Internet.Security

152 INTERNET SECURITY

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Figure 4.13 SHA-1 operation.

Example 4.7 Let the original message be 1a7fd53b4c. Then, the final padded message consists of the following 16 words:

The initial hex values of {Hi } are

H0 = 67452301

H1 = efcdab89

H2 = 98badcfe

H3 = 10325476

H4 = c392e1f0

The hex values of A, B, C, D and E after pass t (0 ≤ t ≤ 79) are computed as follows:

154 INTERNET SECURITY

After all 512-bit blocks have been processed, the output represented by the five words, H0, H1, H2, H3 and H4 is the 160-bit message digest as shown below:

H0: 48878397

H1: 9801d679

H2: 394bd834

H3: 28c28e41

H4: 2b8dee05

The 160-bit message digest is then the data concatenation of {Hi }:

H0||H1||H2||H3||H4 = 488783979801d679394bd83428c28e412b8dee05

As discussed previously, the digitised document or message of any length can create a 160-bit message digest which is produced using the SHA-1 algorithm.

Any change to a digitised message in transit results in a different message digest. In fact, changing a single bit of the data modifies at least half of the resulting digest bits. Furthermore, it is computationally impossible to find two meaningful messages that have the same 160-bit digest. On the other hand, given a 160-bit message digest, it is also impossible to find a meaningful message with that digest.

4.5 Hashed Message Authentication Codes (HMAC)

The keyed-hashing Message Authentication Code (HMAC) is a key-dependent one-way hash function which provides both data integrity and data origin authentication for files sent between two users. HMACs have the same properties as the one-way hash functions discussed earlier in this chapter, but they also include a secret key. HMACs can be used to authenticate data or files between two users (data authentication). They can also be used by a single user to determine whether or not his files have been altered (data integrity).

To evaluate HMAC over the message or file, the following expression is required to compute:

HMAC = H [(K opad)||H [(K ipad)||M]]

where ipad = inner padding

= 0 x 36 (repeated b times)

=00110110 (0 x 36) repeated 64 times (512 bits) opad = outer padding

=0 x 5c (repeated b times)

=01011100 (0 x 5c) repeated 64 times (512 bits)

b: Block length of 64 bytes = 512 bits

h: Length of hash values, i.e. h = 16 bytes = 128 bits for MD5 and h = 20 bytes = 160 bits for SHA-1.

K: Secret key of any length up to b = 512 bits.

H : Hash function where message is hashed by iterating a basic key K.

The HMAC equation is explained as follows:

1.Append zeros to the end of K to create a b-byte string (i.e. if K = 160 bits in length

and b = 512 bits, then K should be appended with 352 zero bits or 44 zero bytes 0x00, resulting in K = (K||0x00)

2.XOR (bitwise exclusive-OR) K with ipad to produce the b-bit block computed in step 1.

3.Append M to the b-byte string resulting from step 2.

4.Apply H to the stream generated in step 3.

5.XOR (bitwise exclusive-OR) K with opad to produce the b-byte string computed in step 1.

6.Append the hash result H from step 4 to the b-byte string resulting from step 5.

7.Apply H to the stream generated in step 6 and output the result.

Figure 4.14 illustrates the overall operation of HMAC, explaining the steps, listed above.

Example 4.8 Consider HMAC computation by using a hash function SHA-1. Assume that the message (M), the key (K) and the initialisation vector (IV) are given as follows:

M: 0x1a7fd53b4c

K: 0x31fa7062c45113e32679fd1353b71264

IV: A = 0x67452301, B = 0xefcdab89, C = 0x98badcfe,

D = 0x10325476, E = 0xc3d2e1f0

Referring to Figure 4.14, the HMAC – SHA-1 calculation proceeds with the steps shown below:

K = K||(0x00 . . . 00)(512 bits)

= 31fa7062 c45113e3 2679fd13 53b71264 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000

K

Padding

h′ = 512 bits

||

160 bits (SHA-1) IV H

128 bits (MD5)

HMAC(M)

Figure 4.14 Overall operation of HMAC computation using either MD5 or SHA-1 (message length computation is based on i ||M).

i = K ipad = K (0x3636 . . . 36)

= 07cc4654 f26725d5 104fcb25 65812452 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636

M = 1a7fd53b 4c800000 00000000 00000000

00000000 00000000 00000000 00000000

00000000 00000000 00000000 00000000

00000000 00000000 00000000 00000228

i ||M :

07cc4654 f26725d5 104fcb25 65812452 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 36363636 1a7fd53b 4c800000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000228

h= H (M , IVi) = Inner SHA-1

= 9691eb0c d263a12f ab7e0e2f e60ced5f 546c857a

o = K opad = K (0x5c5c . . . 5c)

o||h :

6da62c3e 980d4fbf 7a25a14f 0feb4e38 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 5c5c5c5c 9691eb0c d263a12f ab7e0e2f e60ced5f 546c857a 80000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 000002a0

HMAC[ o||h ] = Outer SHA-1

= c19e1236 ae346195 16594259 4c5202b3 4a85c5e

The alternative operation for computation of either HMAC-MD5 or HMAC-SHA-1 is based on the following expression:

HMAC = H [H [M, (IV)i], (IV)o]

(IV)i = f[(K ipad), IV]

(IV)o = f[(K opad), IV]

K = K||(0x00 . . . 0) (512bits)

The procedure can be explained in words as follows:

1.Append zeros to K to create a b-bit string K , where b = 512 bits.

2.XOR K (padding with zero) with ipad to produce the b-bit block.

3.Apply the compression function f(K ipad, IV) to produce (IV)i = 160 bits for SHA-1.

4.Compute the hash code h with (IV)i and Mi.