How to construct random functions
Journal of the ACM (JACM)
On the cryptographic applications of random functions
Proceedings of CRYPTO 84 on Advances in cryptology
Towards a theory of software protection
Proceedings on Advances in cryptology---CRYPTO '86
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Pseudorandomness and Cryptographic Applications
Pseudorandomness and Cryptographic Applications
Stateless Evaluation of Pseudorandom Functions: Security beyond the Birthday Barrier
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Software Protection Scheme
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th 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
Almost random graphs with simple hash functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Synthesizers and their application to the parallel construction of pseudo-random functions
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On Universal Classes of Extremely Random Constant-Time Hash Functions
SIAM Journal on Computing
Journal of Algorithms
Uniform Hashing in Constant Time and Optimal Space
SIAM Journal on Computing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
A proof of security in O(2n) for the Benes scheme
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
A unified method for improving PRF bounds for a class of blockcipher based MACs
FSE'10 Proceedings of the 17th international conference on Fast software encryption
Backyard Cuckoo Hashing: Constant Worst-Case Operations with a Succinct Representation
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Composition does not imply adaptive security
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Composition implies adaptive security in minicrypt
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
From non-adaptive to adaptive pseudorandom functions
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Hardness preserving constructions of pseudorandom functions
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
IEEE Transactions on Information Theory
Explicit and efficient hash families suffice for cuckoo hashing with a stash
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Understanding adaptivity: random systems revisited
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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A common method for increasing the usability and uplifting the security of pseudorandom function families (PRFs) is to 'hash' the inputs into a smaller domain before applying the PRF. This approach, known as 'Levin's trick', is used to achieve 'PRF domain extension' (using a short,e.g,fixed, input length PRF to get a variable-length PRF), and more recently to transform non-adaptive PRFs to adaptive ones. Such reductions, however, are vulnerable to a 'birthday attack': after $\sqrt{|\mathcal{U}}$ queries to the resulting PRF, where $\mathcal{U}$ being the hash function range, a collision (i.e., two distinct inputs have the same hash value) happens with high probability. As a consequence, the resulting PRF is insecure against an attacker making this number of queries. In this work we show how to go beyond the birthday attack barrier, by replacing the above simple hashing approach with a variant of cuckoo hashing — a hashing paradigm typically used for resolving hash collisions in a table, by using two hash functions and two tables, and cleverly assigning each element into one of the two tables. We use this approach to obtain: (i) A domain extension method that requires just two calls to the original PRF, can withstand as many queries as the original domain size and has a distinguishing probability that is exponentially small in the non cryptographic work. (ii) A security-preserving reduction from non-adaptive to adaptive PRFs.