Abstract
Xoring two permutations is a very simple way to construct pseudorandom functions from pseudorandom permutations. The aim of this paper is to get precise security results for this construction when the two permutations on n bits f and g are public. We will first prove that f ⊕ g is indifferentiable from a random function on n bits when the attacker is limited with q queries, with \(q \ll \sqrt {2^n}\). This bound is called the “birthday bound”. We will then prove that this bound can be improved to q 3 ≪ 22n. We essentially instantiate length preserving random functions, starting from fixed key ideal cipher with high security guarantee.
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Mandal, A., Patarin, J., Nachef, V. (2010). Indifferentiability beyond the Birthday Bound for the Xor of Two Public Random Permutations. In: Gong, G., Gupta, K.C. (eds) Progress in Cryptology - INDOCRYPT 2010. INDOCRYPT 2010. Lecture Notes in Computer Science, vol 6498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17401-8_6
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DOI: https://doi.org/10.1007/978-3-642-17401-8_6
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