Cryptography Reference
In-Depth Information
cell for partial multiplicative inversion. The fourth row is sent to
N
l
cells for
normalization, and then the other rows including the second row are sent to
E
1
l
cells for elimination. Therefore, the computation of one iteration can be
performed with one clock cycle.
...
N
1
N
2
N
11
N
12
1...
0
0
...
0
0
...
0
3
...
0...,...,...
0...
aa
a
a
a
§
·
0,1
0,12
¨
¸
...
E
1,1
E
1,2
E
1,11
E
1,12
¨
¸
1,12
¨
¸
¨
¸
2,12
¨
¸
¨
¸
3,12
¨
¸
...
E
2,1
E
2,2
E
2,11
E
2,12
¨
¸
¨
¸
aa
©
¹
11,1
11,12
...
I
E
11,1
E
11,2
E
11,11
E
11,12
Fig. 3.
Pivoting in Solving System of Linear Equations
Normalizing Operation.
The normalizing operation invokes multiplicative
inversions and multiplications, then we can enhance the implementation in two
aspects.
NOR
i
S
1
S
1
S
2
S
4
£
2
£
8
£
32
£
2
£
4
£
8
£
16
£
32
£
64
£
128
R
j
R
Fig. 4.
Optimized Normalization in Solving System of Linear Equations
First, the multiplicative inverse
β
−
1
over
GF
(2
8
) is optimized to the mul-
tiplication of 7 elements due to
β
−
1
=
β
2
β
4
β
8
β
16
β
32
β
64
β
128
, as mentioned in
Section 3.4.
Second, a new multiplier is designed to speed up the multiplication of three ele-
ments that denoted by
ThreeMult
(
v
1
,v
2
,v
3), where
v
1,
v
2and
v
3 are operands,
while the multiplication of two elements is defined by
TwoMult
(
v
1
,v
2).
