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Erschienen in:
2017 | OriginalPaper | Buchkapitel
4. Luby-Rackoff Theorems
verfasst von : Valerie Nachef, Jacques Patarin, Emmanuel Volte
Erschienen in: Feistel Ciphers
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Abstract
In this chapter we will give complete proofs of the two results of Michael Luby and Charles Rackoff published in their important paper of 1988 (Luby and Rackoff, SIAM J. Comput. 17:373–386, 1988). These two results are:
1.
A three (or more) rounds Feistel scheme with random round functions (or with pseudo-random round functions) will give us an invertible pseudo-random permutation generator. This means that we have a cryptosystem which is secure against chosen plaintext attacks.
2.
A four (or more) rounds Feistel scheme with random round functions (or with pseudo-random round functions) will give us an invertible super pseudo-random permutation generator. This means that we have a cryptosystem which is secure against chosen plaintext and chosen ciphertext attacks.
Different kinds of proofs exist for these famous theorems. We will give here Jacques Patarin’s proof of 1990 (Patarin, Pseudorandom permutations based on the DES Scheme, Springer, 1990) based on “H-properties”; i.e. counting arguments on the keys. This proof technique is called the “H-coefficient technique” and was presented in Chap. 3.