Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems

Almost bent functions oppose an optimum resistance to linear and differential cryptanalysis. We present basic properties of almost bent functions; particularly we give an upper bound on the degree. We develop the "coding theory" point of view for studying the existence of almost bent functions, showing explicitly the links with cyclic codes. We also give new characterizations of almost bent functions by means of associated Boolean functions.

[1]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[2]  Serge Vaudenay,et al.  Links Between Differential and Linear Cryptanalysis , 1994, EUROCRYPT.

[3]  G. Lachaud,et al.  The weights of the orthogonals of the extended quadratic binary Goppa codes , 1990, IEEE Trans. Inf. Theory.

[4]  Hans Dobbertin Another Proof of Kasami's Theorem , 1999, Des. Codes Cryptogr..

[5]  A. Robert Calderbank,et al.  On a conjecture of Helleseth regarding pairs of binary m-sequences , 1996, IEEE Trans. Inf. Theory.

[6]  Eli Biham,et al.  Differential cryptanalysis of DES-like cryptosystems , 1990, Journal of Cryptology.

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

[8]  Jean-Marie Goethals,et al.  Nearly perfect binary codes , 1972, Discret. Math..

[9]  Anne Canteaut,et al.  Construction of t-Resilient Functions over a Finite Alphabet , 1996, EUROCRYPT.

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

[11]  Philippe Delsarte,et al.  Four Fundamental Parameters of a Code and Their Combinatorial Significance , 1973, Inf. Control..

[12]  Victor Zinoviev,et al.  On Binary Cyclic Codes with d=3 , 1996 .

[13]  Hans Dobbertin,et al.  Almost Perfect Nonlinear Power Functions on GF(2n): The Niho Case , 1999, Inf. Comput..

[14]  Tadao Kasami,et al.  The Weight Enumerators for Several Clauses of Subcodes of the 2nd Order Binary Reed-Muller Codes , 1971, Inf. Control..

[15]  Rudolf Lide,et al.  Finite fields , 1983 .

[16]  Vera Pless,et al.  Power Moment Identities on Weight Distributions in Error Correcting Codes , 1963, Inf. Control..

[17]  Hans Dobbertin,et al.  Some new three-valued crosscorrelation functions for binary m-sequences , 1996, IEEE Trans. Inf. Theory.

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

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

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

[21]  van Hca Henk Tilborg,et al.  Uniformly packed codes , 1976 .

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

[23]  Hans Dobbertin,et al.  One-to-One Highly Nonlinear Power Functions on GF(2n) , 1998, Applicable Algebra in Engineering, Communication and Computing.

[24]  Heeralal Janwa,et al.  Double-Error-Correcting Cyclic Codes and Absolutely Irreducible Polynomials over GF(2) , 1995 .

[25]  Andries E. Brouwer,et al.  A sharpening of the Johnson bound for binary linear codes and the nonexistence of linear codes with preparata parameters , 1993, Des. Codes Cryptogr..

[26]  Claude Carlet,et al.  Two New Classes of Bent Functions , 1994, EUROCRYPT.

[27]  Yoji Niho Multi-Valued Cross-Correlation Functions between Two Maximal Linear Recursive Sequences , 1972 .

[28]  J. Dillon Elementary Hadamard Difference Sets , 1974 .

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