CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A Proof of Security in O(2n) for the Xor of Two Random Permutations
ICITS '08 Proceedings of the 3rd international conference on Information Theoretic Security
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The sum of PRPs is a secure PRF
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
The security of many-round Luby-Rackoff pseudo-random permutations
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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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.