Generic Attacks for the Xor of k Random Permutations

  • Jacques Patarin
Conference paper

DOI: 10.1007/978-3-642-38980-1_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7954)
Cite this paper as:
Patarin J. (2013) Generic Attacks for the Xor of k Random Permutations. In: Jacobson M., Locasto M., Mohassel P., Safavi-Naini R. (eds) Applied Cryptography and Network Security. ACNS 2013. Lecture Notes in Computer Science, vol 7954. Springer, Berlin, Heidelberg


Xoring the output of k permutations, k ≥ 2 is a very simple way to construct pseudo-random functions (PRF) from pseudo-random permutations (PRP). Moreover such construction has many applications in cryptography (see [2,3,4,5] for example). Therefore it is interesting both from a theoretical and from a practical point of view, to get precise security results for this construction. In this paper, we will describe the best attacks that we have found on the Xor of k random n-bit to n-bit permutations. When k = 2, we will get an attack of computational complexity O(2n). This result was already stated in [2]. On the contrary, for k ≥ 3, our analysis is new. We will see that the best known attacks require much more than 2n computations when not all of the 2n outputs are given, or when the function is changed on a few points. We obtain like this a new and very simple design that can be very useful when a security larger than 2n is wanted, for example when n is very small.


Pseudorandom functions pseudorandom permutations Luby-Rackoff backwards generic attacks 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jacques Patarin
    • 1
  1. 1.Université de VersaillesVersailles CedexFrance

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