A Family of Trapdoor Ciphers

This paper presents several methods to construct trapdoor block ciphers. A trapdoor cipher contains some hidden structure; knowledge of this structure allows an attacker to obtain information on the key or to decrypt certain ciphertexts. Without this trapdoor information the block cipher seems to be secure. It is demonstrated that for certain block ciphers, trapdoors can be built-in that make the cipher susceptible to linear cryptanalysis; however, finding these trapdoors can be made very hard, even if one knows the general form of the trapdoor. In principle such a trapdoor can be used to design a public key encryption scheme based on a conventional block cipher.

[1]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[2]  Matthew J. B. Robshaw,et al.  Non-Linear Approximations in Linear Cryptanalysis , 1996, EUROCRYPT.

[3]  C. K. Yuen,et al.  Walsh Functions and Their Applications , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  D. K. Branstad,et al.  Data Encryption Standard: past and future , 1988, Proc. IEEE.

[5]  E. Tavares,et al.  On the security of the CAST encryption algorithm , 1994, 1994 Proceedings of Canadian Conference on Electrical and Computer Engineering.

[6]  Mitsuru Matsui,et al.  The First Experimental Cryptanalysis of the Data Encryption Standard , 1994, CRYPTO.

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

[8]  Miles E. Smid,et al.  The Data Encryption Standard , 1988 .

[9]  D. Sarason,et al.  Past and Future , 1967 .

[10]  Gustavus J. Simmons,et al.  Contemporary Cryptology: The Science of Information Integrity , 1994 .

[11]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[12]  Richard J. Lipton,et al.  Cryptographic Primitives Based on Hard Learning Problems , 1993, CRYPTO.

[13]  Jennifer Seberry,et al.  Improving Resistance to Differential Cryptanalysis and the Redesign of LOKI , 1991, ASIACRYPT.

[14]  Mitsuru Matsui,et al.  On Correlation Between the Order of S-boxes and the Strength of DES , 1994, EUROCRYPT.

[15]  J.L. Smith,et al.  Some cryptographic techniques for machine-to-machine data communications , 1975, Proceedings of the IEEE.

[16]  Eli Biham,et al.  Differential Cryptanalysis of the Data Encryption Standard , 1993, Springer New York.

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