Security of Random Feistel Schemes with 5 or More Rounds
We study cryptographic attacks on random Feistel schemes. We denote by m the number of plaintext/ciphertext pairs, and by k the number of rounds. In their famous paper , M. Luby and C. Rackoff have completely solved the cases m≪ 2 n/2: the schemes are secure against all adaptive chosen plaintext attacks (CPA-2) when k≥ 3 and against all adaptive chosen plaintext and chosen ciphertext attacks (CPCA-2) when k≥ 4 (for this second result a proof is given in ).
In this paper we study the cases m≪2 n . We will use the “coefficients H technique” of proof to analyze known plaintext attacks (KPA), adaptive or non-adaptive chosen plaitext attacks (CPA-1 and CPA-2) and adaptive or non-adaptive chosen plaitext and chosen ciphertext attacks (CPCA-1 and CPCA-2). In the first part of this paper, we will show that when m≪ 2 n the schemes are secure against all KPA when k≥4, against all CPA-2 when k≥ 5 and against all CPCA-2 attacks when k≥6. This solves an open problem of , , and it improves the result of  (where more rounds were needed and m≪ 2 n(1 − − ε) was obtained instead of m≪ 2 n ). The number 5 of rounds is minimal since CPA-2 attacks on 4 rounds are known when m≥ O(2 n/2) (see , ). Furthermore, in all these cases we have always obtained an explicit majoration for the distinguishing probability. In the second part of this paper, we present some improved generic attacks. For k=5 rounds, we present a KPA with m ≃ 23n/2 and a non-adaptive chosen plaintext attack (CPA-1) with m ≃ 2 n . For k≥ 7 rounds we also show some improved attacks against random Feistel generators (with more than one permutation to analyze and ≥ 22 n computations).
KeywordsRandom Permutation Block Cipher Round Function Generic Attack Plaintext Attack
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