Network Working Group D. Eastlake, 3rd Request for Comments: 3174 Motorola Category: Informational P. Jones Cisco Systems September 2001 US Secure Hash Algorithm 1 (SHA1) Status of this Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (2001). All Rights Reserved. Abstract The purpose of this document is to make the SHA-1 (Secure Hash Algorithm 1) hash algorithm conveniently available to the Internet community. The United States of America has adopted the SHA-1 hash algorithm described herein as a Federal Information Processing Standard. Most of the text herein was taken by the authors from FIPS 180-1. Only the C code implementation is "original". Acknowledgements Most of the text herein was taken from [FIPS 180-1]. Only the C code implementation is "original" but its style is similar to the previously published MD4 and MD5 RFCs [RFCs 1320, 1321]. 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 [MD4] and is modeled after that algorithm [RFC 1320]. Useful comments from the following, which have been incorporated herein, are gratefully acknowledged: Tony Hansen Garrett Wollman Eastlake & Jones Informational [Page 1] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 Table of Contents 1. Overview of Contents........................................... 2 2. Definitions of Bit Strings and Integers........................ 3 3. Operations on Words............................................ 3 4. Message Padding................................................ 4 5. Functions and Constants Used................................... 6 6. Computing the Message Digest................................... 6 6.1 Method 1...................................................... 6 6.2 Method 2...................................................... 7 7. C Code......................................................... 8 7.1 .h file....................................................... 8 7.2 .c file....................................................... 10 7.3 Test Driver................................................... 18 8. Security Considerations........................................ 20 References........................................................ 21 Authors' Addresses................................................ 21 Full Copyright Statement.......................................... 22 1. Overview of Contents NOTE: The text below is mostly taken from [FIPS 180-1] and assertions therein of the security of SHA-1 are made by the US Government, the author of [FIPS 180-1], and not by the authors of this document. This document 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 < 2^64 bits is input, the SHA-1 produces a 160-bit output called a message digest. The message digest can then, for example, be input to a signature algorithm 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. 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 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. Eastlake & Jones Informational [Page 2] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 Section 2 below defines the terminology and functions used as building blocks to form SHA-1. 2. Definitions of 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 2^32 - 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 = 2^8+2^5+2^1+2^0 = 256+32+2+1 is represented by the hex word, 00000123. 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). 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 AND Y = bitwise logical "and" of X and Y. X OR Y = bitwise logical "inclusive-or" of X and Y. X XOR Y = bitwise logical "exclusive-or" of X and Y. NOT X = bitwise logical "complement" of X. Eastlake & Jones Informational [Page 3] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 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 < 2^32 and 0 <= y < 2^32. For positive integers n and m, let n mod m be the remainder upon dividing n by m. Compute z = (x + y) mod 2^32. Then 0 <= z < 2^32. Convert z to a word, Z, and define Z = X + Y. c. The circular left shift operation S^n(X), where X is a word and n is an integer with 0 <= n < 32, is defined by S^n(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 S^n(X) is equivalent to a circular shift of X by n positions to the left. 4. Message Padding 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. 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 the length of the original message. The padded message is then processed by the SHA-1 as n 512-bit blocks. Eastlake & Jones Informational [Page 4] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 Suppose a message has length l < 2^64. 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 < 2^32 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 M(1) , M(2), first characters (or bits) of the message. Eastlake & Jones Informational [Page 5] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 5. Functions and Constants Used A sequence of logical functions f(0), f(1),..., f(79) is used in SHA-1. Each f(t), 0 <= t <= 79, operates on three 32-bit words B, C, D and produces a 32-bit word as output. f(t;B,C,D) is defined as follows: for words B, C, D, f(t;B,C,D) = (B AND C) OR ((NOT B) AND D) ( 0 <= t <= 19) f(t;B,C,D) = B XOR C XOR D (20 <= t <= 39) f(t;B,C,D) = (B AND C) OR (B AND D) OR (C AND D) (40 <= t <= 59) f(t;B,C,D) = B XOR C XOR D (60 <= t <= 79). A sequence of constant words K(0), K(1), ... , K(79) is used in the SHA-1. In hex these are given by K(t) = 5A827999 ( 0 <= t <= 19) K(t) = 6ED9EBA1 (20 <= t <= 39) K(t) = 8F1BBCDC (40 <= t <= 59) K(t) = CA62C1D6 (60 <= t <= 79). 6. Computing the Message Digest The methods given in 6.1 and 6.2 below yield the same message digest. Although using method 2 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). There are other computation methods which give identical results. 6.1 Method 1 The message digest is computed using the message padded as described in section 4. The computation is described using 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 W(0), W(1),..., W(79). A single word buffer TEMP is also employed. To generate the message digest, the 16-word blocks M(1), M(2),..., M(n) defined in section 4 are processed in order. The processing of each M(i) involves 80 steps. Eastlake & Jones Informational [Page 6] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 Before processing any blocks, the H's are initialized as follows: in hex, H0 = 67452301 H1 = EFCDAB89 H2 = 98BADCFE H3 = 10325476 H4 = C3D2E1F0. Now M(1), M(2), ... , M(n) are processed. To process M(i), we proceed as follows: a. Divide M(i) into 16 words W(0), W(1), ... , W(15), where W(0) is the left-most word. b. For t = 16 to 79 let W(t) = S^1(W(t-3) XOR W(t-8) XOR W(t-14) XOR W(t-16)). c. Let A = H0, B = H1, C = H2, D = H3, E = H4. d. For t = 0 to 79 do TEMP = S^5(A) + f(t;B,C,D) + E + W(t) + K(t); E = D; D = C; C = S^30(B); B = A; A = TEMP; e. Let H0 = H0 + A, H1 = H1 + B, H2 = H2 + C, H3 = H3 + D, H4 = H4 + E. After processing M(n), the message digest is the 160-bit string represented by the 5 words H0 H1 H2 H3 H4. 6.2 Method 2 The method above assumes that the sequence W(0), ... , W(79) 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 W(t-3), ... ,W(t-16) in step (b) are easily computed. If space is at a premium, an alternative is to regard { W(t) } as a Eastlake & Jones Informational [Page 7] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 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 M(i) is as follows: a. Divide M(i) 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 AND MASK; if (t >= 16) W[s] = S^1(W[(s + 13) AND MASK] XOR W[(s + 8) AND MASK] XOR W[(s + 2) AND MASK] XOR W[s]); TEMP = S^5(A) + f(t;B,C,D) + E + W[s] + K(t); E = D; D = C; C = S^30(B); B = A; A = TEMP; d. Let H0 = H0 + A, H1 = H1 + B, H2 = H2 + C, H3 = H3 + D, H4 = H4 + E. 7. C Code Below is a demonstration implementation of SHA-1 in C. Section 7.1 contains the header file, 7.2 the C code, and 7.3 a test driver. 7.1 .h file /* * sha1.h * * Description: * This is the header file for code which implements the Secure * Hashing Algorithm 1 as defined in FIPS PUB 180-1 published * April 17, 1995. * * Many of the variable names in this code, especially the * single character names, were used because those were the names * used in the publication. * * Please read the file sha1.c for more information. * */ Eastlake & Jones Informational [Page 8] RFC 3174 US Secure Hash Algorithm 1 (SHA1) September 2001 #ifndef _SHA1_H_ #define _SHA1_H_ #include |