Discrete-chaotic-cryptography.rar_加密解密_系统/网络安全下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/622b6d7915da9b288bc09a40/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b6d7915da9b288bc09a40/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Physics Letters A 309 (2003) 75–82</div><div class="t m0 x2 h2 y2 ff1 fs0 fc1 sc0 ls1 ws0">www.elsevier.com/locate/pla</div><div class="t m0 x3 h3 y3 ff1 fs1 fc0 sc0 ls2 ws0">Discrete chaotic cryptography using external key</div><div class="t m0 x4 h4 y4 ff1 fs2 fc0 sc0 ls3 ws0">N.K. Pareek</div><div class="t m0 x5 h2 y5 ff1 fs0 fc0 sc0 ls4 ws0">a,b</div><div class="t m0 x6 h4 y4 ff1 fs2 fc0 sc0 ls5 ws0">, Vinod Patidar</div><div class="t m0 x7 h2 y5 ff1 fs0 fc0 sc0 ls4 ws0">a</div><div class="t m0 x8 h4 y4 ff1 fs2 fc0 sc0 ls6 ws0">,K.K.Sud</div><div class="t m0 x9 h2 y5 ff1 fs0 fc0 sc0 ls4 ws0">a,b,∗</div><div class="t m0 xa h5 y6 ff1 fs3 fc0 sc0 ls4 ws0">a</div><div class="t m0 xb h6 y7 ff4 fs0 fc0 sc0 ls7 ws0">Department of Physics, College of Science Campus, M.L.S. University, Udaipur 313002, India</div><div class="t m0 xc h5 y8 ff1 fs3 fc0 sc0 ls4 ws0">b</div><div class="t m0 xd h6 y9 ff4 fs0 fc0 sc0 ls8 ws0">Computer Centre, M.L.S. University, Udaipur 313002, India</div><div class="t m0 xe h2 ya ff1 fs0 fc0 sc0 ls9 ws0">Received 23 October 2002; received in revised form 24 December 2002; accepted 7 January 2003</div><div class="t m0 xf h2 yb ff1 fs0 fc0 sc0 lsa ws0">Communicated by C.R. Doering</div><div class="t m0 x10 h7 yc ff5 fs4 fc0 sc0 lsb ws0">Abstract</div><div class="t m0 x11 h8 yd ff1 fs4 fc0 sc0 lsb ws0">In this Letter, we propose a symmetric key block cipher algorithm utilizing the essence of chaos. The proposed cryptosystem</div><div class="t m0 x10 h8 ye ff1 fs4 fc0 sc0 lsc ws0">does not use explicitly the system parameter or initial condition of the chaotic map as a secret key. However, these parameters</div><div class="t m0 x10 h8 yf ff1 fs4 fc0 sc0 lsd ws0">are generated by an external secret key of variable length (maximum 128-bits) and used in our algorithm. The encryption of each</div><div class="t m0 x10 h8 y10 ff1 fs4 fc0 sc0 lse ws0">block of plaintext has been made dependent on the secret key and the cryptosystem is further made robust against any reasonable</div><div class="t m0 x10 h8 y11 ff1 fs4 fc0 sc0 lse ws0">attack by using the feedback technique. Simulation results show that the proposed cryptosystem requires less time to encrypt</div><div class="t m0 x10 h8 y12 ff1 fs4 fc0 sc0 lsf ws0">the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having ﬂat distribution of</div><div class="t m0 x10 h8 y13 ff1 fs4 fc0 sc0 ls10 ws0">same size as the plaintext.</div><div class="t m0 x10 h9 y14 ff6 fs0 fc0 sc0 ls4 ws0"> 2003 Elsevier Science B.V. All rights reserved.</div><div class="t m0 x10 h2 y15 ff4 fs0 fc0 sc0 ls12 ws0">PACS: 05.45.+b</div><div class="t m0 x10 h2 y16 ff4 fs0 fc0 sc0 ls13 ws0">Keywords: Discrete chaotic cryptography (DCC); Block ciphers; Secret-key cryptography</div><div class="t m0 x10 ha y17 ff5 fs5 fc0 sc0 ls15 ws0">1. Introduction</div><div class="t m0 x12 hb y18 ff1 fs5 fc0 sc0 ls16 ws0">The techniques of secure communication by which</div><div class="t m0 x10 hb y19 ff1 fs5 fc0 sc0 ls17 ws0">one can transmit conﬁdential messages secretively are</div><div class="t m0 x10 hb y1a ff1 fs5 fc0 sc0 ls18 ws0">of practical interest in several areas, including data-</div><div class="t m0 x10 hb y1b ff1 fs5 fc0 sc0 ls19 ws0">bases, internet banking, softwares, protection of com-</div><div class="t m0 x10 hb y1c ff1 fs5 fc0 sc0 ls19 ws0">munication channels etc. A cryptosystem is simply an</div><div class="t m0 x10 hb y1d ff1 fs5 fc0 sc0 ls1a ws0">algorithm that converts an original intelligible mes-</div><div class="t m0 x10 hb y1e ff1 fs5 fc0 sc0 ls1b ws0">sage, referred as plaintext, into apparently random</div><div class="t m0 x10 hb y1f ff1 fs5 fc0 sc0 ls1c ws0">non-sense message, referred as ciphertext and recov-</div><div class="t m0 x10 hb y20 ff1 fs5 fc0 sc0 ls1b ws0">ers the message back in its original form. The cryp-</div><div class="t m0 x11 h5 y21 ff1 fs3 fc0 sc0 ls4 ws0">*</div><div class="t m0 x13 h2 y22 ff1 fs0 fc0 sc0 ls1d ws0">Corresponding author.</div><div class="t m0 x13 h2 y23 ff4 fs0 fc0 sc0 ls1e ws0">E-mail address: kksud@yahoo.com (K.K. Sud).</div><div class="t m0 x14 hb y17 ff1 fs5 fc0 sc0 ls20 ws0">tosystems available in the literature can be discussed</div><div class="t m0 x14 hb y24 ff1 fs5 fc0 sc0 ls20 ws0">with respect to the following aspects:</div><div class="t m0 x15 hb y25 ff3 fs5 fc0 sc0 ls4 ws0">• Structure of the encryption algorithm;</div><div class="t m0 x15 hb y26 ff3 fs5 fc0 sc0 ls4 ws0">• Method of distribution of secret keys;</div><div class="t m0 x15 hb y27 ff3 fs5 fc0 sc0 ls4 ws0">• Method of constructing algorithms.</div><div class="t m0 x14 hb y28 ff1 fs5 fc0 sc0 ls23 ws0">Based on the structure of the encryption algorithm</div><div class="t m0 x14 hb y29 ff1 fs5 fc0 sc0 ls24 ws0">we can classify cryptosystems into two categories,</div><div class="t m0 x14 hb y2a ff1 fs5 fc0 sc0 ls25 ws0">namely, stream cipher and block cipher. In a stream</div><div class="t m0 x14 hb y2b ff1 fs5 fc0 sc0 ls26 ws0">cipher algorithm, the message is encrypted bit-by-bit</div><div class="t m0 x14 hb y2c ff1 fs5 fc0 sc0 ls24 ws0">with the application of a secret key generator and the</div><div class="t m0 x14 hb y2d ff1 fs5 fc0 sc0 ls23 ws0">decryptioncan be done by using the same algorithm as</div><div class="t m0 x14 hb y2e ff1 fs5 fc0 sc0 ls27 ws0">in encryption, and with the same secret-key generator.</div><div class="t m0 x14 hb y2f ff1 fs5 fc0 sc0 ls25 ws0">In practice, shift register, non-linear combination gen-</div><div class="t m0 x10 h9 y30 ff1 fs0 fc0 sc0 ls28 ws0">0375-9601/03/$ – see front matter  2003 Elsevier Science B.V. All rights reserved.</div><div class="t m0 x10 h2 y31 ff1 fs0 fc0 sc0 ls2a ws0">doi:10.1016/S0375-9601(03)00122-1</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.758242,0.000000,0.000000,1.758242,-43.956044,-87.912088]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/622b6d7915da9b288bc09a40/bg2.jpg"><div class="t m0 x10 h2 y32 ff1 fs0 fc0 sc0 ls2b ws0">76 N.K. Pareek et al. / Physics Letters A 309 (2003) 75–82</div><div class="t m0 x10 hb y33 ff1 fs5 fc0 sc0 ls27 ws0">erator, clock controlled generators etc. are used as key</div><div class="t m0 x10 hb y34 ff1 fs5 fc0 sc0 ls2c ws0">generators. Unlike the stream cipher, in block cipher</div><div class="t m0 x10 hb y35 ff1 fs5 fc0 sc0 ls21 ws0">a group (blocks) of bits of ﬁxed length are encrypted</div><div class="t m0 x10 hb y36 ff1 fs5 fc0 sc0 ls21 ws0">block-by-block. In an another classiﬁcation, which is</div><div class="t m0 x10 hb y37 ff1 fs5 fc0 sc0 ls2d ws0">based on method of distribution of secret key, one clas-</div><div class="t m0 x10 hb y38 ff1 fs5 fc0 sc0 ls2e ws0">siﬁes the cryptosystems into two classes-private (sym-</div><div class="t m0 x10 hb y39 ff1 fs5 fc0 sc0 ls2f ws0">metric) key and public (asymmetric) key cryptosys-</div><div class="t m0 x10 hb y3a ff1 fs5 fc0 sc0 ls22 ws0">tems. In the private key cryptosystems sender and re-</div><div class="t m0 x10 hb y3b ff1 fs5 fc0 sc0 ls30 ws0">ceiver use the same key for the encryption and decryp-</div><div class="t m0 x10 hb y3c ff1 fs5 fc0 sc0 ls27 ws0">tion, respectively. These systems are efﬁcient and their</div><div class="t m0 x10 hb y3d ff1 fs5 fc0 sc0 ls1b ws0">security depends on the statistical properties of the</div><div class="t m0 x10 hb y3e ff1 fs5 fc0 sc0 ls1b ws0">random bit sequence and the length of the secret key.</div><div class="t m0 x10 hb y3f ff1 fs5 fc0 sc0 ls31 ws0">The main difﬁculty with the private key cryptosystems</div><div class="t m0 x10 hb y40 ff1 fs5 fc0 sc0 ls32 ws0">is in the security of the secret key to be transmitted to</div><div class="t m0 x10 hb y41 ff1 fs5 fc0 sc0 ls33 ws0">the receiver. Some typical examples of such type of</div><div class="t m0 x10 hb y42 ff1 fs5 fc0 sc0 ls34 ws0">cryptosystems are: classical cryptosystems (Substitu-</div><div class="t m0 x10 hb y43 ff1 fs5 fc0 sc0 ls1c ws0">tion and Vigenere), block ciphers (DES, AES, IDEA)</div><div class="t m0 x10 hb y44 ff1 fs5 fc0 sc0 ls35 ws0">and LFSR-based stream ciphers. In the public key</div><div class="t m0 x10 hb y45 ff1 fs5 fc0 sc0 ls25 ws0">cryptosystems sender and receiver use different keys</div><div class="t m0 x10 hb y46 ff1 fs5 fc0 sc0 ls36 ws0">for the encryption and decryption, respectively, i.e.,</div><div class="t m0 x10 hb y47 ff1 fs5 fc0 sc0 ls21 ws0">these cryptosystems work with a pair of public and</div><div class="t m0 x10 hb y48 ff1 fs5 fc0 sc0 ls21 ws0">private keys. All public keys are published while the</div><div class="t m0 x10 hb y49 ff1 fs5 fc0 sc0 ls27 ws0">private keys are kept secret. While communicating we</div><div class="t m0 x10 hb y4a ff1 fs5 fc0 sc0 ls37 ws0">use public key and the private key is not transmitted.</div><div class="t m0 x10 hb y4b ff1 fs5 fc0 sc0 ls38 ws0">A few examples of this kind are RSA, ElGamal, etc.</div><div class="t m0 x12 hb y4c ff1 fs5 fc0 sc0 ls39 ws0">Most of the existing cryptosystems, except a few,</div><div class="t m0 x10 hb y4d ff1 fs5 fc0 sc0 ls3a ws0">utilize number theory, algebra, combinatorics and</div><div class="t m0 x10 hb y4e ff1 fs5 fc0 sc0 ls3b ws0">computer arithmetic, etc. as mathematical tools for</div><div class="t m0 x10 hb y4f ff1 fs5 fc0 sc0 ls23 ws0">constructing the algorithms for the encryption and de-</div><div class="t m0 x10 hb y50 ff1 fs5 fc0 sc0 ls19 ws0">cryption. We refer the readers for complete description</div><div class="t m0 x10 hb y51 ff1 fs5 fc0 sc0 ls3c ws0">of the existing cryptosystems to the Refs. [1–3].</div><div class="t m0 x12 hb y52 ff1 fs5 fc0 sc0 ls36 ws0">In recent years, extensive studies have been done in</div><div class="t m0 x10 hb y53 ff1 fs5 fc0 sc0 ls21 ws0">the theory of chaos in different ﬁelds of physics, math-</div><div class="t m0 x10 hb y54 ff1 fs5 fc0 sc0 ls21 ws0">ematics, engineering, biology, chemistry, economics</div><div class="t m0 x10 hb y55 ff1 fs5 fc0 sc0 ls3d ws0">and atmospheric sciences. At the start of last decade</div><div class="t m0 x10 hb y56 ff1 fs5 fc0 sc0 ls22 ws0">only, the use of the continuous as well as discrete</div><div class="t m0 x10 hb y57 ff1 fs5 fc0 sc0 ls18 ws0">chaotic dynamical systems has been made to develop</div><div class="t m0 x10 hb y58 ff1 fs5 fc0 sc0 ls21 ws0">cryptosystems [4–6]. The chaotic systems are char-</div><div class="t m0 x10 hb y59 ff1 fs5 fc0 sc0 ls3e ws0">acterized by the sensitivity on initial conditions, sys-</div><div class="t m0 x10 hb y5a ff1 fs5 fc0 sc0 ls3b ws0">tem parameters and unpredictability of evolution of its</div><div class="t m0 x10 hb y5b ff1 fs5 fc0 sc0 ls1c ws0">orbits. These properties make the chaotic systems a</div><div class="t m0 x10 hb y5c ff1 fs5 fc0 sc0 ls22 ws0">worthy choice for constructing cryptosystems. Further</div><div class="t m0 x10 hb y5d ff1 fs5 fc0 sc0 ls26 ws0">more, these properties make the chaotic cryptosystems</div><div class="t m0 x10 hb y5e ff1 fs5 fc0 sc0 ls27 ws0">robust against any statistical attacks. The cryptosys-</div><div class="t m0 x10 hb y5f ff1 fs5 fc0 sc0 ls26 ws0">tems based on the continuous chaotic dynamical sys-</div><div class="t m0 x10 hb y60 ff1 fs5 fc0 sc0 ls3f ws0">tem utilize the idea of control and synchronization</div><div class="t m0 x10 hb y61 ff1 fs5 fc0 sc0 ls23 ws0">of chaos [7–9]. The ﬁrst idea to apply the theory of</div><div class="t m0 x10 hb y62 ff1 fs5 fc0 sc0 ls19 ws0">continuous chaotic dynamical systems in cryptogra-</div><div class="t m0 x14 hb y63 ff1 fs5 fc0 sc0 ls19 ws0">phy was given by Pecora and Carroll [4]. The syn-</div><div class="t m0 x14 hb y64 ff1 fs5 fc0 sc0 ls1c ws0">chronizationof chaos has been experimentallydemon-</div><div class="t m0 x14 hb y65 ff1 fs5 fc0 sc0 ls40 ws0">strated by Kocarev et al. [10] and Parlitz et al. [11]</div><div class="t m0 x14 hb y66 ff1 fs5 fc0 sc0 ls1c ws0">using electronic circuits.Further work on synchroniza-</div><div class="t m0 x14 hb y67 ff1 fs5 fc0 sc0 ls23 ws0">tion of chaos has been done by Hayes et al. [12], Chua</div><div class="t m0 x14 hb y68 ff1 fs5 fc0 sc0 ls16 ws0">et al. [13], Murali et al. [14], Martienssen et al. [15]</div><div class="t m0 x14 hb y69 ff1 fs5 fc0 sc0 ls41 ws0">etc.</div><div class="t m0 x16 hb y6a ff1 fs5 fc0 sc0 ls1c ws0">However, the use of discrete chaotic dynamical</div><div class="t m0 x14 hb y6b ff1 fs5 fc0 sc0 ls23 ws0">systems in cryptography has been done for the ﬁrst</div><div class="t m0 x14 hb y6c ff1 fs5 fc0 sc0 ls31 ws0">time by Matthews [5]. Matthews has derived a one-</div><div class="t m0 x14 hb y6d ff1 fs5 fc0 sc0 ls23 ws0">dimensional chaotic map, which exhibits chaotic be-</div><div class="t m0 x14 hb y6e ff1 fs5 fc0 sc0 ls37 ws0">havior for a range of parameter and initial values. In</div><div class="t m0 x14 hb y6f ff1 fs5 fc0 sc0 ls2d ws0">Mathew’s algorithm the map is used for generating</div><div class="t m0 x14 hb y70 ff1 fs5 fc0 sc0 ls1b ws0">a sequence of pseudo-random numbers, which serves</div><div class="t m0 x14 hb y71 ff1 fs5 fc0 sc0 ls2c ws0">as a one time pad for encrypting message. His work</div><div class="t m0 x14 hb y72 ff1 fs5 fc0 sc0 ls42 ws0">has been criticized by Wheeler [16], who showed that</div><div class="t m0 x14 hb y73 ff1 fs5 fc0 sc0 ls19 ws0">when the chaotic map is implemented on digital com-</div><div class="t m0 x14 hb y74 ff1 fs5 fc0 sc0 ls3e ws0">puters, the discretized map produces cycles, which</div><div class="t m0 x14 hb y75 ff1 fs5 fc0 sc0 ls43 ws0">are unpredictable and often short. In 1990 Habutsu</div><div class="t m0 x14 hb y76 ff1 fs5 fc0 sc0 ls3d ws0">et al. [6] developed a cryptosystem based on a piece-</div><div class="t m0 x14 hb y77 ff1 fs5 fc0 sc0 ls23 ws0">wise linear chaotic tent map. In Habutsu’s cryptosys-</div><div class="t m0 x14 hb y78 ff1 fs5 fc0 sc0 ls27 ws0">tem use is made of the parameter of the tent map as</div><div class="t m0 x14 hb y79 ff1 fs5 fc0 sc0 ls1c ws0">a secret key and the encryption and decryption are</div><div class="t m0 x14 hb y7a ff1 fs5 fc0 sc0 ls19 ws0">achieved by performing the inverse and forward it-</div><div class="t m0 x14 hb y7b ff1 fs5 fc0 sc0 ls2c ws0">erations of the chaotic tent map, respectively. Habut-</div><div class="t m0 x14 hb y7c ff1 fs5 fc0 sc0 ls23 ws0">su’s method works only for the chaotic dynamical sys-</div><div class="t m0 x14 hb y7d ff1 fs5 fc0 sc0 ls19 ws0">tems for which the map properties are strongly sen-</div><div class="t m0 x14 hb y7e ff1 fs5 fc0 sc0 ls17 ws0">sitive to the system parameters. Moreover, this prop-</div><div class="t m0 x14 hb y7f ff1 fs5 fc0 sc0 ls2d ws0">erty has been observed for only certain dynamical sys-</div><div class="t m0 x14 hb y80 ff1 fs5 fc0 sc0 ls23 ws0">tems. At the same time, Biham [17] has pointed out</div><div class="t m0 x14 hb y81 ff1 fs5 fc0 sc0 ls1b ws0">that Habutsu’s cryptosystem can be easily broken us-</div><div class="t m0 x14 hb y82 ff1 fs5 fc0 sc0 ls1c ws0">ing a ‘chosen ciphertext attack’ and ‘known plaintext</div><div class="t m0 x14 hb y83 ff1 fs5 fc0 sc0 ls35 ws0">attack’. Bianco et al. [18] has used the logistic map to</div><div class="t m0 x14 hb y84 ff1 fs5 fc0 sc0 ls1b ws0">generate a sequence of ﬂoating point numbers, which</div><div class="t m0 x14 hb y85 ff1 fs5 fc0 sc0 ls1c ws0">is converted to a binary sequence and is XOR-ed with</div><div class="t m0 x14 hb y86 ff1 fs5 fc0 sc0 ls37 ws0">the plaintext. The parameter of the logistic map to-</div><div class="t m0 x14 hb y87 ff1 fs5 fc0 sc0 ls3e ws0">gether with the initial condition form part of the ci-</div><div class="t m0 x14 hb y88 ff1 fs5 fc0 sc0 ls43 ws0">phering key. The conversion from ﬂoating point num-</div><div class="t m0 x14 hb y89 ff1 fs5 fc0 sc0 ls22 ws0">bers to binary values is done by choosing two dis-</div><div class="t m0 x14 hb y8a ff1 fs5 fc0 sc0 ls44 ws0">joint interval ranges representing 0 and 1. However,</div><div class="t m0 x14 hb y8b ff1 fs5 fc0 sc0 ls2f ws0">the fact that this method is based on ﬂoating point</div><div class="t m0 x14 hb y8c ff1 fs5 fc0 sc0 ls2f ws0">arithmetic constitutes a possible disadvantage as this</div><div class="t m0 x14 hb y8d ff1 fs5 fc0 sc0 ls25 ws0">makes it machine dependent, and care needs to be ex-</div><div class="t m0 x14 hb y8e ff1 fs5 fc0 sc0 ls19 ws0">ercised when implementing the scheme. Kotulski and</div><div class="t m0 x14 hb y8f ff1 fs5 fc0 sc0 ls45 ws0">Szczepanski [19] proposed an algorithm of encryption</div><div class="t m0 x14 hb y90 ff1 fs5 fc0 sc0 ls32 ws0">and decryption based on multiple iterations of a cer-</div><div class="t m0 x14 hb y91 ff1 fs5 fc0 sc0 ls21 ws0">tain one-dimensional chaotic map. They proposed to</div><div class="t m0 x14 hb y92 ff1 fs5 fc0 sc0 ls46 ws0">assume some part of initial condition as plaintext and</div></div><div class="pi" data-data='{"ctm":[1.758242,0.000000,0.000000,1.758242,-43.956044,-87.912088]}'></div></div>