On the Representation of Boolean Predicates of the Diffie-Hellman Function

In this work we give a non-trivial upper bound on the spectral norm of various Boolean predicates of the Diffie-Hellman function. For instance, we consider every individual bit and arbitrary unbiased intervals. Combining the bound with recent results from complexity theory we can rule out the possibility that a Boolean function with a too small spectral norm can be represented by simple functions like sparse polynomials over the reals, depth-2 threshold circuits with a small number of gates or Boolean decision trees of small rank. These results give a provable indication of the hardness of computing even a Boolean predicate of the Diffie-Hellman Function in various restricted models of computation