IEEE Consumer Electronics Magazine - January/February 2022 - 45

making it more likely to be deciphered. Based on
this observation, we can boldly assume that as
long as the number of interleaving increases, the
more blocks are enclosed, the larger the total area,
the greater the difference that is expressed by the
purple line, which represents the expected key. All
in all, we can evaluate the quality and dissimilarity
of the key through a numerical value of the combined
area, the number of interleaving, and the
slope of curves. Therefore, the normalized Linear
Programming model of this problem can be shown
as follows.
Maximize G
s:t:
0 Fi;j 255
C 0
0:
The dissimilarity value G can be defined as
follows:
G ¼ð1 þÞ
Xn
i¼0
Xm
j¼0
Fi;jjxp
i;j xk
i;jjð1 þCÞ
(1)
where G is a dissimilarity value. is the number
of interleaves between the plaintext line and the
key line. Fi;j represents the area of line segments
i to j. xp
segments i to j and xk
i;j represents the slope of plaintext line
i;j represents slope of generated
key line segments i to j. If the slopes of
these two curves are closer, the difference will
be zero. This means that the greater the slope,
the greater the difference. The length of the key
is represented by n. Then, we define the C variable
to make the characteristics of the area
prominent as well as highlight the case that
there is no intersection as follows:
C ¼
jFi;kFk;jj
127
0;
; Segments i; j has intersection k :
otherwise
(2)
Line segmentij will be segmented into the two
areas according to the reference point k. Since
there may be an oscillating relationship between
two curves, the similarity judgment will be
affected by such a phenomenon. In order to be
able to distinguish these impact factors, the two
areas must be subtracted to take the absolute
value and divided by 127. On the contrary, if there
January/February 2022
is no any intersections existing in any line segments
ij, the value is represented by 0 since the
similarity is regarded as large. Finally, in order to
avoid that each bit of the generated solution is
always at the extreme value (although the curve
segment will still oscillate, this key will be deciphered
easily due to higher regularity) we first
take the absolute value of the key, and then
decide whether to accept the penalty mechanism
according to the threshold t:
t ¼ 127 h:
(3)
Range of the random value h is 0-10, and the
maximum value of each unit is limited to 127.
When a value is greater than t, it indicates that it
may be closer to the extreme. However, if more
bits of a key are close to the extreme value, the
resulting area may seem large, but it is unbelievable.
Therefore, a punishment mechanism must
be used. When the value in the key bit reaches
the extreme, the key score will be decreased:
G ¼ G vd
(4)
where d is the count of occurrences that the value
is greater than t and v represents a penalty value
between 0 and 1 that v makes the negative influence
be decreased exponentially when the value
of many key bits exceeds t. It means that when
the number of occurrences is more, the area is
smaller and the influence is also lower. After
many tests in this study, it is recommended that
v should be greater than 0.8 as much as possible.
PROPOSED METAHEURISTIC-BASED
KEY GENERATION FRAMEWORK
After the fitness function is set, this problem
can be solved through the metaheuristic algorithm.
The metaheuristics have a generic framework
including three operators such as Transition, Evaluation,
and Determination.13 Transition describes
how a new combination of solution is generated by
the old solution. The old solution carried many historical
information so that the new solution avoids
to fall into the local optimum and always searches
in a better direction. As the evaluation's name
implies, this operator aims to judge the pros and
cons of the new solution and the old solution
through the specially designed fitness function.
Then determination is the part to make a decision
after looking at the quality of the solution.
45
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