A Stream Cipher based on Spatiotemporal Chaos and True Random Synchronization

ABSTRACT Stream ciphers require the use of initialization vectors (IVs) to ensure that the same secret key produces different keystreams. It also synchronizes communication between two parties. However, there are many cryptanalytic attacks that exploit weaknesses in the IV setup of stream ciphers. In an effort to solve this problem, we introduce a chaos-based stream cipher that utilizes a new mode of synchronization called true random synchronization (TRSync). The stream cipher is designed based on spatiotemporal chaos while taking advantage of TRSync to resist various statistical attacks. The stream cipher operations also include data-dependent rotations and chaotic perturbation. As chaotic functions are inherently slow due to floating point operations, we utilize fixed point representation for higher efficiency. TRSync includes a true random number sequence (TRNS) into the synchronization process alongside the public IV. The IV is masked by the TRNS before being used to setup the cipher. Therefore, the cipher's internal state cannot be manipulated by an attacker and constantly changes even if the secret key-IV pairs are constant. TRSync can also be used to secure other stream ciphers with IVs as described in this paper. The security of the proposed chaotic cipher is thoroughly analyzed in terms of randomness, periodicity, entropy, balance, correlation, and complexity.

[1]  Martin E. Hellman,et al.  A cryptanalytic time-memory trade-off , 1980, IEEE Trans. Inf. Theory.

[2]  Frederik Armknecht,et al.  Fault Attacks on Combiners with Memory , 2005, Selected Areas in Cryptography.

[3]  Thomas Johansson,et al.  Cryptanalysis of pomaranch , 2006 .

[4]  Jinyu Kuang,et al.  PERIODICITY OF CHAOTIC TRAJECTORIES IN REALIZATIONS OF FINITE COMPUTER PRECISIONS AND ITS IMPLICATION IN CHAOS COMMUNICATIONS , 2003, nlin/0309005.

[5]  Christophe De Cannière,et al.  KATAN and KTANTAN - A Family of Small and Efficient Hardware-Oriented Block Ciphers , 2009, CHES.

[6]  Ali Kanso,et al.  A fast and efficient chaos-based keyed hash function , 2013, Commun. Nonlinear Sci. Numer. Simul..

[7]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[8]  Thomas Johansson,et al.  A New Version of the Stream Cipher SNOW , 2002, Selected Areas in Cryptography.

[9]  Chenhui Jin,et al.  Cryptanalysis of a Chaos-based Stream Cipher , 2008, 2008 The 9th International Conference for Young Computer Scientists.

[10]  Daesung Kwon,et al.  T-function based streamcipher TSC-4 , 2006 .

[11]  Tor Helleseth,et al.  Cascade Jump Controlled Sequence Generator and Pomaranch Stream Cipher , 2008, The eSTREAM Finalists.

[12]  Lin Jinqiu,et al.  A New Stream Cipher Based on Coupled Map Lattices Map , 2009, 2009 WRI World Congress on Computer Science and Information Engineering.

[13]  Sung-il Pae,et al.  DRAM as source of randomness , 2009 .

[14]  Martin Boesgaard,et al.  Rabbit: A New High-Performance Stream Cipher , 2003, FSE.

[15]  Hu Chuan-Gan,et al.  On The Shift Register Sequences , 2004 .

[16]  Stephan. Mueller.  CPU Time Jitter Based Non-Physical True Random Number Generator , 2014 .

[17]  Amr M. Youssef,et al.  Differential Fault Analysis of Rabbit , 2009, Selected Areas in Cryptography.

[18]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[19]  Erik Zenner.  Why IV Setup for Stream Ciphers is Difficult , 2007, Symmetric Cryptography.

[20]  Ross Ihaka,et al.  Cryptographic Randomness from Air Turbulence in Disk Drives , 1994, CRYPTO.

[21]  K. Deergha Rao,et al.  A New and Secure Cryptosystem for Image Encryption and Decryption , 2011 .

[22]  Guang Gong,et al.  The WG Stream Cipher , 2005 .

[23]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[24]  Gonzalo Alvarez,et al.  Cryptanalysis of a family of self-synchronizing chaotic stream ciphers , 2009, 0903.2928.

[25]  Amir Akhavan,et al.  Parallel chaotic hash function based on the shuffle-exchange network , 2015 .

[26]  Amir Akhavan,et al.  GPUs and chaos: a new true random number generator , 2015, Nonlinear Dynamics.

[27]  Gyungho Lee,et al.  GPUs as high-performance random sources , 2014 .

[28]  Bart Preneel,et al.  Resynchronization Attacks on WG and LEX , 2006, FSE.

[29]  Cécile Canovas,et al.  Fault Analysis of Rabbit: Toward a Secret Key Leakage , 2009, INDOCRYPT.

[30]  Randy Yates,et al.  Fixed-Point Arithmetic: An Introduction , 2013 .

[31]  Joos Vandewalle,et al.  Resynchronization Weaknesses in Synchronous Stream Ciphers , 1994, EUROCRYPT.

[32]  Mohammad Sabzinejad Farash,et al.  An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps , 2014, Nonlinear Dynamics.

[33]  Mark Goresky,et al.  Periodicity and Distribution Properties of Combined FCSR Sequences , 2006, SETA.

[34]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[35]  Xiaoyun Wang,et al.  Differential Cryptanalysis of T-Function Based Stream Cipher TSC-4 , 2007, ICISC.

[36]  Alexander Maximov,et al.  Some Words on Cryptanalysis of Stream Ciphers , 2006 .

[37]  Terry Ritter.  The Efficient Generation of Cryptographic Confusion Sequences , 1991, Cryptologia.