Cryptography Reference
In-Depth Information
Tabl e 2.
Number of Multiplications in
L
1
−
1
,
L
2
−
1
Ane Transformations and Poly-
nomial Evaluations
Components
Number of multiplications
L
1
−
1
transformation
576
The first 12 polynomial evaluations
6324
The second 12 polynomial evaluations
15840
L
2
−
1
transformation
1764
Total
24504
the most time-consuming operation in these computations. Table 2 summarizes
the numbers of multiplications in two ane transformations and polynomial
evaluations. The number of multiplications of the components of polynomial
evaluations is summarized in Table 3.
Tabl e 3.
Number of Multiplications in Components of Polynomial Evaluations
The first layer The second layer
V
i
O
j
2448
4320
V
i
V
j
3672
11160
V
i
204
360
Total
6324
15840
4
Implementations and Experimental Results
4.1 Overview of Our Implementation
Our design is programmed in VHDL and implemented on a EP2S130F1020I4
FPGA device, which is a member of ALTERA Stratix II family. Table 4 summa-
rizes the performance of our implementation of Rainbow signature measured in
clock cycles, which shows that our design takes only 198 clock cycles to generate
a Rainbow signature. In other words, our implementation takes 3960
ns
to gen-
erate a Rainbow signature with the frequency of 50 MHz. All the experimental
results mentioned in this section are extracted after place and route.
Tabl e 4.
Running Time of Our Implementation in Clock Cycles
Steps
Components
Clock cycles
L
1
−
1
transformation
1
5
2
The first 12 polynomial evaluations
45
3
The first round of solving system of linear equations
12
4
The second 12 polynomial evaluations
111
5
The second round of solving system of linear equations
12
L
2
−
1
transformation
6
13
Total
198
