Gyrator transform based double random phase encoding
with sparse representation for information authentication
Jun-xin Chen
a
, Zhi-liang Zhu
b,
n
, Chong Fu
a
, Hai Yu
b
, Li-bo Zhang
b
a
School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
b
Software College, Northeastern University, Shenyang 110004, China
article info
Article history:
Received 6 October 2014
Received in revised form
2 January 2015
Accepted 25 January 2015
Keywords:
Information authentication
Double random phase encoding
Sparse representation
abstract
Optical information security systems h av e drawn long-t erm concerns. In this paper , an optical information
authentication approach using gyrator transform based double random phase encoding with sparse
representation is proposed. Different from traditional optical encryption schemes, only sparse version of
the ciphertext is preserved, and hence the decrypted result is completely unrecognizable and shows no
similarity to the plaintext. However, we demonstrate that the noise-like decipher result can be effectively
authenticated by means of optical correlation approach. Simulations prove that the proposed method is
feasible and effective, and can provide additional protection for optical security systems.
& 2015 Elsevier Ltd. All rights reserved.
1. Introduction
Owing to the superior advantages such as high speed, multi-
dimensional characteristics and parallel processing, optical informa-
tion encryption techniq ues ha ve dr aw n wor ld-wide concerns.
Amounts of cryptosystems have been investigated to protect informa-
tion that needs to be kept secret since the pioneering double random
phase encoding (DRPE) achievement was proposed in 1 995 [1].In
DRPE, the in put image (i.e., plaintext) can be convert ed into stationary
white noise with the help of two independent random phase-only
masks that were placed in the in put plane and F ourier p lane,
respectively. In [2–4], researchers have developed optical cryptosys-
tems by implementing DRPE in fractional Fourier transform (FrFT)
domain, while Situ et al. introduced the DRPE into the Fresnel domain
[5]. In recent years, researchers also developed optical encryption
schemes in gyrator transform (GT) domains [6–9], especially after Liu
et al. addressed the numerical simulation difficulties of GT [1 0].Some
other techniqu es, such as discrete fractional random transform [11–
13],phaseretrieval[1 4,15], diffractive imaging [1 6], arbitrarily modu-
lated beam [17] and many enhancements of DRPE [18–20],havealso
been employed to build optical encryption systems. Meanwhile,
cryptanalysis of optical cryptosystems has also been achieved. It has
been proved that the DRPE is vulnerable to various attacks, such as
chosen-ciphertext attack [21], chosen-plaintext attack [22],and
known-plaintext attack [23]. Moreover, some enhanced DRPE based
cryptosystems have also been broken [24–27]. The vulnerability
originates from the intrinsic flaw that the secret keys for encryption
and decryption are repeatedly used without being updated. In order
to overcome this drawback, some improved optical image encryp-
tion schemes with sparse representation are developed for infor-
mation encoding and authentication in very recent years [29–32].
Such schemes can provide additional protection to the plaintext and
may make the verification process more robust against various
attacks.
In this paper, an information authentication system based on
double random phase encoding with sparse representation in
gyrator transform domain is presented. The input image will be
firstly encrypted with DRPE in gyrator transform domain. Then the
sparse data will be produced under two scenarios: randomly
generated from the cipher data, and randomly extracted from only
the phase distribution of the cipher data. In the receiver end, only
the sparse cipher data is available for decryption, and the decipher
image is totally unrecognizable and cannot reveal any useful
information about plaintext. The decrypted image is intended not
for direct visualization of the primary image but for verification of
the information by means of optical correlation method. It is
demonstrated that the proposed scheme is feasible and robust to
noise contamination, and can provide additional protection for
optical security systems.
2. Theoretical analysis
In the first place, let us recall the knowledge of GT. The GT is
mathematically defined
as a linear canonical transform which
produces the rotation in position-spatial frequency planes
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Optics & Laser Technology
http://dx.doi.org/10.1016/j.optlastec.2015.01.016
0030-3992/& 2015 Elsevier Ltd. All rights reserved.
n
Corresponding author. Fax: þ 84 24 86581232.
E-mail address: zhuzhiliang.sc@gmail.com (Z.-l. Zhu).
Optics & Laser Technology 70 (2015) 50–58