A Brief Outline of Research on Correlation Immune Functions

The correlation immune functions have a rich history of research. Balanced correlation immune Boolean functions with high nonlinearity and algebraic degree are important in the design of stream cipher systems. In this paper we mainly outline the development in the field of constructing such functions. We also briefly survey related issues in this area.

[1]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.

[2]  Dean G. Hoffman,et al.  A Note on a Conjecture Concerning Symmetric Resilient Functions , 1993, Inf. Process. Lett..

[3]  Yuliang Zheng,et al.  Cryptographically resilient functions , 1997, IEEE Trans. Inf. Theory.

[4]  Kwangjo Kim,et al.  Improving Bounds for the Number of Correlation Immune Boolean Functions , 1997, Inf. Process. Lett..

[5]  Kwangjo Kim,et al.  Advances in Cryptology — ASIACRYPT '96 , 1996, Lecture Notes in Computer Science.

[6]  Subhamoy Maitra Autocorrelation Properties of Correlation Immune Boolean Functions , 2001, INDOCRYPT.

[7]  Markus Schneider A Note on the Construction and Upper Bounds of Correlation-Immune Functions , 1997, IMACC.

[8]  Oded Goldreich,et al.  The bit extraction problem or t-resilient functions , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Palash Sarkar,et al.  Cross-Correlation Analysis of Cryptographically Useful Boolean Functions and S-Boxes , 2001, Theory of Computing Systems.

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

[11]  Palash Sarkar,et al.  Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality , 1999, CRYPTO.

[12]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[13]  Subhamoy Maitra,et al.  Further constructions of resilient Boolean functions with very high nonlinearity , 2002, IEEE Trans. Inf. Theory.

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

[15]  Yuriy Tarannikov New Constructions of Resilient Boolean Functions with Maximal Nonlinearity , 2001, FSE.

[16]  Palash Sarkar,et al.  Construction of Nonlinear Boolean Functions with Important Cryptographic Properties , 2000, EUROCRYPT.

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

[18]  Yixian Yang,et al.  Further enumerating boolean functions of cryptographic significance , 2004, Journal of Cryptology.

[19]  Douglas R. Stinson,et al.  An infinite class of counterexamples to a conjecture concerning nonlinear resilient functions , 2004, Journal of Cryptology.

[20]  Palash Sarkar,et al.  Cryptographically significant Boolean functions with five valued Walsh spectra , 2002, Theor. Comput. Sci..

[21]  Yuriy Tarannikov,et al.  Autocorrelation Coefficients and Correlation Immunity of Boolean Functions , 2001, ASIACRYPT.

[22]  Cunsheng Ding,et al.  The Stability Theory of Stream Ciphers , 1991, Lecture Notes in Computer Science.

[23]  Jennifer Seberry,et al.  On Constructions and Nonlinearity of Correlation Immune Functions (Extended Abstract) , 1994, EUROCRYPT.

[24]  O. V. DENISOV An asymptotic formula for the number of correlation-immune of order k Boolean functions , 1992 .

[25]  Nicholas J. Patterson,et al.  The covering radius of the (215, 16) Reed-Muller code is at least 16276 , 1983, IEEE Trans. Inf. Theory.

[26]  Walter Fumy,et al.  Advances in Cryptology — EUROCRYPT ’97 , 2001, Lecture Notes in Computer Science.

[27]  Claude Carlet,et al.  More Correlation-Immune and Resilient Functions over Galois Fields and Galois Rings , 1997, EUROCRYPT.

[28]  Palash Sarkar,et al.  Enumeration of Correlation Immune Boolean Functions , 1999, ACISP.

[29]  Jung Hee Cheon,et al.  Elliptic Curves and Resilient Functions , 2000, ICISC.

[30]  Douglas R. Stinson,et al.  Bounds for Resilient Functions and Orthogonal Arrays , 1994, CRYPTO.

[31]  Kaoru Kurosawa,et al.  Highly Nonlinear t-resilient Functions , 1997, J. Univers. Comput. Sci..

[32]  Enes Pasalic,et al.  A construction of resilient functions with high nonlinearity , 2003, IEEE Trans. Inf. Theory.

[33]  Gilles Brassard,et al.  Privacy Amplification by Public Discussion , 1988, SIAM J. Comput..

[34]  K. Gopalakrishnan A study of correlation-immune, resilient and related cryptographic functions , 1994 .

[35]  Jung Hee Cheon,et al.  Nonlinear Vector Resilient Functions , 2001, CRYPTO.

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

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

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

[39]  Claude Carlet,et al.  On Correlation-Immune Functions , 1991, CRYPTO.

[40]  Sangjin Lee,et al.  On the Correlation Immune Functions and Their Nonlinearity , 1996, ASIACRYPT.

[41]  Johannes Mykkeltveit The covering radius of the (128, 8) Reed-Muller code is 56 (Corresp.) , 1980, IEEE Trans. Inf. Theory.

[42]  Anne Canteaut,et al.  Propagation Characteristics and Correlation-Immunity of Highly Nonlinear Boolean Functions , 2000, EUROCRYPT.

[43]  Palash Sarkar,et al.  Hamming Weights of Correlation Immune Boolean Functions , 1999, Inf. Process. Lett..

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

[45]  Thomas Siegenthaler,et al.  Decrypting a Class of Stream Ciphers Using Ciphertext Only , 1985, IEEE Transactions on Computers.

[46]  Enes Pasalic,et al.  Further Results on the Relation Between Nonlinearity and Resiliency for Boolean Functions , 1999, IMACC.

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

[48]  Nicholas J. Patterson,et al.  Correction to 'The covering radius of the (215, 16) Reed-Muller code is at least 16276' (May 83 354-356) , 1990, IEEE Trans. Inf. Theory.

[49]  Anne Canteaut,et al.  Correlation-Immune and Resilient Functions Over a Finite Alphabet and Their Applications in Cryptography , 1999, Des. Codes Cryptogr..

[50]  Nigel P. Smart,et al.  Selected Areas in Cryptography - SAC 2016 , 2016 .

[51]  Joan Feigenbaum,et al.  Advances in Cryptology-Crypto 91 , 1992 .

[52]  Subhamoy Maitra Correlation Immune Boolean Functions with Very High Nonlinearity , 2000, IACR Cryptol. ePrint Arch..

[53]  C. Pandu Rangan,et al.  Progress in Cryptology — INDOCRYPT 2001 , 2001, Lecture Notes in Computer Science.

[54]  Yuliang Zheng,et al.  On Relationships among Avalanche, Nonlinearity, and Correlation Immunity , 2000, ASIACRYPT.

[55]  William Millan,et al.  Heuristic Design of Cryptographically Strong Balanced Boolean Functions , 1998, EUROCRYPT.

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

[57]  Chengqi Zhang,et al.  Design and Applications of Intelligent Agents , 2001, Lecture Notes in Computer Science.

[58]  Ed Dawson,et al.  Construction of correlation immune Boolean functions , 1997, ICICS.

[59]  Subhamoy Maitra,et al.  Linear Codes in Constructing Resilient Functions with High Nonlinearity , 2001, Selected Areas in Cryptography.

[60]  Susan Stepney,et al.  Evolving Boolean Functions Satisfying Multiple Criteria , 2002, INDOCRYPT.

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

[62]  Joel Friedman,et al.  On the bit extraction problem , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[63]  Palash Sarkar A note on the spectral characterization of correlation immune Boolean functions , 2000, Inf. Process. Lett..

[64]  Yvo Desmedt,et al.  Advances in Cryptology — CRYPTO ’94 , 2001, Lecture Notes in Computer Science.

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

[66]  Yuriy Tarannikov,et al.  On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices , 2001, INDOCRYPT.

[67]  Kaisa Nyberg,et al.  Advances in Cryptology — EUROCRYPT'98 , 1998 .

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

[69]  Palash Sarkar,et al.  Balancedness and Correlation Immunity of Symmetric Boolean Functions , 2003, Electron. Notes Discret. Math..

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

[71]  Colin Boyd,et al.  Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[72]  Eric Filiol,et al.  Highly Nonlinear Balanced Boolean Functions with a Good Correlation-Immunity , 1998, EUROCRYPT.

[73]  Chris J. Mitchell,et al.  Enumerating Boolean functions of cryptographic significance , 1990, Journal of Cryptology.

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