Cryptographic properties of Boolean functions defining elementary cellular automata

References

• Adams , C. M. 1992 . On immunity against Biham and Shamir's ‘differential cryptanalysis’ . Inform. Proc. Lett. , 41 : 77 – 80 .
   Google Scholar
• Biham , E. and Shamir , A. 1991 . Differential cryptanalysis of DES-like cryptosystems . J. Cryptol. , 4 ( 1 ) : 3 – 72 .
   Google Scholar
• Biham , E. and Shamir , A. 1993 . Differential Cryptanalysis of the Data Encryption Standard , Berlin : Springer-Verlag .
   Google Scholar
• Chaudhuri , P. P. , Chowdhury , D. R. , Nandi , S. and Chattopadhyay , S. 1997 . Additive Cellular Automata. Theory and Applications , Vol. 1 , Los Alamitos, CA : IEEE Computer Society Press .
   Google Scholar
• Evertse , J. H. 1988 . “ Linear structures in block ciphers ” . In Advances in Cryptology , Edited by: Chaum , D. and Price , W. L. 249 – 266 . Berlin/Heidelberg : Springer . Proceedings of Eurocrypt’87, Lecture Notes in Computer Science, vol. 304
   Google Scholar
• Fúster , A. and Caballero , P. 2006 . On the use of cellular automata in symmetric cryptography . Acta Appl. Math. , 93 ( 2 ) : 215 – 236 .
   Google Scholar
• Fúster , A. and de la Guía , D. 2004 . Cellular automata applications to the linearization of stream cipher generators , 612 – 621 . Berlin/Heidelberg : Springer . Proceedings of ACRI 2004, Lecture Notes in Computer Science, vol. 3305
   Google Scholar
• Knudsen , L. R. 1995 . Truncated and higher order differentials , 196 – 211 . Berlin/Heidelberg : Springer . Proceedings of 2nd FSE, Lecture Notes in Computer Science, vol. 1008
   Google Scholar
• Lai , X. 1994 . Higher order derivatives and differential cryptanalysis , Edited by: Blahut , R. E. , Costello , D. J. Jr. , Maurer , U. and Mittelholzer , T. 227 – 233 . Berlin : Kluwer Academic Publishers . Communications and Cryptology
   Google Scholar
• Martin , B. 2008 . A Walsh exploration of elementary CA rules . J. Cellular Automata , 3 ( 2 ) : 145 – 156 .
   Google Scholar
• Martín del Rey , A. and Rodríguez Sánchez , G. 2007 . Sharing secrets using elementary cellular automata . Int. J. Mod. Phys. C , 18 : 1707 – 1716 .
   Google Scholar
• Matsui , M. 1995 . On correlation between the order of S-boxes and the strength of DES , Edited by: Pieprzyk , J. and Safavi-Nauti , R. Vol. 950 , 366 – 375 . Berlin/Heidelberg : Springer . Advances in Cryptology, Proceedings of Asiacrypt’94, Lecture Notes in Computer Science
   Google Scholar
• Meier , W. and Staffelbach , O. 1990 . Nonlinearity criteria for cryptographic functions , Edited by: Quisquater , J.-J. and Vandewalle , J. Vol. 434 , 549 – 562 . Berlin/Heidelberg : Springer . Advances in Cryptology, Proceedings of Eurocrypt’89, Lecture Notes in Computer Science
   Google Scholar
• Mukherjee , M. , Ganguly , N. and Chaudhuri , P. P. 2002 . Cellular automata based authentication Vol. 2493 , 259 – 269 . in Proceedings of ACRI 2002, Lecture Notes in Computer Science
   Google Scholar
• Nandi , S. , Kar , B. K. and Pal Chaudhuri , P. 1994 . Theory and applications of cellular automata in cryptography . IEEE Trans. Comput. , 43 ( 12 ) : 1346 – 1357 .
   Web of Science ®Google Scholar
• Preneel , B. , Van Leekwijck , W. , Van Linden , L. , Govaerts , R. and Vandevalle , J. 1991 . Propagation characteristic of boolean functions Vol. 473 , 161 – 173 . Advances in Cryptology, Proceedings of Eurocrypt’90, Lecture Notes in Computer Science
   Google Scholar
• Rueppel , R. A. and Staffelbach , O. J. 1987 . Products of linear recurring sequences with maximum complexity . IEEE Trans. Inform. Theory , 33 ( 1 ) : 124 – 131 .
   Google Scholar
• Seredynski , M. and Bouvry , P. 2004 . Block encryption using reversible cellular automata Vol. 3305 , 785 – 792 . Proceedings of ACRI 2004, Lecture Notes in Computer Science
   Google Scholar
• Siegenthaler , T. 1984 . Correlation-immunity of nonlinear combining functions for cryptographic applications . IEEE Trans. Inform. Theory , 30 ( 5 ) : 776 – 780 .
   Web of Science ®Google Scholar
• Tan , S. K. and Guan , S.-U. 2007 . Evolving cellular automata to generate nonlinear sequences with desirable properties . Appl. Soft Comput. , 7 ( 3 ) : 1131 – 1134 .
   Google Scholar
• Tomassini , M. and Perrenoud , M. 2001 . Cryptography with cellular automata . Appl. Software Comput. , 1 : 151 – 160 .
   Google Scholar
• Webster , A. F. and Tavares , S. E. 1985 . “ On the design of S-boxes ” . In Advances in Cryptology , Edited by: Williams , H. C. Vol. 219 , 523 – 534 . Berlin/Heidelberg : Springer . Proceedings of Crypto’85, Lecture Notes in Computer Science
   Google Scholar
• Wolfram , S. 1986 . Random sequence generation by cellular automata . Adv. Appl. Math. , 7 : 123 – 169 .
   Web of Science ®Google Scholar
• Wolfram , S. 1986 . “ Cryptography with cellular automata ” . In Advances in Cryptology , Edited by: Williams , H. C. Vol. 218 , 429 – 432 . Berlin/Heidelberg : Springer . Proceedings of Crypto’85, Lecture Notes in Computer Science
   Google Scholar
• Wolfram , S. 2002 . A New Kind of Science , Champaign, IL : Wolfram Media Inc .
   Google Scholar
• Xiao , G. Z. and Massey , J. L. 1988 . A spectral characterization of correlation-immune combining functions . IEEE Trans. Inform. Theory , 34 ( 3 ) : 569 – 571 .
   Google Scholar