IEEE Consumer Electronics Magazine - January/February 2022 - 48

Metaheuristic Methods Can Decrease the Probability of Weak Keys Being Generated
Table 2. Comparison of counts of weak keys.
GA-based
encryption
DES PSO GA SA
Figure 5. Comparison of key similarity.
1 10 0
2 20 0
3 30 0
4 20 0
5 11 0
6 30 0
7 10 0
8 20 0
9 31 0
10 20 0
Total
20
Figure 6. Comparison of convergence rate.
improve the ability of global search such as
crossover, but this operator may break the continuity
structure of the solution. Therefore, the
best solution was found by GA, but overall its
quality is not very stable. PSO itself is a search
method designed to solve the numerical function
optimization problem so that PSO will be
weak in dealing with discrete problems like this
study. Fortunately, the results of PSO are still
better than DES and GA-based encryption. This
shows that the proposed framework can effectively
improve the dissimilarity of keys.
Figure 6 shows a comparison of convergence
curves of SADES, GADES, and PSODES. SADES will
execute 800 iterations. We can see that SADES
has a very fast convergence rate within 0-300 iterations.
However, due to the limitation of global
search ability of single-solution, after 300 iteration,
the frequency with which this method
climbs up sharply decreases. Finally, it will converge
at approximately 20,200 at 800th iterations.
Compared to GADES, the growth trend of GADES
is more stable and fast. Because GA is a population-based
algorithm, it is unfair to compare with
the same times of iterations as SADES. Although
there are 2 chromosomes interacting in each iteration,
we use 4 chromosomes to compare in the
competition law, which means we should use
quarter of SADES, about 200 times. It will converge
at approximately 19,000 at the 180th
iteration. PSODES is also a population-based
48
algorithm, it will use 12 particles to search at the
same time; hence, the iteration setting is 1/12 of
SADES, about 67. However, current encoding
design is more suitable for the discrete problem
such that although PSODES has a quite good convergence
rate, it is only convergent in 11,400.
As the mentioned before, the weak keys are a
fatal risk to security. In Table 2, we conducted
experiments on the number of weak key generations.
We can see that although GA-based encryption
can increase the complexity of keys via a
random process, it has 20 weak key occurrences
due to using of Shannon entropy. It means that it
still has the risk of being cracked. DES will also
have two weak key occurrences, indicating that it
is also insecure. The framework proposed in this
study, no matter which method, can effectively
avoid the generation of weak keys.
CONCLUSION
In response to the changes in human life habits,
people hope that they can get a response in time
when using consumer electronics products. In
order to meet this requirement, the symmetric
encryption is a first choice for providing faster and
more convenient encryption. However, the existing
symmetric encryption methods usually have more
linear process so that this kind of encryption ways
have a higher probability of generating continuous
weak keys. In short, the randomness of such methods
is not high, and the possibility of being cracked
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