In this paper, we propose an accumulation encoding scheme based on double random phase encryption (DRPE) for multiple-image transmission. The proposed scheme can be used for a low-complexity DRPE system due to the simple structure of the accumulation encoder and decoder. For accumulation encoding of multiple images, all of the previously encrypted data are added, and hence the accumulation encoding can improve the security of the DRPE-encrypted data. We present a scheme for encryption and decryption for DRPE-based accumulation encoding, and a method for accumulation encoding and decoding. Finally, simulation results verify that the DRPE-based accumulation encoding scheme for multiple images is powerful in terms of data security.
I. INTRODUCTION
Information security is one of the most important issues in data transmission. Optical encryption has been widely investigated for information security because of its high encryption speed
[1
-
23]
. As a representative optical encryption technique, double random phase encryption (DRPE) has been well studied
[1
-
21]
and improvements have been developed, such as DRPE using the Fresnel domain
[2]
, DRPE using a full-phase processor
[3]
, DRPE using digital holography
[4
,
5]
, photon-counting DRPE
[6
,
7]
, and DRPE using fractional Fourier transform
[8
-
10]
.
Since DRPE uses double random phase masks for encryption, a security defect can be introduced
[11]
, so updating the phase masks is required to resolve the security problem. However, such a resolution may lead to a cost problem. Therefore, advanced DRPE techniques without phasemask updating have been introduced
[8
-
10
,
18
-
21]
. In particular, DRPE using fractional Fourier transform has been presented
[8
-
10]
to enhance the security of DRPE systems, where security is improved by increasing the number of encryption parameters. However, DRPE systems using fractional Fourier transform can be more complicated because of many encryption parameters. Hence, DRPE using orthogonal encoding has been presented as a low-complexity DRPE system in which the orthogonal encoder contains simple linear functions
[20
,
21]
.
In this paper we propose a DRPE-based accumulation encoding scheme for multiple-image transmission. It can be considered a low-complexity DRPE scheme because of the simple structure of its accumulation encoder and decoder. In addition, data security can be enhanced by introducing accumulation encoding into DRPE. We provide a detailed method for DRPE-based accumulation encoding and decoding, and show simulation results verifying that decryption of the image encrypted by the DRPE-based accumulation encoding scheme becomes more difficult as the number of accumulated images increases, even when the phase key used in DRPE is known.
The paper is organized as follows. Section II presents the concepts behind DRPE. The DRPE-based accumulation encoding scheme for multiple-image transmission is described in Section III. To verify this optical encryption scheme, simulation results produced by DRPE using accumulation encoding are provided in Section IV. Finally, we conclude the paper in Section V.
II. DOUBLE RANDOM PHASE ENCRYPTION
DRPE, an optical encryption technique, uses double random phase masks to encrypt data. Data encrypted by DRPE look like noise. For decryption, the key random phase mask used for encryption is required. For the sake of simplicity, in this paper we consider the encryption of one-dimensional data.
Let
p
(
x
) denote the primary data in the spatial domain, and let
ms
(
x
) and
mf
(
w
) represent the random phases in the spatial and spatial frequency domains respectively.
ms
(
x
) and
mf
(
w
) are uniformly distributed over [0, 1].
Figures 1(a)
and
(b)
depict the schematic setup of encryption and decryption for DRPE respectively, where
f
is the focal length and two lenses are used for Fourier transform and inverse Fourier transform. As shown in
Fig. 1(a)
, for encryption first the primary data is multiplied by the random phase mask exp[
i
2
πms
(
x
)] in the spatial domain. After passing the signal through the first lens we obtain ℑ {
p
(
x
)exp[
i
2
π ms
(
x
)]}, where ℑ denotes the Fourier transform. Next it is multiplied by the random phase mask exp[
i
2
πmf
(
w
)] in the spatial frequency domain. After passing through the second lens, the data encrypted by DRPE,
se
(
x
), are obtained as follows
[6]
:
Schematic setup of (a) encryption and (b) decryption for DRPE.
where ℑ
−1
represent the inverse Fourier transform. Exploiting the characteristics of a complex-valued function, the encrypted data can be expressed as amplitude and phase parts, i.e.
se
(
x
) = |
se
(
x
)|exp[
iφe
(
x
)].
As shown in
Fig. 1(b)
, for decryption the encrypted data are multiplied by the complex conjugate of the key information, i.e. exp[
-i
2
πmf
(
w
)]. The decrypted data are then obtained as follows
[6]
:
III. DRPE-BASED ACCUMULATION ENCODING AND DECODING
Figures 2(a)
and
(b)
depict the schemes for DRPE-based accumulation encoding and decoding for encryption and decryption, respectively. As shown in
Fig. 2(a)
, the
n
th
primary image
pn
(
x
) is encrypted and encoded for transmission. It is noted that DRPE with the same random phase mask is used for encryption of all the primary images. The data encrypted by DRPE,
se,n
(
x
), are encoded with the accumulation encoding scheme as follows:
Scheme for DRPE-based accumulation encoding: (a) encryption and (b) decryption.
where
ye,n
(
x
) represents the
n
th
encoded data. As seen in Eq. (3), for accumulation encoding all the previous encrypted data are added, which can enhance the security of the DRPE-encrypted data. Eq. (3) can be simply rewritten as
After accumulation encoding of the
n
th
encrypted data, the
n
th
encoded data are normalized by the factor 1/
n
, and finally the
n
th
encoded data
zn
(
x
) are obtained as follows:
For perfect decryption of the accumulation-encoded data, as shown in
Fig. 2(b)
, the encoded data are multiplied by
n
to scale it. Then the accumulation decoding is performed as follows:
where
sd,n
(
x
) denotes the
n
th
decoded data and
yd,n
(
x
) =
nzn
(
x
). By inserting Eq. (5) into Eq. (6), we obtain
sd,n
(
x
) =
se,n
(
x
), which means that the encoded data are perfectly decoded. The
n
th
decoded data are then decrypted by DRPE using the same random phase mask as for encryption. Finally the
n
th
decrypted data
dn
(
x
) are obtained as
dn
(
x
) =
pn
(
x
).
The accumulation encoder and decoder require only a simple linear operation and storage to store the data with the size of a single image, as seen in Eqs. (3) and (6). Therefore, the addition of the accumulation encoder and decoder to the DRPE system requires low cost and effort.
IV. SIMULATION RESULTS
To evaluate the performance of DRPE-based accumulation encoding we consider 20 primary images with 500(H)×500(V) pixels, as shown in
Fig. 3.
Figures 4(a)
-
(t)
show the simulated results of DRPE-based accumulation encoding, meaning
zn
(
x
) in
Fig. 2(a)
. From the figures we can see that the accumulation-encoded images are perfectly encrypted because they look like noise.
Figures 5
and
6
show the decrypted images without and with accumulation decoding respectively, where it is assumed that the DRPE key information is perfectly known for decryption. When no decoding is used, the encoded data are not decoded with the accumulation decoder but are directly decrypted by DRPE decryption; thus,
sd,n
(
x
) =
zn
(
x
). From
Figs. 5(a)
-
(t)
, it is observed that when no decoding is used the image recognition becomes worse as the index of accumulation encoding
n
increases, even though perfect DRPE key informationis known for decryption. This also, means that accumulation encoding is able to improve the security of DRPE-encrypted data even when the DRPE key information is known.
Figures 6(a)
-
(t)
indicate that the encoded images are perfectly decrypted when correct decoding and decryption are performed.
Primary images.
Simulated results of DRPE-based accumulation encoding: (a)-(t) the 1st-20th encoded images.
Simulated results of decryption of DRPE-based accumulation encoding when no decoding is used: (a)-(t) 1st-20th decrypted images.
Simulated results of decryption of DRPE-based accumulation encoding when decoding is used: (a)-(t) 1st-20th decrypted images.
To quantify the differences between the primary images in
Figs. 3(a)
-
(t)
and the decrypted images without decoding in
Figs. 5(a)
-
(t)
respectively, mean square error (MSE) results are calculated, as shown in
Fig. 7
, where we assume that the image pixel values are integers ranging from 0 to 255. In
Fig. 7
the average MSE for the
n
th
accumulation encoding is obtained as follows:
MSE results for primary versus decrypted images, without decoding.
When no decoding is used, the
n
th
decrypted data
dn
(
x
) contain the data for the 1
st
through
n
th
primary images, as described in Eq. (5). Thus we show the average of MSE results between the
n
th
decrypted image and the 1
st
through
n
th
primary images, as in Eq. (7).
Figure 7
demonstrates that the average MSE increases with the accumulation encoding index
n
. Especially when
n
≥ 11 the average MSE increases greatly because the 11
th
through 20
th
primary images have a different color pattern than the 1
st
through 10
th
primary images. From these results it can be seen that the encoded data become more secure as the accumulation encoding index rises, even though the DRPE key is known in decryption. However, for the first accumulation encoding the MSE result is zero, as the decrypted data contain only the data for the first primary image.
V. CONCLUSIONS
We propose a DRPE-based accumulation encoding technique for multiple-image transmission. In particular, we present the schemes for encryption and decryption for DRPE-based accumulation encoding and decoding, respectively, and methods for accumulation encoding and decoding. The simulation results verify that DRPE-based accumulation encoding for multiple-image transmission can enhance the security of DRPE-encrypted data when the key information of DRPE is perfectly known in decryption. Furthermore, since the accumulation encoder and decoder require only a simple linear operation and enough storage to hold a dataset of a single image, the DRPE system with accumulation encoding can be implemented with little cost and effort.
Color versions of one or more of the figures in this paper are available online.
Refregier P.
,
Javidi B.
1995
Optical-image encryption based on input plane and Fourier plane random encoding
Opt. Lett.
http://dx.doi.org/10.1364/OL.20.000767
20
767 -
769
Matoba O.
,
Javidi B.
1999
Encrypted optical memory system using three-dimensional keys in the Fresnel domain
Opt. Lett.
http://dx.doi.org/10.1364/OL.24.000762
24
762 -
764
Towghi N.
,
Javidi B.
,
Luo Z.
1999
Fully phase encrypted image processor
J. Opt. Soc. Am. A
16
1915 -
1927
Tajahuerce E.
,
Javidi B.
2000
Encrypting three-dimensional information with digital holography
Appl. Opt.
http://dx.doi.org/10.1364/AO.39.006595
39
6595 -
6601
Tu H.-Y.
,
Chiang J.-S.
,
Chou J.-W.
,
Cheng C.-J.
2008
Full phase encoding for digital holographic encryption using liquid crystal spatial light modulators
Jpn. J. Appl. Phys.
http://dx.doi.org/10.1143/JJAP.47.8838
47
8838 -
8843
Perez-Cabre E.
,
Cho M.
,
Javidi B.
2011
Information authentication using photon-counting double-random-phase encrypted images
Opt. Lett.
http://dx.doi.org/10.1364/OL.36.000022
36
22 -
24
Cho M.
,
Javidi B.
2013
Three-dimensional photon counting double-random-phase encryption
Opt. Lett.
http://dx.doi.org/10.1364/OL.38.003198
38
3198 -
3201
Joshi M.
,
Shakher C.
,
Singh K.
2010
Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys
Opt. Commun.
http://dx.doi.org/10.1016/j.optcom.2010.02.024
283
2496 -
2505
Unnikrishnan G.
,
Joseph J.
,
Singh K.
2000
Optical encryption by double-random phase encoding in the fractional Fourier domain
Opt. Lett.
http://dx.doi.org/10.1364/OL.25.000887
25
887 -
889
Joshi M.
,
Singh K.
2007
Color image encryption and decryption using fractional Fourier transform
Opt. Commun.
http://dx.doi.org/10.1016/j.optcom.2007.07.012
279
35 -
42
Frauel Y.
,
Castro A.
,
Naughton T.
,
Javidi B.
2007
Resistance of the double random phase encryption against various attacks
Opt. Express
http://dx.doi.org/10.1364/OE.15.010253
15
10253 -
10265
Nomura T.
,
Javidi B.
2000
Optical encryption system with a binary key code
Appl. Opt.
http://dx.doi.org/10.1364/AO.39.004783
39
4783 -
4787
Monaghan D. S.
,
Gopinathan U.
,
Naughton T. J.
,
Sheridan J. T.
2007
Key-space analysis of double random phase encryption technique
Appl. Opt.
http://dx.doi.org/10.1364/AO.46.006641
46
6641 -
6647
Singh M.
,
Kumar A.
,
Singh K.
2008
Secure optical system that uses fully phase-based encryption and lithium niobate crystal as phase contrast filter for decryption
Opt. Laser Technol.
http://dx.doi.org/10.1016/j.optlastec.2007.09.007
40
619 -
624
Sarkadi T.
,
Koppa P.
2012
Quantitative security evaluation of optical encryption using hybrid phase- and amplitudemodulated keys
Appl. Opt.
http://dx.doi.org/10.1364/AO.51.000745
51
745 -
750
Tashima H.
,
Takeda M.
,
Suzuki H.
,
Obi T.
,
Yamaguchi M.
,
Ohyama N.
2010
Known plaintext attack on double random phase encoding using fingerprint as key and a method for avoiding the attack
Opt. Express
http://dx.doi.org/10.1364/OE.18.013772
18
13772 -
13781
Barrera J. F.
,
Henao R.
,
Tebaldi M.
,
Torroba R.
,
Bolognini N.
2006
Multiplexing encryption-decryption via lateral shifting of a random phase mask
Opt. Commun.
http://dx.doi.org/10.1016/j.optcom.2005.09.027
259
532 -
536
Tan X.
,
Matoba O.
,
Okada-Shudo Y.
,
Ide M.
,
Shimura T.
,
Kuroda K.
2001
Secure optical memory system with polarization encryption
Appl. Opt.
http://dx.doi.org/10.1364/AO.40.002310
40
2310 -
2315
Chen W.
,
Chen X.
2010
Space-based optical image encryption
Opt. Express
http://dx.doi.org/10.1364/OE.18.027095
18
27095 -
27104
Lee I.-H.
,
Cho M.
2014
Double random phase encryption based orthogonal encoding technique for color images
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2014.18.2.129
18
129 -
133
Lee I.-H.
,
Cho M.
2014
Double random phase encryption using orthogonal encoding for multiple-image transmission
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2014.18.3.201
18
201 -
206
Jeon S. H.
,
Gil S. K.
2012
Dual optical encryption for binary data and secret key using phase-shifting digital holography
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2012.16.3.263
16
263 -
269
Gil S. K.
2012
2-step quadrature phase-shifting digital holographic optical encryption using orthogonal polarization and error analysis
J. Opt. Soc. Korea
http://dx.doi.org/10.3807/JOSK.2012.16.4.354
16
354 -
364