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SHA-1

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SHA-1

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  1. SHA-1 Secure Hash Algorithm 1

  2. 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 264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

  3. 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 1010 0001 0000 0011 1111 1110 0010 0011 = A103FE23. • 一個介於0到232-1的數字也可以轉換成16進位,而成為八位的Hex Digit 當一整數232<= Z? • Block = 512-bit string. 所以一個Block可以代表16個words所組成的序列.

  4. SHA-1 –Operations on Words • AND , OR, XOR, NOT • The operation X + Y (where 0 <= x < 232 and 0 <= y < 232.) • The circular left shift operation Sn(X)

  5. SHA-1 –Message Padding • 在字串後面增加“1”. “01010000”,進行此步驟後會變成 “010100001” • “0”的填置. • 01100001 01100010 01100011 01100100 01100101 (1). 61626364 65800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000. • 如果string長度小於232如上例 l = 40 • Hex過後將變成00000000 00000028. • 而完成的sequence就被之後當成M(n)使用

  6. 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).

  7. SHA-1 –Computing the Message Digest • Before processing any blocks, the H’s are initialized as follows: in hex, • H0 = 67452301 • H1 = EFCDAB89 • H2 = 98BADCFE • H3 = 10325476 • H4 = C3D2E1F0.

  8. SHA-1 –Computing the Message Digest • 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.

  9. SHA-1 –Computing the Message Digest • c. For t = 0 to 79 do s = t AND MASK; if (t >= 16) W [s] = S1 (W [(s + 13) AND MASK] XOR W [(s + 8) AND MASK] XOR W [(s + 2) AND MASK] XOR W [s]); TEMP = S5 (A) + f (t;B,C,D) + E + W [s] + K (t); 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.

  10. SHA-1 – graph

  11. SHA-1 – code • (Initialize variables:) a = h0 = 0x67452301 b = h1 = 0xEFCDAB89 c = h2 = 0x98BADCFE d = h3 = 0x10325476 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 = 0x5A827999 (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