76f988da 983e5152 a831c66d b00327c8 bf597fc7 c6e00bf3 d5a79147 06ca6351 14292967 27b70a85 2e1b2138 4d2c6dfc 53380d13 650a7354 766a0abb 81c2c92e 92722c85 a2bfe8a1 a81a664b c24b8b70 c76c51a3 d192e819 d6990624 f40e3585 106aa070 19a4c116 1e376c08 2748774c 34b0bcb5 391c0cb3 4ed8aa4a 5b9cca4f 682e6ff3 748f82ee 78a5636f 84c87814 8cc70208 90befffa a4506ceb bef9a3f7 c67178f2 5.2. SHA-384 and SHA-512 SHA-384 and SHA-512 each use six logical functions, where each function operates on 64-bit words, which are represented as x, y, and z. The result of each function is a new 64-bit word. CH( x, y, z) = (x AND y) XOR ( (NOT x) AND z) MAJ( x, y, z) = (x AND y) XOR (x AND z) XOR (y AND z) BSIG0(x) = ROTR^28(x) XOR ROTR^34(x) XOR ROTR^39(x) BSIG1(x) = ROTR^14(x) XOR ROTR^18(x) XOR ROTR^41(x) SSIG0(x) = ROTR^1(x) XOR ROTR^8(x) XOR SHR^7(x) SSIG1(x) = ROTR^19(x) XOR ROTR^61(x) XOR SHR^6(x) SHA-384 and SHA-512 use the same sequence of eighty constant 64-bit words, K0, K1, ... K79. These words represent the first 64 bits of the fractional parts of the cube roots of the first eighty prime numbers. In hex, these constant words are as follows (from left to right): Eastlake & Hansen Informational [Page 11]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 428a2f98d728ae22 7137449123ef65cd b5c0fbcfec4d3b2f e9b5dba58189dbbc 3956c25bf348b538 59f111f1b605d019 923f82a4af194f9b ab1c5ed5da6d8118 d807aa98a3030242 12835b0145706fbe 243185be4ee4b28c 550c7dc3d5ffb4e2 72be5d74f27b896f 80deb1fe3b1696b1 9bdc06a725c71235 c19bf174cf692694 e49b69c19ef14ad2 efbe4786384f25e3 0fc19dc68b8cd5b5 240ca1cc77ac9c65 2de92c6f592b0275 4a7484aa6ea6e483 5cb0a9dcbd41fbd4 76f988da831153b5 983e5152ee66dfab a831c66d2db43210 b00327c898fb213f bf597fc7beef0ee4 c6e00bf33da88fc2 d5a79147930aa725 06ca6351e003826f 142929670a0e6e70 27b70a8546d22ffc 2e1b21385c26c926 4d2c6dfc5ac42aed 53380d139d95b3df 650a73548baf63de 766a0abb3c77b2a8 81c2c92e47edaee6 92722c851482353b a2bfe8a14cf10364 a81a664bbc423001 c24b8b70d0f89791 c76c51a30654be30 d192e819d6ef5218 d69906245565a910 f40e35855771202a 106aa07032bbd1b8 19a4c116b8d2d0c8 1e376c085141ab53 2748774cdf8eeb99 34b0bcb5e19b48a8 391c0cb3c5c95a63 4ed8aa4ae3418acb 5b9cca4f7763e373 682e6ff3d6b2b8a3 748f82ee5defb2fc 78a5636f43172f60 84c87814a1f0ab72 8cc702081a6439ec 90befffa23631e28 a4506cebde82bde9 bef9a3f7b2c67915 c67178f2e372532b ca273eceea26619c d186b8c721c0c207 eada7dd6cde0eb1e f57d4f7fee6ed178 06f067aa72176fba 0a637dc5a2c898a6 113f9804bef90dae 1b710b35131c471b 28db77f523047d84 32caab7b40c72493 3c9ebe0a15c9bebc 431d67c49c100d4c 4cc5d4becb3e42b6 597f299cfc657e2a 5fcb6fab3ad6faec 6c44198c4a475817 6. Computing the Message Digest The output of each of the secure hash functions, after being applied to a message of N blocks, is the hash quantity H(N). For SHA-224 and SHA-256, H(i) can be considered to be eight 32-bit words, H(i)0, H(i)1, ... H(i)7. For SHA-384 and SHA-512, it can be considered to be eight 64-bit words, H(i)0, H(i)1, ..., H(i)7. As described below, the hash words are initialized, modified as each message block is processed, and finally concatenated after processing the last block to yield the output. For SHA-256 and SHA-512, all of the H(N) variables are concatenated while the SHA-224 and SHA-384 hashes are produced by omitting some from the final concatenation. 6.1. SHA-224 and SHA-256 Initialization For SHA-224, the initial hash value, H(0), consists of the following 32-bit words in hex: H(0)0 = c1059ed8 H(0)1 = 367cd507 H(0)2 = 3070dd17 H(0)3 = f70e5939 H(0)4 = ffc00b31 H(0)5 = 68581511 H(0)6 = 64f98fa7 H(0)7 = befa4fa4 Eastlake & Hansen Informational [Page 12]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 For SHA-256, the initial hash value, H(0), consists of the following eight 32-bit words, in hex. These words were obtained by taking the first 32 bits of the fractional parts of the square roots of the first eight prime numbers. H(0)0 = 6a09e667 H(0)1 = bb67ae85 H(0)2 = 3c6ef372 H(0)3 = a54ff53a H(0)4 = 510e527f H(0)5 = 9b05688c H(0)6 = 1f83d9ab H(0)7 = 5be0cd19 6.2. SHA-224 and SHA-256 Processing SHA-224 and SHA-256 perform identical processing on message blocks and differ only in how H(0) is initialized and how they produce their final output. They may be used to hash a message, M, having a length of L bits, where 0 <= L < 2^64. The algorithm uses (1) a message schedule of sixty-four 32-bit words, (2) eight working variables of 32 bits each, and (3) a hash value of eight 32-bit words. The words of the message schedule are labeled W0, W1, ..., W63. The eight working variables are labeled a, b, c, d, e, f, g, and h. The words of the hash value are labeled H(i)0, H(i)1, ..., H(i)7, which will hold the initial hash value, H(0), replaced by each successive intermediate hash value (after each message block is processed), H(i), and ending with the final hash value, H(N), after all N blocks are processed. They also use two temporary words, T1 and T2. The input message is padded as described in Section 4.1 above, then parsed into 512-bit blocks that are considered to be composed of sixteen 32-bit words M(i)0, M(i)1, ..., M(i)15. The following computations are then performed for each of the N message blocks. All addition is performed modulo 2^32. For i = 1 to N 1. Prepare the message schedule W: For t = 0 to 15 Wt = M(i)t For t = 16 to 63 Wt = SSIG1(W(t-2)) + W(t-7) + SSIG0(w(t-15)) + W(t-16) Eastlake & Hansen Informational [Page 13]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 2. Initialize the working variables: a = H(i-1)0 b = H(i-1)1 c = H(i-1)2 d = H(i-1)3 e = H(i-1)4 f = H(i-1)5 g = H(i-1)6 h = H(i-1)7 3. Perform the main hash computation: For t = 0 to 63 T1 = h + BSIG1(e) + CH(e,f,g) + Kt + Wt T2 = BSIG0(a) + MAJ(a,b,c) h = g g = f f = e e = d + T1 d = c c = b b = a a = T1 + T2 4. Compute the intermediate hash value H(i) H(i)0 = a + H(i-1)0 H(i)1 = b + H(i-1)1 H(i)2 = c + H(i-1)2 H(i)3 = d + H(i-1)3 H(i)4 = e + H(i-1)4 H(i)5 = f + H(i-1)5 H(i)6 = g + H(i-1)6 H(i)7 = h + H(i-1)7 After the above computations have been sequentially performed for all of the blocks in the message, the final output is calculated. For SHA-256, this is the concatenation of all of H(N)0, H(N)1, through H(N)7. For SHA-224, this is the concatenation of H(N)0, H(N)1, through H(N)6. 6.3. SHA-384 and SHA-512 Initialization For SHA-384, the initial hash value, H(0), consists of the following eight 64-bit words, in hex. These words were obtained by taking the first 64 bits of the fractional parts of the square roots of the ninth through sixteenth prime numbers. Eastlake & Hansen Informational [Page 14]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 H(0)0 = cbbb9d5dc1059ed8 H(0)1 = 629a292a367cd507 H(0)2 = 9159015a3070dd17 H(0)3 = 152fecd8f70e5939 H(0)4 = 67332667ffc00b31 H(0)5 = 8eb44a8768581511 H(0)6 = db0c2e0d64f98fa7 H(0)7 = 47b5481dbefa4fa4 For SHA-512, the initial hash value, H(0), consists of the following eight 64-bit words, in hex. These words were obtained by taking the first 64 bits of the fractional parts of the square roots of the first eight prime numbers. H(0)0 = 6a09e667f3bcc908 H(0)1 = bb67ae8584caa73b H(0)2 = 3c6ef372fe94f82b H(0)3 = a54ff53a5f1d36f1 H(0)4 = 510e527fade682d1 H(0)5 = 9b05688c2b3e6c1f H(0)6 = 1f83d9abfb41bd6b H(0)7 = 5be0cd19137e2179 6.4. SHA-384 and SHA-512 Processing SHA-384 and SHA-512 perform identical processing on message blocks and differ only in how H(0) is initialized and how they produce their final output. They may be used to hash a message, M, having a length of L bits, where 0 <= L < 2^128. The algorithm uses (1) a message schedule of eighty 64-bit words, (2) eight working variables of 64 bits each, and (3) a hash value of eight 64-bit words. The words of the message schedule are labeled W0, W1, ..., W79. The eight working variables are labeled a, b, c, d, e, f, g, and h. The words of the hash value are labeled H(i)0, H(i)1, ..., H(i)7, which will hold the initial hash value, H(0), replaced by each successive intermediate hash value (after each message block is processed), H(i), and ending with the final hash value, H(N) after all N blocks are processed. The input message is padded as described in Section 4.2 above, then parsed into 1024-bit blocks that are considered to be composed of sixteen 64-bit words M(i)0, M(i)1, ..., M(i)15. The following computations are then performed for each of the N message blocks. All addition is performed modulo 2^64. Eastlake & Hansen Informational [Page 15]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 For i = 1 to N 1. Prepare the message schedule W: For t = 0 to 15 Wt = M(i)t For t = 16 to 79 Wt = SSIG1(W(t-2)) + W(t-7) + SSIG0(W(t-15)) + W(t-16) 2. Initialize the working variables: a = H(i-1)0 b = H(i-1)1 c = H(i-1)2 d = H(i-1)3 e = H(i-1)4 f = H(i-1)5 g = H(i-1)6 h = H(i-1)7 3. Perform the main hash computation: For t = 0 to 79 T1 = h + BSIG1(e) + CH(e,f,g) + Kt + Wt T2 = BSIG0(a) + MAJ(a,b,c) h = g g = f f = e e = d + T1 d = c c = b b = a a = T1 + T2 4. Compute the intermediate hash value H(i) H(i)0 = a + H(i-1)0 H(i)1 = b + H(i-1)1 H(i)2 = c + H(i-1)2 H(i)3 = d + H(i-1)3 H(i)4 = e + H(i-1)4 H(i)5 = f + H(i-1)5 H(i)6 = g + H(i-1)6 H(i)7 = h + H(i-1)7 After the above computations have been sequentially performed for all of the blocks in the message, the final output is calculated. For SHA-512, this is the concatenation of all of H(N)0, H(N)1, through H(N)7. For SHA-384, this is the concatenation of H(N)0, H(N)1, through H(N)5. Eastlake & Hansen Informational [Page 16]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 7. HKDF- and SHA-Based HMACs Below are brief descriptions and pointers to more complete descriptions and code for (1) SHA-based HMACs and (2) an HMAC-based extract-and-expand key derivation function. Both HKDF and HMAC were devised by Hugo Krawczyk. 7.1. SHA-Based HMACs HMAC is a method for computing a keyed MAC (Message Authentication Code) using a hash function as described in [RFC2104]. It uses a key to mix in with the input text to produce the final hash. Sample code is also provided, in Section 8.3 below, to perform HMAC based on any of the SHA algorithms described herein. The sample code found in [RFC2104] was written in terms of a specified text size. Since SHA is defined in terms of an arbitrary number of bits, the sample HMAC code has been written to allow the text input to HMAC to have an arbitrary number of octets and bits. A fixed-length interface is also provided. 7.2. HKDF HKDF is a specific Key Derivation Function (KDF), that is, a function of initial keying material from which the KDF derives one or more cryptographically strong secret keys. HKDF, which is described in [RFC5869], is based on HMAC. Sample code for HKDF is provided in Section 8.4 below. 8. C Code for SHAs, HMAC, and HKDF Below is a demonstration implementation of these secure hash functions in C. Section 8.1 contains the header file sha.h that declares all constants, structures, and functions used by the SHA and HMAC functions. It includes conditionals based on the state of definition of USE_32BIT_ONLY that, if that symbol is defined at compile time, avoids 64-bit operations. It also contains sha- private.h that provides some declarations common to all the SHA functions. Section 8.2 contains the C code for sha1.c, sha224-256.c, sha384-512.c, and usha.c. Section 8.3 contains the C code for the HMAC functions, and Section 8.4 contains the C code for HKDF. Section 8.5 contains a test driver to exercise the code. For each of the digest lengths $$$, there is the following set of constants, a structure, and functions: Eastlake & Hansen Informational [Page 17]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Constants: SHA$$$HashSize number of octets in the hash SHA$$$HashSizeBits number of bits in the hash SHA$$$_Message_Block_Size number of octets used in the intermediate message blocks Most functions return an enum value that is one of: shaSuccess(0) on success shaNull(1) when presented with a null pointer parameter shaInputTooLong(2) when the input data is too long shaStateError(3) when SHA$$$Input is called after SHA$$$FinalBits or SHA$$$Result Structure: typedef SHA$$$Context an opaque structure holding the complete state for producing the hash Functions: int SHA$$$Reset(SHA$$$Context *context); Reset the hash context state. int SHA$$$Input(SHA$$$Context *context, const uint8_t *octets, unsigned int bytecount); Incorporate bytecount octets into the hash. int SHA$$$FinalBits(SHA$$$Context *, const uint8_t octet, unsigned int bitcount); Incorporate bitcount bits into the hash. The bits are in the upper portion of the octet. SHA$$$Input() cannot be called after this. int SHA$$$Result(SHA$$$Context *, uint8_t Message_Digest[SHA$$$HashSize]); Do the final calculations on the hash and copy the value into Message_Digest. In addition, functions with the prefix USHA are provided that take a SHAversion value (SHA$$$) to select the SHA function suite. They add the following constants, structure, and functions: Constants: shaBadParam(4) constant returned by USHA functions when presented with a bad SHAversion (SHA$$$) parameter or other illegal parameter values USAMaxHashSize maximum of the SHA hash sizes SHA$$$ SHAversion enumeration values, used by USHA, HMAC, and HKDF functions to select the SHA function suite Eastlake & Hansen Informational [Page 18]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Structure: typedef USHAContext an opaque structure holding the complete state for producing the hash Functions: int USHAReset(USHAContext *context, SHAversion whichSha); Reset the hash context state. int USHAInput(USHAContext context*, const uint8_t *bytes, unsigned int bytecount); Incorporate bytecount octets into the hash. int USHAFinalBits(USHAContext *context, const uint8_t bits, unsigned int bitcount); Incorporate bitcount bits into the hash. int USHAResult(USHAContext *context, uint8_t Message_Digest[USHAMaxHashSize]); Do the final calculations on the hash and copy the value into Message_Digest. Octets in Message_Digest beyond USHAHashSize(whichSha) are left untouched. int USHAHashSize(enum SHAversion whichSha); The number of octets in the given hash. int USHAHashSizeBits(enum SHAversion whichSha); The number of bits in the given hash. int USHABlockSize(enum SHAversion whichSha); The internal block size for the given hash. const char *USHAHashName(enum SHAversion whichSha); This function will return the name of the given SHA algorithm as a string. The HMAC functions follow the same pattern to allow any length of text input to be used. Structure: typedef HMACContext an opaque structure holding the complete state for producing the keyed message digest (MAC) Functions: int hmacReset(HMACContext *ctx, enum SHAversion whichSha, const unsigned char *key, int key_len); Reset the MAC context state. int hmacInput(HMACContext *ctx, const unsigned char *text, int text_len); Incorporate text_len octets into the MAC. int hmacFinalBits(HMACContext *ctx, const uint8_t bits, unsigned int bitcount); Incorporate bitcount bits into the MAC. int hmacResult(HMACContext *ctx, uint8_t Message_Digest[USHAMaxHashSize]); Eastlake & Hansen Informational [Page 19]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Do the final calculations on the MAC and copy the value into Message_Digest. Octets in Message_Digest beyond USHAHashSize(whichSha) are left untouched. In addition, a combined interface is provided, similar to that shown in [RFC2104], that allows a fixed-length text input to be used. int hmac(SHAversion whichSha, const unsigned char *text, int text_len, const unsigned char *key, int key_len, uint8_t Message_Digest[USHAMaxHashSize]); Calculate the given digest for the given text and key, and return the resulting MAC. Octets in Message_Digest beyond USHAHashSize(whichSha) are left untouched. The HKDF functions follow the same pattern to allow any length of text input to be used. Structure: typedef HKDFContext an opaque structure holding the complete state for producing the keying material Functions: int hkdfReset(HKDFContext *context, enum SHAversion whichSha, const unsigned char *salt, int salt_len) Reset the key derivation state and initialize it with the salt_len octets of the optional salt. int hkdfInput(HKDFContext *context, const unsigned char *ikm, int ikm_len) Incorporate ikm_len octets into the entropy extractor. int hkdfFinalBits(HKDFContext *context, uint8_t ikm_bits, unsigned int ikm_bit_count) Incorporate ikm_bit_count bits into the entropy extractor. int hkdfResult(HKDFContext *context, uint8_t prk[USHAMaxHashSize], const unsigned char *info, int info_len, uint8_t okm[ ], int okm_len) Finish the HKDF extraction and perform the final HKDF expansion, storing the okm_len octets into output keying material (okm). Optionally store the pseudo-random key (prk) that is generated internally. In addition, combined interfaces are provided, similar to that shown in [RFC5869], that allows a fixed-length text input to be used. int hkdfExtract(SHAversion whichSha, const unsigned char *salt, int salt_len, const unsigned char *ikm, int ikm_len, uint8_t prk[USHAMaxHashSize]) Eastlake & Hansen Informational [Page 20]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 Perform HKDF extraction, combining the salt_len octets of the optional salt with the ikm_len octets of the input keying material (ikm) to form the pseudo-random key prk. The output prk must be large enough to hold the octets appropriate for the given hash type. int hkdfExpand(SHAversion whichSha, const uint8_t prk[ ], int prk_len, const unsigned char *info, int info_len, uint8_t okm[ ], int okm_len) Perform HKDF expansion, combining the prk_len octets of the pseudo-random key prk with the info_len octets of info to form the okm_len octets stored in okm. int hkdf(SHAversion whichSha, const unsigned char *salt, int salt_len, const unsigned char *ikm, int ikm_len, const unsigned char *info, int info_len, uint8_t okm[ ], int okm_len) This combined interface performs both HKDF extraction and expansion. The variables are the same as in hkdfExtract() and hkdfExpand(). 8.1. The Header Files 8.1.1. The .h file The following sha.h file, as stated in the comments within the file, assumes that <stdint.h> is available on your system. If it is not, you should change to including <stdint-example.h>, provided in Section 8.1.2, or the like. /**************************** sha.h ****************************/ /***************** See RFC 6234 for details. *******************/ /* Copyright (c) 2011 IETF Trust and the persons identified as authors of the code. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: - Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Eastlake & Hansen Informational [Page 21]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 - Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. - Neither the name of Internet Society, IETF or IETF Trust, nor the names of specific contributors, may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ #ifndef _SHA_H_ #define _SHA_H_ /* * Description: * This file implements the Secure Hash Algorithms * as defined in the U.S. National Institute of Standards * and Technology Federal Information Processing Standards * Publication (FIPS PUB) 180-3 published in October 2008 * and formerly defined in its predecessors, FIPS PUB 180-1 * and FIP PUB 180-2. * * A combined document showing all algorithms is available at * http://csrc.nist.gov/publications/fips/ * fips180-3/fips180-3_final.pdf * * The five hashes are defined in these sizes: * SHA-1 20 byte / 160 bit * SHA-224 28 byte / 224 bit * SHA-256 32 byte / 256 bit * SHA-384 48 byte / 384 bit * SHA-512 64 byte / 512 bit * Eastlake & Hansen Informational [Page 22]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 * Compilation Note: * These files may be compiled with two options: * USE_32BIT_ONLY - use 32-bit arithmetic only, for systems * without 64-bit integers * * USE_MODIFIED_MACROS - use alternate form of the SHA_Ch() * and SHA_Maj() macros that are equivalent * and potentially faster on many systems * */ #include <stdint.h> /* * If you do not have the ISO standard stdint.h header file, then you * must typedef the following: * name meaning * uint64_t unsigned 64-bit integer * uint32_t unsigned 32-bit integer * uint8_t unsigned 8-bit integer (i.e., unsigned char) * int_least16_t integer of >= 16 bits * * See stdint-example.h */ #ifndef _SHA_enum_ #define _SHA_enum_ /* * All SHA functions return one of these values. */ enum { shaSuccess = 0, shaNull, /* Null pointer parameter */ shaInputTooLong, /* input data too long */ shaStateError, /* called Input after FinalBits or Result */ shaBadParam /* passed a bad parameter */ }; #endif /* _SHA_enum_ */ /* * These constants hold size information for each of the SHA * hashing operations */ enum { SHA1_Message_Block_Size = 64, SHA224_Message_Block_Size = 64, SHA256_Message_Block_Size = 64, SHA384_Message_Block_Size = 128, SHA512_Message_Block_Size = 128, USHA_Max_Message_Block_Size = SHA512_Message_Block_Size, Eastlake & Hansen Informational [Page 23]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 SHA1HashSize = 20, SHA224HashSize = 28, SHA256HashSize = 32, SHA384HashSize = 48, SHA512HashSize = 64, USHAMaxHashSize = SHA512HashSize, SHA1HashSizeBits = 160, SHA224HashSizeBits = 224, SHA256HashSizeBits = 256, SHA384HashSizeBits = 384, SHA512HashSizeBits = 512, USHAMaxHashSizeBits = SHA512HashSizeBits }; /* * These constants are used in the USHA (Unified SHA) functions. */ typedef enum SHAversion { SHA1, SHA224, SHA256, SHA384, SHA512 } SHAversion; /* * This structure will hold context information for the SHA-1 * hashing operation. */ typedef struct SHA1Context { uint32_t Intermediate_Hash[SHA1HashSize/4]; /* Message Digest */ uint32_t Length_High; /* Message length in bits */ uint32_t Length_Low; /* Message length in bits */ int_least16_t Message_Block_Index; /* Message_Block array index */ /* 512-bit message blocks */ uint8_t Message_Block[SHA1_Message_Block_Size]; int Computed; /* Is the hash computed? */ int Corrupted; /* Cumulative corruption code */ } SHA1Context; /* * This structure will hold context information for the SHA-256 * hashing operation. */ typedef struct SHA256Context { uint32_t Intermediate_Hash[SHA256HashSize/4]; /* Message Digest */ uint32_t Length_High; /* Message length in bits */ uint32_t Length_Low; /* Message length in bits */ int_least16_t Message_Block_Index; /* Message_Block array index */ /* 512-bit message blocks */ uint8_t Message_Block[SHA256_Message_Block_Size]; Eastlake & Hansen Informational [Page 24]
RFC 6234 SHAs, HMAC-SHAs, and HKDF May 2011 int Computed; /* Is the hash computed? */ int Corrupted; /* Cumulative corruption code */ } SHA256Context; /* * This structure will hold context information for the SHA-512 * hashing operation. */ typedef struct SHA512Context { #ifdef USE_32BIT_ONLY uint32_t Intermediate_Hash[SHA512HashSize/4]; /* Message Digest */ uint32_t Length[4]; /* Message length in bits */ #else /* !USE_32BIT_ONLY */ uint64_t Intermediate_Hash[SHA512HashSize/8]; /* Message Digest */ uint64_t Length_High, Length_Low; /* Message length in bits */ #endif /* USE_32BIT_ONLY */ int_least16_t Message_Block_Index; /* Message_Block array index */ /* 1024-bit message blocks */ uint8_t Message_Block[SHA512_Message_Block_Size]; int Computed; /* Is the hash computed?*/ int Corrupted; /* Cumulative corruption code */ } SHA512Context; /* * This structure will hold context information for the SHA-224 * hashing operation. It uses the SHA-256 structure for computation. */ typedef struct SHA256Context SHA224Context; /* * This structure will hold context information for the SHA-384 * hashing operation. It uses the SHA-512 structure for computation. */ typedef struct SHA512Context SHA384Context; /* * This structure holds context information for all SHA * hashing operations. */ typedef struct USHAContext { int whichSha; /* which SHA is being used */ union { SHA1Context sha1Context; SHA224Context sha224Context; SHA256Context sha256Context; SHA384Context sha384Context; SHA512Context sha512Context; } ctx; Eastlake & Hansen Informational [Page 25]