# Preliminaries

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## Abstract

In this chapter we provide formal definitions for verifiable computing schemes and their relevant properties. More precisely, first, we define *verifiable computing schemes* in general and *privately verifiable computing schemes* and *publicly verifiable computing schemes* in particular. Then, we provide a definition for *weak* and *adaptive security*. Following, we discuss the different types of privacy protection, i.e. *input privacy w.r.t. the server*, *input privacy w.r.t. the verifier*, *output privacy w.r.t. the server*, *output privacy w.r.t. the verifier* and give a definition for each property. Finally, we define efficiency distinguishing between *efficiency* and *amortized efficiency*. Many verifiable computing schemes presented in the subsequent chapters are constructed with the help of cryptographic primitives that come with additional definitions for the underlying hardness assumptions. However, since these are very specific to the individual solutions they are presented in Appendix A.

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