Secure binary arithmetic coding based on digitalized modified
logistic map and linear feedback shift register
Yushu Zhang
a,b
, Di Xiao
b,
⇑
, Wenying Wen
c
, Hai Nan
b
, Moting Su
d
a
School of Electronics and Information Engineering, Southwest University, Chongqing 400715, China
b
College of Computer Science, Chongqing University, Chongqing 400044, China
c
School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China
d
School of Economics and Business Administration, Chongqing University, Chongqing 400044, China
article info
Article history:
Received 22 October 2013
Received in revised form 17 February 2015
Accepted 28 February 2015
Available online 6 March 2015
Keywords:
Randomized arithmetic coding
Digitalized modified logistic map
Linear feedback shift register
Shift
Perturbance
abstract
In this paper, we propose a novel secure arithmetic coding based on digitalized modified
logistic map (DMLM) and linear feedback shift register (LFSR). An input binary sequence
is first mapped into a table, which is then scrambled by two cyclic shift steps driven by
the keys resulting from DMLM–LFSR. Next, each column is encoded using traditional
arithmetic coding (TAC) and randomized arithmetic coding (RAC). During the RAC process,
the exchange of two intervals is controlled by the keystream generated from the DMLM. At
the same time, a few bits of the present column sequence are extracted to interfere the
generation of new keystream used for the next column. The final ciphertext sequence is
obtained by XORing the compressed sequence and the keystream generated by the LFSR.
Results show the compression ratio of our scheme is slightly higher than that of TAC,
but the security is improved due to the architecture of shift–perturbance. DMLM and
LFSR theories also ensure high sensitivity and strong randomness. The appended complex-
ity is only OðNÞ, where N is the number of the input symbols.
Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction
Arithmetic coding (AC) [1,2] has been widely developed over several decades and is incorporated into image and video cod-
ing standards like JPEG2000 [3] and H.264 [4]. AC is optimal since it can be arbitrarily close to the true entropy of the proba-
bility. Due to similarity between AC and cryptography, it is also regarded as an encryption scheme for some specific
applications. Moreover, the current state in an adaptive model depends directly or indirectly upon the initial conditions
and all of the messages encoded so far, therefore the adaptive AC approach may offer high level of security [5].
Nevertheless, it was proved that neither fixed AC model nor adaptive AC model can provide well-pleasing level of security
[6–8]. Furthermore, many variant versions were researched and reported for the purpose of enhancing the security [9–14].
In [9], a secure compression method was presented by renovating the coding probabilities in random time intervals. The poor
synchronization property of AC is utilized to design an encryption scheme by processing only the first few bits of the gener-
ated bit stream [10,11]. Random bit substitution is used to construct a cryptosystem during the encoding process of AC [12].
Randomized arithmetic coding (RAC) and key-based interval splitting AC were proposed in [13,14], respectively. However,
they are vulnerable to some classic attacks as the result of the fact that the same key is used to encode many messages
[15–17]. Besides, the security enhancement version of key-based interval splitting AC [15] was also cryptanalyzed in [18–20].
http://dx.doi.org/10.1016/j.cnsns.2015.02.025
1007-5704/Ó 2015 Elsevier B.V. All rights reserved.
⇑
Corresponding author.
E-mail address: xiaodi_cqu@hotmail.com (D. Xiao).
Commun Nonlinear Sci Numer Simulat 27 (2015) 22–29
Contents lists available at ScienceDirect
Commun Nonlinear Sci Numer Simulat
journal homepage: www.elsevier.com/locate/cnsns