Cryptographically resilient functions

This correspondence studies resilient functions which have applications in fault-tolerant distributed computing, quantum cryptographic key distribution, and random sequence generation for stream ciphers. We present a number of new methods for synthesizing resilient functions. An interesting aspect of these methods is that they are applicable both to linear and nonlinear resilient functions. Our second major contribution is to show that every linear resilient function can be transformed into a large number of nonlinear resilient functions with the same parameters. As a result, we obtain resilient functions that are highly nonlinear and have a high algebraic degree.

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

[2]  Kaisa Nyberg,et al.  On the Construction of Highly Nonlinear Permutations , 1992, EUROCRYPT.

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

[4]  H. Niederreiter,et al.  Finite Fields: Encyclopedia of Mathematics and Its Applications. , 1997 .

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

[6]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[7]  Cunsheng Ding,et al.  On Almost Perfect Nonlinear Permutations , 1994, EUROCRYPT.

[8]  Douglas R. Stinson,et al.  Three characterizations of non-binary correlation-immune and resilient functions , 1995, Des. Codes Cryptogr..

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

[10]  Marcel van der Vlugt.  Non-BCH triple-error-correcting codes , 1996, IEEE Trans. Inf. Theory.

[11]  Jennifer Seberry,et al.  Nonlinearity and Propagation Characteristics of Balanced Boolean Functions , 1995, Inf. Comput..

[12]  Yuliang Zheng,et al.  Characterizing the Structures of Cryptographic Functions Satisfying the Propagation Criterion for Almost All Vectors , 1996, Des. Codes Cryptogr..

[13]  J. Massey,et al.  An Innnite Class of Counterexamples to a Conjecture concerning Non-linear Resilient Functions , 1995 .

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

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

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

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

[18]  Yuliang Zheng,et al.  Characterizing the structures of cryptographic functions satisfying the propagation criterion for almost all vectors , 1996 .

[19]  Kaisa Nyberg,et al.  Differentially Uniform Mappings for Cryptography , 1994, EUROCRYPT.

[20]  Jennifer Seberry,et al.  Nonlinearly Balanced Boolean Functions and Their Propagation Characteristics (Extended Abstract) , 1993, CRYPTO.

[21]  D. Stinson,et al.  Resilient functions and large sets of orthogonal arrays , 2022 .

[22]  Douglas R Stinson,et al.  Contemporary design theory : a collection of surveys , 1992 .

[23]  J. Seberry,et al.  Relationships among nonlinearity criteria , 1994 .

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

[25]  Mitsuru Matsui,et al.  Linear Cryptanalysis Method for DES Cipher , 1994, EUROCRYPT.

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

[27]  J. Seberry,et al.  Hadamard matrices, Sequences, and Block Designs , 1992 .

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

[29]  T. Kasami.  WEIGHT DISTRIBUTION OF BOSE-CHAUDHURI-HOCQUENGHEM CODES. , 1966 .