We introduce the black-box model for cryptographic primitives. In this
model cryptographic primitives are given by a computation graph, wher
e the computation boxes sitting on the vertices of the graph act as ra
ndom oracles. We formalize and study a family of generic attacks which
generalize exhaustive search and the birthday paradox. We establish c
omplexity lower bounds for these attacks and we apply it to compressio
n functions based on the FFT network.