Transform domain analysis of DES

The Data Encryption Standard (DES) can be regarded as a nonlinear feedback shift register (NLFSR) with input. From this point of view, the tools for pseudo-random sequence analysis are applied to the S-boxes in DES. The properties of the S-boxes of DES under the Fourier transform, Hadamard transform, extended Hadamard transform, and the Avalanche transform are investigated. Two important results about the S-boxes of DES are found. The first result is that nearly two-thirds of the total 32 functions from GF (2/sup 6/) to GF(2) which are associated with the eight S-boxes of DES have the maximal linear span G3, and the other one-third have linear span greater than or equal to 57. The second result is that for all S-boxes, the distances of the S-boxes approximated by monomial functions has the same distribution as for the S-boxes approximated by linear functions. Some new criteria for the design of permutation functions for use in block cipher algorithms are discussed.

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

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

[3]  Burton S. Kaliski,et al.  On Differential and Linear Crytoanalysis of the RC5 Encryption Algorithm , 1995, CRYPTO.

[4]  Ronald L. Rivest,et al.  The RC5 Encryption Algorithm , 1994, FSE.

[5]  Edwin L. Key,et al.  An analysis of the structure and complexity of nonlinear binary sequence generators , 1976, IEEE Trans. Inf. Theory.

[6]  Whitfield Diffie,et al.  Special Feature Exhaustive Cryptanalysis of the NBS Data Encryption Standard , 1977, Computer.

[7]  J.L. Massey,et al.  Theory and practice of error control codes , 1986, Proceedings of the IEEE.

[8]  염흥렬,et al.  [서평]「Applied Cryptography」 , 1997 .

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

[10]  D. Chaum,et al.  Di(cid:11)erential Cryptanalysis of the full 16-round DES , 1977 .

[11]  Willi Meier,et al.  Improved Differential Attacks on RC5 , 1996, CRYPTO.

[12]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[13]  James L. Massey,et al.  SAFER K-64: A Byte-Oriented Block-Ciphering Algorithm , 1993, FSE.

[14]  John Manferdelli,et al.  DES Has No Per Round Linear Factors , 1985, CRYPTO.

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

[16]  Eli Biham,et al.  Differential Cryptanalysis of the Full 16-Round DES , 1992, CRYPTO.

[17]  Eli Biham,et al.  On Matsui's Linear Cryptanalysis , 1994, EUROCRYPT.

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

[19]  Ingrid Schaumüller-Bichl,et al.  Cryptonalysis of the Data Encryption Standard by the Method of Formal Coding , 1982, EUROCRYPT.

[20]  Ralph Howard,et al.  Data encryption standard , 1987 .

[21]  Xuejia Lai,et al.  A Proposal for a New Block Encryption Standard , 1991, EUROCRYPT.

[22]  Yvo Desmedt,et al.  Dependence of Output on Input in DES: Small Avalanche Characteristics , 1985, CRYPTO.