Information Technology Reference
In-Depth Information
Table 2.
Results of Result 3(a) and 3(b) on CAA and MD5
Input
Result 3(a)
Result 3(b)
size
No. of ones for CAA
No. of
No. of ones for CAA
No. of
) ones for (
C
K
(
M
)
⊕ C
K
(
M
) ones for
file in key-length 128 key-length 256 MD5 key-length 1 28 key-length 256 MD5
bytes p=4 p=8 p=8 p=16 128 bit p=4 p=8 p=8 p=16 128 bit
3239 34
of
(
C
K
(
M
)
⊕ C
K
(
M
70
128 122
69
54
63
134 130
64
3239 56
67
124 132
69
70
66
140 132
69
3239 45
66
122 138
70
52
64
136 126
66
65780 55
76
114 138
64
64
66
130 142
70
65780 57
65
140 128
65
45
64
104 134
68
65780 59
65
118 140
67
66
63
118 120
62
259120 38
62
134 136
70
46
69
122 126
67
259120 51
64
130 130
65
55
64
132 128
66
259120 55
66
132 132
67
48
70
140 128
76
For example, let the length ofthe plain text and message digest are of8 bit
and the fixed bit difference
D
taken as 3. For a pair ofplaintexts X=11001011,
X
=10011001, corresponding message digests are (say)
MD
=00110101,
MD
is
calculated for all plaintext pairs with
D
=3. Then from the distribution of
D
=10000110, i.e, with difference
D
=5. The value of
D
,
we can calculate the standard deviation (
σ
). In general, a one-way hash function
is said to be protected from differential cryptanalytic attack if
σ
is lower than
10 % [12].
We have performed differential cryptanalysis on our scheme with 50 different
files having 5 different size. For each file, we take 5 different fixed input differ-
ences. Table 3 depicts results ofdifferential cryptanalysis on CAA. From Table
3 (Column 2 to 7) this is clear that as
p
increases (
p
is the dimension ofGalois
field GF(2
p
))
σ
decreases. The experimental results at Table 3 establish that
CAA
can defend differential attack in a better way than MD5 (Column 6).
Execution time
Comparative results for GF(2) CA based authentication algorithm [9], MD5 and
CAA at GF(2
p
) in respect of
CPU time
are displayed in the Table 3 (Column
9 to 13). These experimental results establish the higher speed ofexecution of
CAA scheme based on GF(2
p
)
SACA
. Higher value of
p
leads to reduction of
computation time because rather than handling
np × np
matrix with GF(2) el-
ements we deal with
n × n
matrix with GF(2
p
) elements. In software the speed
is almost one and halftimes more than MD5 at
p
=16. The throughput ofthe
Hardwired implementation ofscheme is ofthe order oftens ofGigabits/sec.
3.4
CAA for Watermarking
Digital watermarking research has generally focused upon two classes of water-
marks, fragile and robust. Fragile watermarks is ideal for image authentication
applications [13,14]. In this watermarking it allows a user with an appropriate
