IEEE Consumer Electronics Magazine - January/February 2022 - 46

Metaheuristic Methods Can Decrease the Probability of Weak Keys Being Generated
Figure 2. Metaheuristic-based key generation framework.
Figure 2 shows a metaheuristic-based key
generation framework including the abovementioned
three important operators. These operators
may change slightly in response to different
problems. The following are the characteristics
of the key generation operators.
1) Transition: In transition, the first step is to digitalize
the consumer's plaintext for mapping
into a two-dimensional Euler coordinates. The
X-axis represents the length of the plaintext,
and theY-axis reflects the value of each character.
For example, " ABC " has three bytes characters
and their digitalization are 65, 66, and 67 in
the decimal ASCII. In this way, we can obtain a
curve of the plaintext, then the point value on
this curve can be regarded as the initialization
of the solution encoding of the algorithm so
that the ciphertext will be generated based on
this solution. Each value can be adjusted up or
down freely according to the chosenmetaheuristics.
For example, if there is a curve c1 ¼
½65; 66; 67; 68; 69; 70 that is undergoing mutation,
a position will be chosen and then a random
value is added, which is restricted to a
range. The random value can be positive or
negative. If the random position is 3, the random
value is10. Then this solution will
become c
are shown in the bold arrow in the Transition
layer of Figure 2.
2) Evaluation: After the process of transition, a
new ciphertext will be generated so that there
are two or more curves in the coordinates after
two or more iterations. The value of any position
in the solution is the Y-axis coordinate in
this two-dimensional space, and the X-axis
coordinate is the index value of the position.
46
Therefore, we can easily obtain the position of
any intersection, the area of any block enclosed
by two curves, and the slope of any curve. Next,
we can begin to calculate the fitness values
according to the area enclosed by these curves
and the original curve via the proposed similaritymodel
that are shown in (1)-(4).
3) Determination: Determination aims to compare
and choose an acceptable key through
the calculated pros and cons from an Evaluation
operator and then record the best result
to date in this moment. Then the selected
key will be used as input for the next iteration.
Usually, the selected key is the best one
so far. However, in order not to fall into the
local optimum, it is possible to accept the
second best key for discovering the new key
so that the overall global search and local
search can be balanced.
1 ¼½65; 66; 57; 68; 69; 70. The details
After the abovementioned process of metaheuristic-based
key generation, a best key will
be found, which has higher dissimilarity. The
quality of the found key depends on the encoding
ways. This study uses a decimal code, which
provides more intuitive visualization. If a higher
hexadecimal approach is chosen, it can make
the area-based dissimilarity model more accurate.
But if the binary method is chosen, the
diversity of the area model may decrease. In
addition, this study adopts a discrete combinatorial
optimization problem definition so that it
allows the change of the key value to converge
within a countable range; hence, it is more difficult
to find the best solution for some metaheuristics,
which are suitable for the continuous
problems such as particle swarm optimization
(PSO). Fortunately, the result will still be better
than the original encryption method.
IEEE Consumer Electronics Magazine
IEEE Consumer Electronics Magazine - January/February 2022

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