2010 | OriginalPaper | Buchkapitel
Indifferentiability beyond the Birthday Bound for the Xor of Two Public Random Permutations
verfasst von : Avradip Mandal, Jacques Patarin, Valerie Nachef
Erschienen in: Progress in Cryptology - INDOCRYPT 2010
Verlag: Springer Berlin Heidelberg
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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
≪ 2
2
n
. We essentially instantiate length preserving random functions, starting from fixed key ideal cipher with high security guarantee.