Chaotic block ciphers: from theory to practical algorithms

Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto components from both dynamical-system and cryptographical points of view, thus to explore connection between these two fields. In the due course, we also apply dynamical system theory to create cryptographically secure transformations and evaluate cryptographical security measures

[1]  Michael Peter Kennedy,et al.  FM-DCSK: a novel method for chaotic communications , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[2]  L. Kocarev,et al.  Pseudorandom bits generated by chaotic maps , 2003 .

[3]  Vincent Rijmen,et al.  Recent Developments in the Design of Conventional Cryptographic Algorithms , 1997, State of the Art in Applied Cryptography.

[4]  C. Robinson.  Dynamical Systems: Stability, Symbolic Dynamics, and Chaos , 1994 .

[5]  L. Kocarev,et al.  Chaos and cryptography: block encryption ciphers based on chaotic maps , 2001 .

[6]  Vincent Rijmen,et al.  The Cipher SHARK , 1996, FSE.

[7]  Ljupco Kocarev,et al.  Analysis of some recently proposed chaos-based encryption algo-rithms , 2001 .

[8]  Nigel P. Smart,et al.  p-adic Chaos and Random Number Generation , 1998, Exp. Math..

[9]  Ljupco Kocarev,et al.  Finite-space Lyapunov exponents and pseudochaos. , 2004, Physical review letters.

[10]  Eli Biham,et al.  Cryptanalysis of the Chaotic-Map Cryptosystem Suggested at EUROCRYPT'91 , 1991, EUROCRYPT.

[11]  Zbigniew Kotulski,et al.  Discrete chaotic cryptography , 1997 .

[12]  Ljupco Kocarev,et al.  From chaotic maps to encryption schemes , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

[13]  Bertram E. Shi,et al.  IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS — I : REGULAR PAPERS , VOL . ? ? , NO . ? ? , ? ? ? ? , 2007 .

[14]  Nikolai F. Rulkov,et al.  Chaotic pulse position modulation: a robust method of communicating with chaos , 2000, IEEE Communications Letters.

[15]  Thomas Beth,et al.  Cryptanalysis of Cryptosystems Based on Remote Chaos Replication , 1994, CRYPTO.

[16]  Ljupco Kocarev,et al.  RSA encryption algorithm based on torus automorphisms , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[17]  M. Blank.  Pathologies generated by round-off in dynamical systems , 1994 .

[18]  Ljupco Kocarev,et al.  Cryptographically secure substitutions based on the approximation of mixing maps , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  M. Saraceno,et al.  Quantization of multidimensional cat maps , 1999, chao-dyn/9904042.

[20]  L. Kocarev.  Chaos-based cryptography: a brief overview , 2001 .

[21]  Neelima Gupte,et al.  A perspective on nonlinear dynamics , 2005 .

[22]  Iwao Sasase,et al.  A Secret Key Cryptosystem by Iterating a Chaotic Map , 1991, EUROCRYPT.

[23]  Xuejia Lai,et al.  A Proposal for a New Block Encryption Standard , 1991, EUROCRYPT.

[24]  Kazuyuki Aihara,et al.  Dynamical Characteristics of Discretized Chaotic Permutations , 2002, Int. J. Bifurc. Chaos.

[25]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[26]  Jung Hee Cheon,et al.  S-boxes with Controllable Nonlinearity , 1999, EUROCRYPT.

[27]  Bernard P. Zajac.  Applied cryptography: Protocols, algorithms, and source code in C , 1994 .

[28]  Vincent Rijmen,et al.  The Design of Rijndael: AES - The Advanced Encryption Standard , 2002 .

[29]  John Guckenheimer,et al.  Dynamical Systems: C.I.M.E. Lectures, Bressanone, Italy, June 1978 , 1980 .

[30]  J. Fridrich.  Symmetric Ciphers Based on Two-Dimensional Chaotic Maps , 1998 .

[31]  K. Aihara,et al.  Cryptosystems with discretized chaotic maps , 2002 .

[32]  Kevin M. Short,et al.  UNMASKING A MODULATED CHAOTIC COMMUNICATIONS SCHEME , 1996 .

[33]  James L. Massey,et al.  SAFER K-64: A Byte-Oriented Block-Ciphering Algorithm , 1993, FSE.