Encryption algorithms on BMP and JPEG images
SARA CHILLALI, LAHCEN OUGHDIR
Sidi Mohamed Ben Abdellah University
FP, LSI, TAZA, MOROCCO
Abstract: - In this article we carried out a comparative study between certain encryption algorithms on BMP
and JPEG images, we established a comparison between certain types of encryption systems and our algorithm.
We made the comparison with data implemented on the same computer and our implementation.
Key-Words: -Image, Algorithm, Encryption, Comparative.
Received: March 16, 2021. Revised: January 7, 2022. Accepted: January 25, 2022. Published: February 18, 2022.
1 Introduction
As you The need for disk space envisaged by the
storage or the transmission of a digital image or any
other graphic form comprising thousands of bytes
and at a rate more than 500 images per day, we let
think about the good encryption of this data
produced for stokers in a confidential way, without
someone being able to see or use them other than
those who have the right of access. This problem is
supposed to be solved by a few encryption
algorithms. In order to prove the performance of our
encryption algorithm, we made a comparison
between some algorithms already implemented and
our.
The comparison will be made on several points and
according to certain criteria; (see [4, 5]):
• Type and size of keys.
• The visibility and performance of the encryption
operation applied to the image.
• The encryption and decryption time.
• Type and size of images (BMP or JPEG).
• Comparison graph.
For symmetrical systems:
Simple algorithms use any keys.
Secret key algorithms:
DES (64 bits)
3-WAY (96 bit)
RC5 (128 bit)
IDEA (128 bit)
On the other hand, asymmetric systems call on
arithmetic operations based on finite fields, the
factorization of large numbers into two prime
numbers, elliptic curves ..., the size of an RSA key
of 1024 bits corresponding to a size of 256 bits for
elliptical curves.
2 Encryption and Decryption
Algorithms
2.1 Problem Formulation
Find a method of encryption and decryption to keep
encrypted images without anyone being able to see
or use them other than those who have the rights of
access to information, add more these methods must
be effective and better than the already existing.
2.2 Problem Solution
In our article [1, 2], we established an encryption
method based on matrices, in this part we present
another method using elliptic curves.
Let an elliptic curve on the field where
is a large prime number, such that discrete logarithm
problem in is difficult. [2, 6]
Using a Diffie–Hellman key exchange, see [2, 3], on
such a chosen curve we can build a secret key
which allows us to generate a secret matrix to
encrypt and decrypt our images. Suppose Ali has
created such a secret key and shares it
with the people who have the right to access the
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DOI: 10.37394/232014.2022.18.3
Sara Chillali, Lahcen Oughdir
E-ISSN: 2224-3488
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encrypted database. Ali wants to stock an image
confidentially « img », it follows the structure of the
proposed algorithm which consists of five
encryption steps, as described by:
Setp1 :
Turn the image, img into a matrix ;
This matrix is obtained from the
transformation of the original image into matrix.
Setp2 :
For each calculate :
Setp3 :
Pixel 0 receives the value ,
for i from 1 to 255 do,
pixel i receives the value ,
if is already taken by a pixel then pixel
i receives the value , so the pixels
will be transformed to
where and for i from 1 to 255,
Setp4 :
In class in ascending order, the
smallest value receives the pixel 0, the next value
receives the pixel 1 so on, the last value receives the
pixel 255.
Setp5 :
The bijective function defined by:
; is the value
of the pixel establish in setp4, we transform the
matrix by the function to the matrix
.
The matrix , thus constructed represents ;
"cryptimg" the encrypted image of "img".
Decryption Algorithm :
A person who wants to use a stored image;
"cryptimg" encrypted by Ali, it has the private
key which allows it to calculate the reciprocal
function of ; and find the matrix
, that we can transform it to the
image "img".
3 Comparison of the Encryption
Quality
To study the performance of the encrypted image,
we divide the performance of the encrypted image
into four categories, Excellent, Good, Average and
Bad, then assign each category a statistical class in
the interval form of our choice as follows:
Excellent:=]15,20]; Good:=]12,15]; Way:=]8,12];
and Bad:=]0,8].
3.1. Encryption Len Image
In this sub-section, we present the results of the
encrypted images obtained from different types of
standard Lena image, the results are presented as
follows:
Fig.1: Encrypt Lena Image by our Algorithm
Fig. 2: Encrypt Lena Image by various Algorithms
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Fig. 3: Encrypt Lena (type) by various Algorithms
3.2 Results Interpretation
The results of the performance of the encrypted
image are grouped in the following table:
Table 1. Performance of the encrypted image
Encryption
method
Image
1
2
NG
Image
2
16N
G
Image
3
256
NG
Image
4
Colo
r
Lena
JPE
G
Lena
256
grays
cale
our method
]15,20]
]15,20]
]15,20]
]15,20]
]15,20]
]15,20]
or exclusive
]0,8]
]0,8]
]0,8]
]0,8]
]0,8]
]0,8]
substitution
]0,8]
]8,12]
]15,20]
]15,20]
]0,8]
]8,12]
RSA
]0,8]
]0,8]
]8,12]
]8,12]
]8,12]
]12,15]
transposition
]0,8]
]0,8]
]8,12]
]12,15]
]8,12]
]0,8]
Let X be the mean of this performance, which we
will calculate for each algorithm and then conclude
the performance of each algorithm from the interval
where X belongs, the results are gathered in this
table which follows:
Table 2. Mean : X
Encryption method
X
Performance
our method
]15,20]
Excellent
or exclusive
]0,8]
Bad
substitution
]8,12]
Way
RSA
]8,12]
Way
transposition
]0,8]
Bad
3.3 Interpretation
The quality of the image encryption
operation by our secret key encryption
algorithm is better compared to
conventional encryption algorithms such as
transposition, substitution, or exclusive and
RSA.
The higher the gray level, the better the
quality for encryption.
The quality of the image encryption
operation by our secret key encryption
algorithm is better compared to
conventional encryption algorithms such as
transposition, substitution, or exclusive and
RSA.
4 Comparison of Execution Times of
Different Algorithms
We will do a calculation of the encryption and
decryption time between these different encryption
algorithms, then give an interpretation of the results
obtained, also increasing the size of the image to be
encrypted ; noted that 1 Ko = 8000 bit, which is
what we get for this encryption time. The results are
grouped in the following tables:
Table 3. The encryption time in seconds
Encrypti
on
method
Image
6464
(12 Ko)
Image
128128
(48Ko)
Image
256256
(192 Ko)
Image
512512
(768Ko)
Our
method
0.010
0.085
0.125
0.677
or
exclusive
0.028
0.176
0.625
1.641
substituti
on
0.028
0.185
0.625
1.656
RSA
0.052
0.453
0.877
2.937
transposi
tion
0.028
0.185
0.625
1.677
Table 4. The decryption time in seconds
Decryption
method
Image
6464
(12Ko)
Image
128128
(48 Ko)
Image
256256
(192Ko)
Image
512512
(768Ko)
Our method
0.010
0.085
0.125
0.677
or exclusive
0.060
0.192
0.625
1.641
substitution
0.062
0.203
0.630
1.676
RSA
0.092
0.520
0.911
3.256
transposition
0.062
0.203
0.630
1.677
Remark:
According to the results obtained in the calculation
of encryption and decryption time between these
different encryption algorithms, we remark that:
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- The encryption algorithms like transposition,
substitution and RSA are slower than our encryption
algorithm.
- Note also that each time increases in the size of the
image to be encrypted, obtains a greater encryption
time.
- In the comparison between the two encryption and
decryption tables, note that the encryption time and
faster compared to the decryption time in these
algorithms except in our algorithm where we have
the equality of the two times.
Open Problem :
Find an encryption algorithm for images better than
existing algorithms and rank existing algorithms
according to their efficiency.
5 Conclusion
In this study, the ECC image encryption technique
was proposed. Thus, the effectiveness of this type of
encryption was studied and we established a
comparison between certain types of encryption
systems and our algorithm.
References:
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[2] Chillali, S., Oughdir, L., “ECC Image
Encryption Using Matlab Simulink Blockset”,
Lecture Notes in Networks and Systems, 2021,
211 LNNS, pp. 835–846, DOI: 10.1007/978-3-
030-73882-2_76
[3] Diffie, W., Hellman, M.,”New directions in
cryptography”, IEEE Transactions on
Information Theory, (1976).
[4] Keinert, J., Teich, J.,”Design of Image
Processing Embedded Systems Using
Multidimensional Data Flow”, Springer New
York, (2011).
[5] Haouzia, A., Noumei, R.,”Methods for image
authentication: a survey”, Multimed Tools
Appl. 39(146), (2008).
[6] Silverman, J.,‘The Arithmetic of Elliptic
Curves’, Graduate Texts in Mathematics,
Springer, (2009).
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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