Literature survey on nonlinear components and chaotic nonlinear components of block ciphers

In the modern era of secure communication, it is important to create uncertainty in the original data in order to avoid unauthorized entities to extract or manipulate information. From simple methods such as permutations of original data to different mapping algorithms, the security of the ciphers rely on the substitution process. There are many types of components proposed in literature that are evolved by different methodologies and ideas. The prevailing ciphers use substitution boxes (S-boxes) to do this transformation process. In this work, we present a literature review of the design, construction, and analysis of the S-boxes used in block ciphers.The performance of S-boxes depends on the design and algebraic structure used for the construction and is contingent upon its ability to resist against cryptanalysis. We present the details of the S-box synthesis process and issues pertaining to creating resistance against various types of attacks, and highlight the consequences of a particular design methodology.In the infancy of the development of modern block ciphers, Shannon (Bell Syst. Tech. J. 28(4):656–715, 1949) presented the idea of encryption with the implementation of substitution-permutation network (SPN). In this process, the data is initially transformed by the substation process and then permuted that ends the first round supported by the secret key for this step. This substitution-permutation process is repeated several times to ensure reliability of encrypted data. The objective of using the substitution-permutation network is to create confusion between cipher text and secret key, and add diffusion in the plaintext.

[1]  Xiaofeng Liao,et al.  A method for designing dynamical S-boxes based on hyperchaotic Lorenz system , 2011, IEEE 10th International Conference on Cognitive Informatics and Cognitive Computing (ICCI-CC'11).

[2]  Yuliang Zheng,et al.  On plateaued functions , 1999, IEEE Trans. Inf. Theory.

[3]  Ping Wang,et al.  A Method to Construct Dynamic S-box Based on Chaotic Map , 2007 .

[4]  Yuriy Tarannikov,et al.  On Resilient Boolean Functions with Maximal Possible Nonlinearity , 2000, INDOCRYPT.

[5]  Xiangyang Xu A new genetic algorithm and tabu search for s-box optimization , 2010, 2010 International Conference On Computer Design and Applications.

[6]  X. Liao,et al.  An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps , 2007 .

[7]  Eli Biham,et al.  Cryptanalysis of Patarin's 2-Round Public Key System with S Boxes (2R) , 2000, EUROCRYPT.

[8]  Thomas Siegenthaler,et al.  Correlation-immunity of nonlinear combining functions for cryptographic applications , 1984, IEEE Trans. Inf. Theory.

[9]  Vincent Rijmen,et al.  The Design of Rijndael , 2002, Information Security and Cryptography.

[10]  Stafford E. Tavares,et al.  On the Design of S-Boxes , 1985, CRYPTO.

[11]  Josef Pieprzyk,et al.  Error propagation property and application in cryptography , 1989 .

[12]  Debdeep Mukhopadhyay,et al.  Preventing the Side-Channel Leakage of Masked AES S-Box , 2007, 15th International Conference on Advanced Computing and Communications (ADCOM 2007).

[13]  Donald W. Davies,et al.  Advances in Cryptology — EUROCRYPT ’91 , 2001, Lecture Notes in Computer Science.

[14]  Jennifer Seberry,et al.  Construction of bent functions from two known bent functions , 1994, Australas. J Comb..

[15]  Jovan Dj. Golic,et al.  Fast Low Order Approximation of Cryptographic Functions , 1996, EUROCRYPT.

[16]  H. Feistel Cryptography and Computer Privacy , 1973 .

[17]  Kulkarni,et al.  Optimized S-box design AES core , 2007 .

[18]  Josef Pieprzyk,et al.  Towards effective nonlinear cryptosystem design , 1988 .

[19]  Ming-Der Shieh,et al.  Exploration of Low-Cost Configurable S-Box Designs for AES Applications , 2008, 2008 International Conference on Embedded Software and Systems.

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

[21]  Kaoru Kurosawa,et al.  Almost security of cryptographic Boolean functions , 2004, IEEE Transactions on Information Theory.

[22]  Ueli Maurer,et al.  Advances in Cryptology — EUROCRYPT ’96 , 2001, Lecture Notes in Computer Science.

[23]  Dongho Won,et al.  Information Security and Cryptology — ICISC 2000 , 2001, Lecture Notes in Computer Science.

[24]  William Millan Low Order Approximation of Cipher Functions , 1995, Cryptography: Policy and Algorithms.

[25]  Amr M. Youssef,et al.  Resistance of Balanced s-Boxes to Linear and Differential Cryptanalysis , 1995, Inf. Process. Lett..

[26]  N. Idris,et al.  The memory-less method of generating multiplicative inverse values for S-box in AES algorithm , 2008, 2008 International Conference on Electronic Design.

[27]  Willi Meier,et al.  Fast correlation attacks on certain stream ciphers , 1989, Journal of Cryptology.

[28]  O. S. Rothaus,et al.  On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[29]  Robert L. McFarland,et al.  A Family of Difference Sets in Non-cyclic Groups , 1973, J. Comb. Theory A.

[30]  Yuriy Tarannikov,et al.  Spectral analysis of high order correlation immune functions , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[31]  Tor Helleseth,et al.  Advances in Cryptology — EUROCRYPT ’93 , 2001, Lecture Notes in Computer Science.

[32]  Bora Aslan,et al.  Classifying 8-Bit to 8-Bit S-Boxes Based on Power Mappings from the Point of DDT and LAT Distributions , 2008, WAIFI.

[33]  R. Leveugle,et al.  Influence of error detecting or correcting codes on the sensitivity to DPA of an AES S-box , 2009, 2009 3rd International Conference on Signals, Circuits and Systems (SCS).

[34]  Luke O'Connor,et al.  On the distribution of characteristics in bijective mappings , 1994, Journal of Cryptology.

[35]  Claude Carlet,et al.  A construction of bent function , 1996 .

[36]  Guang Gong,et al.  Algebraic Immunity of S-Boxes Based on Power Mappings: Analysis and Construction , 2009, IEEE Transactions on Information Theory.

[37]  Yuliang Zheng,et al.  Improved Upper Bound on the Nonlinearity of High Order Correlation Immune Functions , 2000, Selected Areas in Cryptography.

[38]  James L. Massey,et al.  A spectral characterization of correlation-immune combining functions , 1988, IEEE Trans. Inf. Theory.

[39]  Thomas W. Cusick,et al.  Boolean Functions Satisfying a Higher Order Strict Avalanche Criterion , 1994, EUROCRYPT.

[40]  Serge Vaudenay,et al.  An experiment on DES statistical cryptanalysis , 1996, CCS '96.

[41]  Gerhard Goos,et al.  Fast Software Encryption , 2001, Lecture Notes in Computer Science.

[42]  Eligijus Sakalauskas,et al.  Matrix Power S-Box Construction , 2007, IACR Cryptol. ePrint Arch..

[43]  Willi Meier,et al.  Nonlinearity Criteria for Cryptographic Functions , 1990, EUROCRYPT.

[44]  Thuc Dinh Nguyen,et al.  A New S-Box Structure to Increase Complexity of Algebraic Expression for Block Cipher Cryptosystems , 2009, 2009 International Conference on Computer Technology and Development.

[45]  Claude Carlet On the Coset Weight Divisibility and Nonlinearity of Resilient and Correlation-Immune Functions , 2001, SETA.

[46]  Kaoru Kurosawa,et al.  Almost k -Wise Independent Sample Spaces and Their Cryptologic Applications , 2001, Journal of Cryptology.

[47]  Claude Carlet,et al.  On Plateaued Functions and Their Constructions , 2003, FSE.

[48]  T. Aaron Gulliver,et al.  Heuristic S-box Design , 2008 .

[49]  Kaisa Nyberg,et al.  Constructions of Bent Functions and Difference Sets , 1991, EUROCRYPT.

[50]  Yuliang Zheng,et al.  Auto-Correlations and New Bounds on the Nonlinearity of Boolean Functions , 1996, EUROCRYPT.

[51]  Joos Vandewalle,et al.  Propagation Characteristics of Boolean Functions , 1991, EUROCRYPT.

[52]  Kwangjo Kim,et al.  Semi-bent Functions , 1994, ASIACRYPT.

[53]  Ernest F. Brickell,et al.  Advances in Cryptology — CRYPTO’ 92 , 2001, Lecture Notes in Computer Science.

[54]  Stafford E. Tavares,et al.  On the Design of SP Networks From an Information Theoretic Point of View , 1992, CRYPTO.

[55]  Shafi Goldwasser,et al.  Advances in Cryptology — CRYPTO’ 88: Proceedings , 1990, Lecture Notes in Computer Science.

[56]  Dengguo Feng,et al.  An Effective Genetic Algorithm for Self-Inverse S-Boxes , 2007 .

[57]  Sheelagh Lloyd,et al.  Properties of Binary Functions , 1991, EUROCRYPT.

[58]  Roger Y. Lee Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing , 2008 .

[59]  Palash Sarkar,et al.  Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions , 2000, IACR Cryptol. ePrint Arch..

[60]  Yuliang Zheng,et al.  GAC - the Criterion for Global Avalance Characteristics of Cryptographic Functions , 1995, J. Univers. Comput. Sci..

[61]  J. Massey,et al.  Communications and Cryptography: Two Sides of One Tapestry , 1994 .

[62]  Xiaofeng Liao,et al.  A novel method for designing S-boxes based on chaotic maps , 2005 .

[63]  Jean-Jacques Quisquater,et al.  Advances in Cryptology — EUROCRYPT ’89 , 1991, Lecture Notes in Computer Science.

[64]  Claude Carlet Partially-bent functions , 1993, Des. Codes Cryptogr..

[65]  Palash Sarkar,et al.  Nonlinearity Bounds and Constructions of Resilient Boolean Functions , 2000, CRYPTO.

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

[67]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[68]  Stafford E. Tavares,et al.  An Expanded Set of S-box Design Criteria Based on Information Theory and its Relation to Differential-Like Attacks , 1991, EUROCRYPT.

[69]  Yuliang Zheng,et al.  Connections among nonlinearity, avalanche and correlation immunity , 2003, Theor. Comput. Sci..

[70]  M. Smit,et al.  Elliptic waveguide beam focusing and collimating elements in InP: analysis and experiment , 1995 .

[71]  Hans Dobbertin,et al.  Construction of Bent Functions and Balanced Boolean Functions with High Nonlinearity , 1994, FSE.

[72]  J. A. Gordon,et al.  Are Big S-Boxes Best? , 1982, EUROCRYPT.

[73]  Carlisle M. Adams,et al.  On Immunity Against Biham and Shamir's "Differential Cryptanalysis" , 1992, Information Processing Letters.

[74]  Kaisa Nyberg,et al.  Perfect Nonlinear S-Boxes , 1991, EUROCRYPT.

[75]  Thuc Dinh Nguyen,et al.  A New S-Box Structure Based on Graph Isomorphism , 2009, 2009 International Conference on Computational Intelligence and Security.

[76]  Lansheng Han,et al.  Evolutionary Design of S-Box with Cryptographic Properties , 2011, 2011 IEEE Ninth International Symposium on Parallel and Distributed Processing with Applications Workshops.

[77]  F. Ayoub Probabilistic completeness of substitution-permutation encryption networks , 1982 .

[78]  Bimal Roy,et al.  Progress in Cryptology —INDOCRYPT 2000 , 2002, Lecture Notes in Computer Science.

[79]  Jennifer Seberry,et al.  The Relationship Between Propagation Characteristics and Nonlinearity of Cryptographic Functions , 1996 .

[80]  Yuanqing Deng,et al.  Analysis of the avalanche effect of the AES S box , 2011, 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC).

[81]  Réjane Forré,et al.  The Strict Avalanche Criterion: Spectral Properties of Boolean Functions and an Extended Definition , 1988, CRYPTO.

[82]  Arash Reyhani-Masoleh,et al.  A low-cost S-box for the Advanced Encryption Standard using normal basis , 2009, 2009 IEEE International Conference on Electro/Information Technology.

[83]  Thomas Johansson,et al.  Fast Software Encryption, FSE 2003 , 2003 .

[84]  Yuliang Zheng,et al.  New Results on Correlation Immunity , 2000, ICISC.

[85]  Yong Wang,et al.  A Software for S-box Performance Analysis and Test , 2009, 2009 International Conference on Electronic Commerce and Business Intelligence.

[86]  Josef Pieprzyk,et al.  Non-linearity of Exponent Permutations , 1990, EUROCRYPT.

[87]  Mihir Bellare Advances in Cryptology — CRYPTO 2000 , 2000, Lecture Notes in Computer Science.

[88]  Franciszek Seredynski,et al.  Cryptographically Strong S-Boxes Based on Cellular Automata , 2008, ACRI.

[89]  John B. Kam,et al.  Structured Design of Substitution-Permutation Encryption Networks , 1979, IEEE Transactions on Computers.

[90]  A. K. Nandi,et al.  Composite field GF(((22)2)2) AES S-Box with direct computation in GF(24) inversion , 2011, 2011 7th International Conference on Information Technology in Asia.

[91]  Ivan Bjerre Damgård,et al.  Advances in Cryptology — EUROCRYPT ’90 , 2001, Lecture Notes in Computer Science.

[92]  Baodian Wei,et al.  An AES S-box to increase complexity and cryptographic analysis , 2005, 19th International Conference on Advanced Information Networking and Applications (AINA'05) Volume 1 (AINA papers).

[93]  Runtong Zhang,et al.  A block cipher using key-dependent S-box and P-boxes , 2008, 2008 IEEE International Symposium on Industrial Electronics.

[94]  Palash Sarkar,et al.  New Constructions of Resilient and Correlation Immune Boolean Functions Achieving Upper Bound on Nonlinearity , 2001, Electron. Notes Discret. Math..

[95]  Yong Wang,et al.  An S-box Construction Algorithm Based on Spatiotemporal Chaos , 2010, 2010 International Conference on Communications and Mobile Computing.

[96]  Amr M. Youssef,et al.  Linear approximation of injective s-boxes , 1995 .

[97]  William Millan Analysis and design of Boolean functions for cryptographic applications , 1997 .

[98]  Ed Dawson,et al.  Cryptography: Policy and Algorithms , 1996, Lecture Notes in Computer Science.