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Publications: Abstract

{L}uby-{R}ackoff Ciphers from Weak Round Functions?

Ueli Maurer and Yvonne Anne Oswald and Krzysztof Pietrzak and Johan Sjödin

The Feistel-network is a popular structure underlying many block-ciphers where the cipher is constructed from many simpler rounds, each defined by some function which is derived from the secret key. Luby and Rackoff showed that the three-round Feistel-network – each round instantiated with a pseudorandom function secure against adaptive chosen plaintext attacks (CPA) – is a CPA secure pseudorandom permutation, thus giving some confidence in the soundness of using a Feistel-network to design block-ciphers. But the round functions used in actual block-ciphers are – for efficiency reasons – far from being pseudorandom. We investigate the security of the Feistel-network against CPA distinguishers when the only security guarantee we have for the round functions is that they are secure against non-adaptive chosen plaintext attacks (NCPA). We show that in the information-theoretic setting, four rounds with NCPA secure round functions are sufficient (and necessary) to get a CPA secure permutation. Unfortunately, this result does not translate into the more interesting pseudorandom setting. In fact, under the so-called Inverse Decisional Diffie-Hellman assumption the Feistel-network with four rounds, each instantiated with a NCPA secure pseudorandom function, is in general not a CPA secure pseudorandom permutation.

We also consider other relaxations of the Luby-Rackoff construction and prove their (in)security against different classes of attacks.