SHA-1 Secure Hash Algorithm 1

SHA-1 – Brief Introduction 家族是美國國家安全局 (NSA) 設計，美國國家標 準與技術研究院 (NIST) 發佈的一系列密碼雜湊函 數，發表於 1993 年 從一個最大 2 64 位元的訊息中產生一串 160 位元 的摘要 設計 MD4 及 MD5 訊息摘要演算法的 MIT 教授 Ronald L. Rivest 類似的原理為基礎來加密

SHA-1 – Definitions of Bit Strings and Integers Hex Digit 為 16 進位，可用 4-bit 的 string 表現 7 = 0111, A = 1010 一個 word 可表示成 32-bit 的 string ，而每 4-bit 就等同一 個 Hex Digit = A103FE23. 一個介於 0 到 的數字也可以轉換成 16 進位，而成 為八位的 Hex Digit 當一整數 2 32 <= Z? Block = 512-bit string. 所以一個 Block 可以代表 16 個 words 所組成的序列.

SHA-1 – Operations on Words AND, OR, XOR, NOT The operation X + Y (where 0 <= x < 2 32 and 0 <= y < 2 32.) The circular left shift operation S n(X)

SHA-1 – Message Padding 在字串後面增加 “1”. “ ”, 進行此步驟後會變成 “ ” “0” 的填置 (1) 如果 string 長度小於 2 32 如上例 l = 40 Hex 過後將變成 而完成的 sequence 就被之後當成 M(n) 使用

SHA-1 – Functions and Constants Used 在 SHA-1 裡方程式 f (0), f (1)……f (79) 每一個方程式解 as a 32-bit word as output f (t;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).

SHA-1 – Computing the Message Digest Before processing any blocks, the H’s are initialized as follows: in hex, H0 = H1 = EFCDAB89 H2 = 98BADCFE H3 = H4 = C3D2E1F0.

SHA-1 – Computing the Message Digest MASK = F. 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.

SHA-1 – Computing the Message Digest 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.

SHA-1 – graph

SHA-1 – code (Initialize variables:) a = h0 = 0x b = h1 = 0xEFCDAB89 c = h2 = 0x98BADCFE d = h3 = 0x e = h4 = 0xC3D2E1F0 (Pre-processing:) paddedmessage = (message) append 1 while length(paddedmessage) mod 512 <> 448: paddedmessage = paddedmessage append 0 paddedmessage = paddedmessage append (length(message) in 64-bit format) (Process the message in successive 512-bit chunks:) while 512-bit chunk(s) remain(s): break the current chunk into sixteen 32-bit words w(i), 0 <= i <= 15 (Extend the sixteen 32-bit words into eighty 32-bit words:) for i from 16 to 79: w(i) = (w(i-3) xor w(i-8) xor w(i-14) xor w(i-16)) leftrotate 1 (Main loop:) for i from 0 to 79: temp = (a leftrotate 5) + f(b,c,d) + e + k + w(i) (note: all addition is mod 2^32) where: (0 <= i <= 19): f(b,c,d) = (b and c) or ((not b) and d), k = 0x5A (20 <= i <= 39): f(b,c,d) = (b xor c xor d), k = 0x6ED9EBA1 (40 <= i <= 59): f(b,c,d) = (b and c) or (b and d) or (c and d), k = 0x8F1BBCDC (60 <= i <= 79): f(b,c,d) = (b xor c xor d), k = 0xCA62C1D6 e = d d = c c = b leftrotate 30 b = a a = temp h0 = h0 + a h1 = h1 + b h2 = h2 + c h3 = h3 + d h4 = h4 + e digest = hash = h0 append h1 append h2 append h3 append h4