...U [B2(M,x) 6= B2(M ′, x)], where x is chosen uniformly at random from U . Using this notation we prove the following claim which is very similar to what is known as “Occam’s Razor” in learning theory =-=[BEHW89]-=-. 2The algorithm can invert the function for infinitely many input sizes. Thus, the adversary we construct will succeed in its attack on the same (infinitely many) input sizes. 13 The Algorithm Attack...

...n explored before (already in his 1984 paper introducing the PAC model Valiant’s observed that the nascent pseudorandom random functions imply hardness of learning [Val84]). In particular Blum et al. =-=[BFKL93]-=- showed how to construct several cryptographic primitives (pseudorandom bit generators, one-way functions and private-key cryptosystems) based on certain assumptions on the difficulty of learning. The...

...Cuckoo hashing construction [PR04, Pag08]. Using cuckoo hashing as the underlying dictionary was already shown to yield good constructions for Bloom filters by Pagh et al. [PPR05] and Arbitman et al. =-=[ANS10]-=-. Among the many advantages of Cuckoo hashing (e.g., succinct memory representation, constant lookup time) is the simplicity of its structure. It consists of two tables T1 and T2 and two hash function...

... and a very high independence hash family G. We begin by describing these ingredients. The Hash Function Family G. Pagh and Pagh [PP08] and Dietzfelbinger and Woelfel [DW03] (see also Aumuller et al. =-=[ADW14]-=-) showed how to construct a family G of hash functions g : U → V so that on any set of k inputs it behaves like a truly random function with high probability (1 − 1/poly(k)). Furthermore, g can be eva...