How to construct random functions
Journal of the ACM (JACM)
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
On the construction of pseudo-random permutations: Luby-Rackoff revisited (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved security bounds for pseudorandom permutations
Proceedings of the 4th ACM conference on Computer and communications security
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
New Results on Pseudorandom Permutation Generators Based on the DES Scheme
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Indistinguishability of Random Systems
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
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
Benes and butterfly schemes revisited
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
A Double-Piped Mode of Operation for MACs, PRFs and PROs: Security beyond the Birthday Barrier
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Generic attacks on misty schemes
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Hardness preserving reductions via cuckoo hashing
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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In [1], W. Aiello and R. Venkatesan have shown how to construct pseudorandom functions of 2n bits → 2n bits from pseudorandom functions of n bits → n bits. They claimed that their construction, called "Benes" reaches the optimal bound (m ≪ 2n) of security against adversaries with unlimited computing power but limited by m queries in an Adaptive Chosen Plaintext Attack (CPA-2). This result may have many applications in Cryptography (cf [1,19,18] for example). However, as pointed out in [18] a complete proof of this result is not given in [1] since one of the assertions in [1] is wrong. It is not easy to fix the proof and in [18], only a weaker result was proved, i.e. that in the Benes Schemes we have security when m ≪ f(Ɛ)ċ 2n-Ɛ, where f is a function such that limƐ→0 f(Ɛ) = +∞ (f depends only of Ɛ, not of n). Nevertheless, no attack better than in O(2n) was found. In this paper we will in fact present a complete proof of security when m ≪ O(2n) for the Benes Scheme, with an explicit O function. Therefore it is possible to improve all the security bounds on the cryptographic constructions based on Benes (such as in [19]) by using our O(2n) instead of f(Ɛ) ċ2n-Ɛ of [18].