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A Partial Image Encryption Method
with Pseudo Random Sequences
Y.V. Subba Rao, Abhijit Mitra, and S.R. Mahadeva Prasanna
Department of Electronics and Communication Engineering,
Indian Institute of Technology Guwahati, North Guwahati 781039, India
{subba,a.mitra,prasanna}@iitg.ernet.in
Abstract. We propose an effective approach for partial image encryp-
tion with pseudo random sequences (PRS). It is known that an image can
be considered as a combination of correlated and uncorrelated data as
well as most of the perceptual information are present in the correlated
data rather than the uncorrelated data. Hence, the amount of residual
intelligence present in an encrypted image depends on the correlated
data. It is, therefore, sufficient to encrypt the correlated data instead of
encryptingtheentireimageinordertospeeduptheentireoperation.
From the perception point of view, the most significant bit (MSB) planes
have high adjacent correlation between the pixels whereas the least sig-
nificant bit (LSB) planes contain comparatively more uncorrelated data.
PRS with simple hardware like m-sequences and Gold sequences have
less correlation between the adjacent bits. These can therefore serve as a
good alternative for partially encrypting the MSB planes with low com-
plexity to provide security against casual listeners. It is observed from
the results that the new approach is able to reduce the residual intelli-
gence as would have been obtained by encrypting the entire image.
Keywords: Partial encryption, Residual intelligence, Pseudo random
sequence.
1 Introduction
In the present era, it is important to protect the information when it is passed
through an insecure channel. One way to provide such protection is to convertthe
intelligible data into the unintelligible ones prior to transmission and such a pro-
cess of conversion with a key is called encryption [1]-[5]. Decryption is a reverse
process of the encryption. To protect the information from unauthorized users,
the key must be kept secret. Private and public key encryptions are two kinds
in cryptography. In symmetric or private key encryption [3]-[4], the encryption
anddecryptionprocessesareperformedwiththesamekey.Butinasymmet-
ric or public key encryption [2], these operations are performed with different
keys. The entire security of the encryption technique depends on the key. Fur-
ther, the security needed may be against two types of attackers, namely, casual
listeners/observers or professional unauthorized recipients, termed as cryptan-
alysts. In the former case, the security is needed only in terms of hours while
A. Bagchi and V. Atluri (Eds.): ICISS 2006, LNCS 4332, pp. 315–325, 2006.
c
Springer-Verlag Berlin Heidelberg 2006
316 Y.V. Subba Rao, A. Mitra, and S.R. Mahadeva Prasanna
in the later it may be in terms of years. The duration roughly indicates the
amount of time that is needed to analyze the information available in unintelli-
gible form in the insecure channel without the knowledge of keys to derive the
underlying information. The scenario where security is needed against casual
listener/observer, the cryptographic structure should be as simple as possible in
order to reduce the cost.
Our proposed scheme is mainly concentrated towards the private key en-
cryption. Both symmetric and asymmetric key encryption provides nearly same
amount of security. Depending on the application either of the technique is pre-
ferred. In real time applications, where security needs to be provided against
casual listeners, the encryption of the entire image with classical techniques
[6]-[8] like advanced encryption standard (AES), or, international data encryp-
tion algorithm (IDEA) are not always advantageous due to high computational
complexity. Further, in multimedia applications classical techniques consume
enough computational time for encryption due to its bulk size. Partial encryp-
tion approach therefore outperforms the conventional ones when speed is the
main criteria. In partial encryption techniques usually the significant informa-
tion have to be encrypted and insignificant information remain non-encrypted.
Considerable amount of recent research papers have focused towards different
kinds of partial encryption techniques in image processing. Such partial encryp-
tion techniques, reported in the literature [9]-[12], can be categorized into three
broad classes with the first one being encrypting only the AC-coefficients in dis-
crete cosine transform (DCT) domain. This technique, however, does not provide
sufficient security due to the perceptual information present in DC-coefficients
[9]. The next method is to encrypt the first few significant coefficients or few
subbands in wavelet domain which becomes complex in selection of significant
coefficients, and, the last one is the encryption of selective bitplanes in the im-
age with classical algorithms with high computational complexity. We focus on
a partial encryption technique with pseudo random sequences which is less com-
putationally complex yet effective. To the best of our knowledge, no work has
been reported in the literature using the same technique till now.
Pseudo random sequences (PRS) [13]-[15] are simple to generate yet offer rea-
sonably considerable security and can be produced with linear feedback shift
registers in high speed. The PRS are widely used in communications due to
their randomness based on the properties of low cross correlations. Images usu-
ally have high correlation between the neighborhood pixels, demanding the need
of sequences which would possess low adjacent correlation properties to pro-
vide sufficient security. PRS with simple hardware like m-sequences and Gold
sequences therefore emerge as a good alternative for partially encrypting the
MSB planes. It can also be observed from the results that the new approach
provides is able to reduce the residual intelligence as would have been obtained
by encrypting the entire image.
The paper is organized as follows. In Section 2, we deal with the PRS, and in
particular, m-sequences and Gold sequences. Section 3 provides the main idea
behind the partial encryption techniques at length. The proposed scheme of
A Partial Image Encryption Method with Pseudo Random Sequences 317
SS
CC C0
C1
n−1
n−1 n−2
n−2 1 0
SS
++ +
(INITIAL SEED ( which is transmitted through secured channel )
sequence
random Pseudo
Fig. 1. Block diagram of a m-sequence generator
partial encryption with PRS is introduced in Section 4. Section 5 presents the
results and also briefs about the effectiveness of the proposed scheme. The paper
is concluded by summarizing the present work along with the scope of future
work in Section 6.
2 Pseudo Random Sequences (PRS)
PRS are periodic sequences that contain the following noise like properties: (i)
balance property, (ii) single peak auto correlation function property, and, (iii)
run property. These three properties make PRS efficient for encryption. However,
due to the second property, adjacent bits’ correlation becomes considerably less,
thereby making the PRS more effective for image encryption when compared
with data encryption due to high adjacent correlation present in the images.
2.1 Maximal Length Sequences
The m-sequence generator is usually constructed with linear feedback shift reg-
isters (LFSR). The general structure of such a m-sequence generator is shown
in Fig. 1. The m-sequences are, by definition, the largest codes that can be gen-
erated by a given shift register or a delay element of given length. A m-sequence
generator contains nshift registers and is initiated with a starting seed, which is
usually transmitted through a secured channel for intended users only. The out-
puts of the shift registers are multiplied with the coefficients (Cn−1,C
n−2,...,C
1,
C0) of a primitive polynomial with respect to mod-2 operation. The resultant
output obtained by the modulo operation is then fed back to the first shift regis-
ter. The resultant output is called as m-sequence. Note that the periodicity of a
m-sequence generator is 2n−1, which, in turn, means the length of the sequence
depends on the length of the LFSR. The primitive polynomial can be also be
found from the 2nlength sequence. M-sequences contains the following two au-
tocorrelation values: 1 and −1
N. M-sequences produce the autocorrelation value
−1
Nwith even one bit delay, making the adjacent correlation value very low.
318 Y.V. Subba Rao, A. Mitra, and S.R. Mahadeva Prasanna
aaaa132
a4
b b b
324
b 1b
0
0
Fig. 2. A typical Gold sequence generator
2.2 Gold Sequences
As shown in Fig. 2 the Gold sequences can be generated by the xor operation
of the two m-sequences. Note that with only a few chosen pairs of m-sequences
we can produce the Gold sequences which are called preferred pairs. The length
of the Gold sequences is also same as the individual m-sequence’s length. But it
provides more security compared to m-sequences. Gold sequences are very simple
to generate. Using two preferred m-sequence generators of degree n, with a fixed
non-zero seed in the first generator, 2nGold codes are obtained by changing
the seed of the second generator from 0 to 2n−1. Another Gold sequence can
be obtained by setting all zero to the first generator, which is the second m-
sequence itself. In total, 2n+1 Gold codes are available. Consider an m-sequence
represented by a binary vector aof length N, and a second sequence aobtained
by sampling every qth symbol of a.Inotherwords,a=a[q], where qis odd and
either q=2
k+1orq=2
2k−2k+1. Two m-sequences aand aare called the
preferred pair if
n= 0 (mod 4) (1)
i.e., nis odd or n= 2 (mod 4). The relation between nand kin such Gold
sequences follows the below stated property.
gcd(n, k)=1fornodd
2forn=2 (mod4) (2)
Gold sequence autocorrelation Rxx(k) and cross correlation functions Rxy (k)
can be defined as
Rxx(k)=1k=0
{−t(n)
N,−1
N,t(n)+2
N}k=0 (3)
Rxy(k)={−t(n)
N,−1
N,t(n)+2
N}(4)
A Partial Image Encryption Method with Pseudo Random Sequences 319
Fig. 3. Autocorrelation function of a Gold sequence
Fig. 4. Crosscorrelation function of Gold sequences
where
t(n)=1+2
0.5(n+1) for nodd
1+2
0.5(n+2) for neven
The auto and cross correlations for one/multiple typical Gold sequence(s) of
period 219 −1areshowninFig.3andFig.4.
3 Partial Encryption Techniques
In these schemes the significant and insignificant information is separated from
the image. The significant part of the image is to be encrypted and insignificant
320 Y.V. Subba Rao, A. Mitra, and S.R. Mahadeva Prasanna
ORIGINAL
IMAGE
ENCRYPTED
IMAGE
KEY
DATA
CORRELATED UNCORRELATED
DATA
ENCRYPTION WITH
PSEUDO RANDOM
SEQUENCE
Fig. 5. Block diagram of partial encryption technique
part remains non-encrypted. After the encryption the significant and insignifi-
cant parts are combined before transmission. This encrypted image is transmit-
ted through an insecure channel to the receiver. At the receiver the encrypted
image is again decomposed into significant and insignificant components, the
decryption operation is performed only on significant part and then combined
to get original image. If the significant information is very less the public key
encryption techniques will be preferred or otherwise the private key techniques
are often used.
4 The Proposed Scheme
In the proposed scheme, the image is initially separated into correlated and
uncorrelated data by dividing it into first four MSB planes and last four LSB
planes. The correlated data (first four MB planes) are encrypted with the highly
uncorrelated PRS while keeping the uncorrelated data as unencrypted ones.
After the encryption of correlated data, it is combined with the remaining data
to form the final encrypted image. The block diagram of the proposed scheme
is shown in Fig. 5. In the present work we consider the first four MSB planes as
correlated data as it is seen that for reducing the residual intelligence as could
be obtained by encrypting the entire image, we need to encrypt a minimum of
these four bit planes. Here first we encrypt the MSB planes of the image with
the m-sequence generated by the pseudo random generator as shown in Fig. 1.
A Partial Image Encryption Method with Pseudo Random Sequences 321
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Fig. 6. Decomposition of image. (a) Original image. (b)-(i) The bitplanes starting from
the MSB to LSB planes respectively.
4.1 Partial Encryption with Gold Sequences
M-sequences can be estimated if some part of the sequence is known. To over-
come this disadvantage, the length of LFSR should be large. Therefore, encryp-
tion with m-sequence trades off security against the length of the shift register.
One good alternative to overcome this problem is to use Gold sequences. With
four different auto correlation values, sometimes Gold sequences produce ad-
jacent correlation less than the m-sequence. Due to less adjacent correlation
Gold sequence offers more security and removes the redundancy better than m-
sequences. The adjacent correlation will be very high in first four MSB planes
compared to the remaining bitplanes. After the encryption, the correlation de-
creases very significantly and achieves nearly equal to the LSB planes.
5 Results and Discussions
The proposed scheme has been implemented in the Matlab with several test
images. Below are some results applied on the standard Peppers gray scale image.
The Fig. 6 shows the bit planes in the Peppers image. The most significant
bitplanes have high adjacent correlation between the bits and least significant
bitplanes have very less correlation. So they appear as noisy bitplanes.
5.1 Partial Encryption with M-Sequences
We can observe that the adjacent correlation is present in the first four bit-
planes in Fig. 6. Fig. 7 shows the partial encryption of image. The bit planes
322 Y.V. Subba Rao, A. Mitra, and S.R. Mahadeva Prasanna
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Fig. 7. Partial encryption with m-sequences. (a) Original image. (b, d, f, h) Bit planes
to be encrypted from the MSB plane. (c, e, g, i) Encrypted images using the combina-
tion of encrypted and remaining bit planes.
to be encrypted and encrypted images after combining the encrypted and un-
encrypted bit planes are shown in Fig. 7. After the encryption of the first two
MSB planes the encrypted image appears as the noisy image. However, it is also
necessary to encrypt the third and fourth MSB planes because these planes have
some perceptual information. The resultant image doesn’t have the significant
information after the encryption of four MSB plane. Fig. 8 shows the decryption
process of the partial encryption. If the correlation is measured among the pixels
in the encrypted images, it will be found that, compared to original image, the
correlation decreases significantly. But the correlation among the pixels in the
image after the encryption of first four bitplanes is nearly same as that of the
encryption of all bitplanes.
5.2 Partial Encryption with Gold Sequences
Fig. 9 shows the original image, the bit planes to be encrypted and the en-
crypted images after combining the encrypted and unencrypted bit planes. The
encrypted image after encryption of first four bit planes has no perceptual infor-
mation. The redundancy reduces in the encrypted bitplanes and the encrypted
image appeared as a random noisy image. The decryption process of the partial
encryption with Gold sequences is shown in Fig. 10. The adjacent correlation of
the encrypted bitplanes and encrypted images contains very less value compared
to the images encrypted with m-sequences.
A Partial Image Encryption Method with Pseudo Random Sequences 323
(a) (b) (c)
(d) (e) (f)
(g) (h)
Fig. 8. Decryption of partial encryption with m-sequences. (a, c, e, g) Decrypted bit
planes from the MSB plane. (b, d, f, h) Decrypted images using the combination of
decrypted and the remaining bitplanes.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Fig. 9. Partial encryption with Gold sequences. (a) Original image. (b, d, f, h) Bit
planes to be encrypted from the MSB plane. (c, e, g, i) Encrypted images using the
combination of encrypted and remaining bitplanes.
324 Y.V. Subba Rao, A. Mitra, and S.R. Mahadeva Prasanna
(a) (b) (c)
(d) (e) (f)
(g) (h)
Fig. 10. Decryption of partial encryption with Gold sequences. (a, c, e, g) Decrypted
bit planes from the MSB bitplane. (b, d, f, h) Decrypted images using the combination
of decrypted and the remaining bitplanes.
6 Conclusions
A simple yet effective technique for partial image encryption is proposed. The
main idea stems from the fact that the most information in an image is present
in the correlated data. This information is converted into unintelligible form by
encrypting with the uncorrelated sequences. This paper has presented an ap-
proach for the partial encryption of image using pseudo random sequences with
simple hardware. From the results, it is observed that partial encryption method
achieves the same security with the improvement in processing speed. The per-
formance of the method mainly depends on the differentiation of correlated and
uncorrelated information in the image. Here we have treated the MSB planes as
correlated information. However, even in MSB planes sometimes uncorrelated
data are present. A better approach might reduce the computational time fur-
ther if proper importance is given for separating the correlated data in the image
considering the above point.
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