We show that homomorphic evaluation of any non-trivial functionality of sufficiently many inputs with respect to any CPA secure homomorphic encryption scheme cannot be implemented by circuits of polynomial size and constant depth, i.e., in the class AC. In contrast, we observe that there exist ordinary public-key encryption schemes of quasipolynomial security in AC assuming noisy parities are e...

Garbled circuits is a cryptographic technique, which has been used among other things for the construction of two and threeparty secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We define a generalization of garbling schemes called reactive garbling schemes. We conside...

Finite difference schemes providing an improved representation of a range of scales (spectral-like resolution) in the evaluation of first, second, and higher order derivatives are presented and compared with well-known schemes. The schemes may be used on non-uniform meshes and a variety of boundary conditions may be imposed. Schemes are also presented for derivatives at mid-cell locations, for ...

We show that secure homomorphic evaluation of any non-trivial functionality of sufficiently many inputs with respect to any CPA secure encryption scheme cannot be implemented by constant depth, polynomial size circuits, i.e. in the class AC. In contrast, we observe that certain previously studied encryption schemes (with quasipolynomial security) can be implemented in AC. We view this as eviden...

The conceptual phase of the aircraft design process demands a parsimonious description of the airframe geometry. While there is no hard and fast upper limit on the affordable number of variables, the so-called ‘curse of dimensionality’ must always be kept in mind: if a thorough, conceptual level search of a one-variable space can be accomplished by the evaluation of n candidate designs, the sam...

We consider issues of stability of time-discretization schemes with exact treatment of the linear part (ELP schemes) for solving nonlinear PDEs. A distinctive feature of ELP schemes is the exact evaluation of the contribution of the linear term, that is if the nonlinear term of the equation is zero, then the scheme reduces to the evaluation of the exponential function of the operator representi...