SHA-1

1
SHA-1

• Secure Hash Algorithm 1

2
SHA-1 Brief Introduction

• ?????????? (NSA) ??,???????????? (NIST)
  ????????????,???1993?
• ????? 264 ?????????? 160 ?????
• ?? MD4 ? MD5 ???????? MIT ?? Ronald L. Rivest
  ???????????

3
SHA-1 Definitions of Bit Strings and Integers

• Hex Digit?16??,??4-bit?string??
  7 0111, A 1010
• ??word????32-bit?string,??4-bit?????Hex Digit
  1010 0001 0000 0011 1111 1110 0010 0011
  A103FE23.
• ????0?232-1?????????16??,??????Hex Digit
  ????232lt Z?
• Block 512-bit string. ????Block????16?words?????
  ?.

4
SHA-1 Operations on Words

• AND , OR, XOR, NOT
• The operation X Y (where 0 lt x lt 232
  and 0 lt y lt 232.)
• The circular left shift operation Sn(X)

5
SHA-1 Message Padding

• ???????1.
  01010000,????????? 010100001
• 0???.
• 01100001 01100010 01100011 01100100 01100101 (1).
  
• 61626364 65800000 00000000 00000000 00000000
  00000000 00000000 00000000 00000000 00000000
  00000000 00000000 00000000 00000000.
• ??string????232??? l 40
• Hex?????00000000 00000028.
• ????sequence??????M(n)??

6
SHA-1 Functions and Constants Used

• ?SHA-1????f (0), f (1)f (79)
  ???????as a 32-bit word as output f (tB,C,D)
• F (tB,C,D) (B AND C) OR ((NOT B) AND D) ( 0 lt
  t lt 19)
• F (tB,C,D) B XOR C XOR D (20 lt t lt 39)
• F (tB,C,D) (B AND C) OR (B AND D) OR (C AND D)
  (40 lt t lt 59)
• F (tB,C,D) B XOR C XOR D (60 lt t lt 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 lt t lt 19)
• K (t) 6ED9EBA1(20 lt t lt 39)
• K (t) 8F1BBCDC(40 lt t lt 59)
• K (t) CA62C1D6(60 lt t lt 79).

7
SHA-1 Computing the Message Digest

• Before processing any blocks, the Hs 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 W0, ... , W15,
  where W0 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 gt 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 (tB,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 ltgt 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 lt i lt
  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 232) where (0 lt i
  lt 19) f(b,c,d) (b and c) or ((not b) and d),
  k 0x5A827999 (20 lt i lt 39) f(b,c,d) (b xor
  c xor d), k 0x6ED9EBA1 (40 lt i lt 59)
  f(b,c,d) (b and c) or (b and d) or (c and d), k
  0x8F1BBCDC (60 lt i lt 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