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**Provable security against a differential attack.**
*(English)*
Zbl 0817.94016

Summary: The purpose of this paper is to show that DES-like iterated ciphers that are provably resistant against differential attacks exist. The main result on the security of a DES-like cipher with independent round keys is Theorem 1, which gives an upper bound to the probability of \(s\)-round differentials, as defined in [X. Lai and J. L. Massey, Eurocrypt 1991, Lect. Notes Comput. Sci. 547, 17–38 (1991; Zbl 0777.94013)] and this upper bound depends only on the round function of the iterated cipher. Moreover, it is shown that functions exist such that the probabilities of differentials are less than or equal to \(2^{3-n}\), where \(n\) is the length of the plaintext block. We also show a prototype of an iterated block cipher, which is compatible with DES and has proven security against differential attack.

### MSC:

94A60 | Cryptography |

### Keywords:

differential cryptanalysis; almost perfect nonlinear permutations; Markov ciphers; data encryption standard; DES-like cipher### Citations:

Zbl 0777.94013
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\textit{K. Nyberg} and \textit{L. R. Knudsen}, J. Cryptology 8, No. 1, 27--37 (1995; Zbl 0817.94016)

Full Text:
DOI

### References:

[1] | Biham, E.; Shamir, A., Differential cryptanalysis of DES-like cryptosystems, Journal of Cryptology, Vol. 4, No. 1, 3-72 (1991) · Zbl 0729.68017 |

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[7] | K. Nyberg. Perfect nonlinear S-boxes. Advances in Cryptology—Eurocrypt ’91. Lecture Notes in Computer Science, Vol. 547. Springer-Verlag, Berlin, 1991, pp. 378-386. · Zbl 0766.94012 |

[8] | K. Nyberg. On the construction of highly nonlinear permutations. Advances in Cryptology—Eurocrypt ’92. Lecture Notes in Computer Science, Vol. 658. Springer-Verlag, Berlin, 1993, pp. 92-98. · Zbl 0794.94008 |

[9] | K. Nyberg. Differentially uniform mappings for cryptography. Advances in Cryptology—Eurocrypt ’93. Lecture Notes in Computer Science, Vol. 765. Springer-Verlag, Berlin, 1994,pp. 55-64. · Zbl 0951.94510 |

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